Welcome to the Data Science Seminar. The topics of the talks will vary among multiple topics in applied analysis, probability, applied mathematics related to data and dynamical systems, statistical and machine learning, signal processing, and computation.
To the attending graduate students: together with each talk we include a list of papers that are relevant to that talk, and we strongly encourage the graduate students to read those papers both in advance of the talk and after it. 
Organizers: Xiong Wang, Mauro Maggioni, Fei Lu. Contact us if you would like to meet with the speakers. 
Spring 2024: The Data Science Seminar will be held in person Krieger 411, at 3:004:00pm EST on Wednesdays . 
April 10
In person, Krieger 411
Inbar Serrousi
Department of Mathematics,
From Stochastic to Deterministic: SGD dynamics of nonconvex
models in high dimensions
Stochastic gradient descent (SGD) stands as a cornerstone of optimization and modern machine learning. However, understanding why SGD performs so well remains a major challenge. In this talk, I will present a theory for SGD in high dimensions when the number of samples and problem dimensions are large. We show that the dynamics of onepass SGD applied to generalized linear models and multiindex problems with data possessing a general covariance matrix become deterministic in the large sample and dimensional limit. In particular, the limiting dynamics are governed by a set of lowdimensional ordinary differential equations (ODEs). Our setup encompasses many optimization problems, including linear regression, logistic regression, and twolayer neural networks. In addition, it unveils the implicit bias inherent in SGD. For each of these problems, the deterministic equivalent of SGD enables us to derive a close approximation of the generalization error (with explicit and vanishing error bounds). Furthermore, we leverage our theorem to establish explicit conditions on the step size, ensuring the convergence and stability of SGD within highdimensional settings. This is joint work with ElizabethCollinsWoodfin, Courtney Paquette, and Elliot Paquette, for more information see arXiv2308.08977. 

May 1, 3:004:00pm EST
In person, Krieger 413
Richard Zhang
Department of Electrical and Computer Engineering, UIUC
Rank Overparameterization and Chordal Conversion for LargeScale Lowrank Optimization
Optimization problems over lowrank matrices are ubiquitous in the realworld. In principle, these can be reliably solved to global optimality via convex relaxation, but the computational costs can become prohibitive on a large scale. In practice, it is much more common to optimize over the lowrank matrices directly, as in the BurerMonteiro approach, but their nonconvexity can cause failure by getting stuck at a spurious local minimum. For safetycritical societal applications, such as the operation and planning of an electricity grid, our inability to reliably achieve global optimality can have significant realworld consequences. In the first part of this talk, we investigate global optimality guarantees by overparameterizing the lowrank factorization. In the smooth and stronglyconvex setting, we rigorously show that, as the rank is increased, spurious local minima become increasingly rare in a stepwise fashion. In other words, rank2 has fewer spurious local minima than rank1, and rank3 has fewer than rank2, etc. Once the rank exceeds an O(1) threshold, every remaining local minimum is a global minimum, and every saddle point can be escaped. In the second part of this talk, we revisit convex relaxations. Here, chordal conversion is a heuristic widely used to reduce the periteration cost of interiorpoint methods to as low as linear time, but a theoretical explanation for this speedup was previously unknown. We give a sufficient condition for the speedup, which covers many successful applications of chordal conversion, including the MAXkCUT relaxation, the Lovasz Theta problem, sensor network localization, polynomial optimization, and the AC optimal power flow relaxation, thus allowing theory to match practical experience. Main related papers: https://arxiv.org/abs/2207.01789 and https://arxiv.org/abs/2306.15288 . 

May 3, 3:004:00pm EST
In person, Krieger 413
Zhenfu Whang
Beijing International Center for Mathematical Research (BICMR), Peking University
Uniformintime propagation of chaos for second order interacting particle systems
We study the long time behavior of second order particle systems interacting through global Lipschitz kernels. Combining the hypocoercivity method by Villani and the relative entropy method by Jabin and Wang, we are able to overcome the degeneracy of diffusion in position direction by controlling the relative entropy and relative Fisher information together. This implies the uniformintime propagation of chaos through the strong convergence of all marginals. Our method works at the level of Liouville equation and relies on the Log Sobolev inequality of equilibrium of VlasovFokkerPlanck equation. This is based on a joint work with Yun Gong (Peking University) and Pengzhi Xie (Fudan University). 

Organizers: Mauro Maggioni, Fei Lu. Contacts us if you would like to meet with the speakers. 
The Data Science Seminar will be held on ZOOM and/or inperson (see location for each talk) at 3:004:00pm EST on Wednesdays. Meeting ID: 936 4120 5752 Passcode: 507989 
Sep.7
In person, Krieger 411
Weiqi Chu
Department of Mathematics, UCLA
Opinion dynamics models on networks and their meanfield description
The perspectives and opinions of people change and spread through social interactions on a daily basis. In the study of opinion dynamics on networks, one often models entities as nodes and their social relationships as edges, and examines how opinions evolve as dynamical processes on networks, including graphs, hypergraphs, multilayer networks, etc. In this talk, I will review some agentbased opinion dynamics models on graphs and extend one type of models to hypergraphs, whose edges can connect an arbitrary number of nodes and encode interactions that involve three or more nodes. I will also derive a meanfield model using the density description, whose governing equation follows a kinetic equation of Kac type. We prove that the opinion density converges to a sum of Dirac delta measures as time goes to infinity, which means the opinions will always form isolated opinion clusters at equilibrium. 

Oct.12
ZOOM
Hoang Tran
Oak Ridge National Laboratory
BlackBox Optimization with a Novel Nonlocal Gradient and Its Applications to Deep Learning
The problem of minimizing multimodal loss functions with a large number of local optima frequently arises in machine learning and model calibration problems. Since the local gradient points to the direction of the steepest slope in an infinitesimal neighborhood, an optimizer guided by the local gradient is often trapped in a local minimum. To address this issue, we develop a novel nonlocal gradient to skip small local minima by capturing major structures of the loss's landscape in blackbox optimization. The nonlocal gradient is defined by a directional Gaussian smoothing (DGS) approach. The key idea of DGS is to conducts 1D longrange exploration with a large smoothing radius along d orthogonal directions in R^d, each of which defines a nonlocal directional derivative as a 1D integral. Such longrange exploration enables the nonlocal gradient to skip small local minima. The d directional derivatives are then assembled to form the nonlocal gradient. We use the GaussHermite quadrature rule to approximate the d 1D integrals to obtain an accurate estimator. The superior performance of our method is demonstrated in several benchmark tests and machine learning problems, including reinforcement learning and exploring the latent space of deep networks. Enabling longrange exploration in minimization of multimodal functions AdaDGS: An adaptive blackbox optimization method with a nonlocal directional Gaussian smoothing gradient Model Calibration of the Liquid Mercury Spallation Target using Evolutionary Neural Networks and Sparse Polynomial Expansions 

Oct.19
Postponed
Roy Lederman
Department of Statistics and Data Science, Yale University
The Geometry of Molecular Conformations in CryoEM
CryoElectron Microscopy (cryoEM) is an imaging technology that is revolutionizing structural biology. Cryoelectron microscopes produce many very noisy twodimensional projection images of individual frozen molecules; unlike related methods, such as computed tomography (CT), the viewing direction of each particle image is unknown. The unknown directions and extreme noise make the determination of the structure of molecules challenging. While other methods for structure determination, such as xray crystallography and NMR, measure ensembles of molecules, cryoelectron microscopes produce images of individual particles. Therefore, cryoEM could potentially be used to study mixtures of conformations of molecules. We will discuss a range of recent methods for analyzing the geometry of molecular conformations using cryoEM data and some new issues that arise. 

Oct.26
ZOOM
Christos Mavridis
Department of Electrical & Computer Engineering, University of Maryland
Online Deterministic Annealing: Progressive Learning for CyberPhysical Systems
The continuously increasing interest in intelligent autonomous systems is accentuating the need for new developments on cyberphysical systems that can learn, adapt, and reason. Towards this direction, we will formally analyze the properties of learning as a continuous, dynamic, and adaptive process of such systems, in applications where computational resources are limited, and robustness and interpretability are prioritized. We will focus on the notion of progressive learning: the ability to hierarchically approximate the solution of an optimal decisionmaking problem given realtime observations from the system and its environment. We will introduce the Online Deterministic Annealing (ODA) algorithm as a gradientfree stochastic optimization method to construct a learning model that progressively increases its complexity as needed, through an intuitive bifurcation phenomenon. We will discuss the properties of robustness and interpretability, and the importance of being able to control the performancecomplexity tradeoff. Finally, we will showcase its use in constructing supervised, unsupervised, and reinforcement learning algorithms with applications in robotics, multiagent systems, and communication networks. 

Nov.2
Krieger 413
Enrique Mallada
ECE@JHU
ModelFree Analysis of Dynamical Systems Using Recurrent Sets
In this talk, we develop modelfree methods for the analysis of dynamical systems using data. Our key insight is to replace the notion of invariance, a core concept in Lyapunov Theory, with the more relaxed notion of recurrence. A set is τrecurrent (resp. krecurrent) if every trajectory that starts within the set returns to it after at most τ seconds (resp. k steps). We then leverage the notion of recurrence to develop several analysis tools and algorithms to study dynamical systems. We first consider the problem of learning an inner approximation of the region of attraction (ROA) of an asymptotically stable equilibrium point without an explicit model of the dynamics. We show that a τrecurrent set containing a stable equilibrium must be a subset of its ROA under mild assumptions. We then leverage this property to develop algorithms that compute inner approximations of the ROA using counterexamples of recurrence that are obtained by sampling finitelength trajectories. Our algorithms process samples sequentially, which allows them to continue being executed even after an initial offline training stage. We will finalize by providing some recent extensions of this work that generalizes Lyapunov's Direct Method to allow for nondecreasing functions to certify stability, and illustrate future directions of research. 

Nov.30
ZOOM
Ruoyu Wu
Department of Mathematics, Iowa State University
Graphon mean field systems: large population and longtime asymptotics
We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with (random) weights characterized by an underlying graphon. The limit is given by a graphon particle system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. A law of large numbers result is established as the system size increases and the underlying graphons converge. Under suitable convexity assumptions, we show the exponential ergodicity for the system, establish the uniform in time law of large numbers and concentration bounds, and analyze the uniform in time Euler approximation. The precise rate of convergence of the Euler approximation is provided. Based on joint works with Erhan Bayraktar and Suman Chakraborty. 

Organizers: Mauro Maggioni, Fei Lu, MarieJose Kuffner, and Christian Kümmerle. Contacts us if you would like to meet with the speakers. 
The Data Science seminar will be held on ZOOM and/or inperson at at 3:004:00pm EST on Wednesdays. Meeting ID: 936 4120 5752 Passcode: 507989 
Feb.23
Zoom
Evelyn Lunasin
United States Naval Academy
An Efficient Continuous Data Assimilation Algorithm for the Sabra Shell Model of Turbulence
Complex nonlinear turbulent dynamical systems are ubiquitous in many areas of research. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this talk I will present an efficient continuous in time data assimilation scheme which exploits closed analytic formulae for updating the unobserved state variables. It is computationally efficient and accurate. The new data assimilation scheme is combined with a simple reduced order modeling technique that involves a cheap closure approximation and a noise inflation. In such a way, many complicated turbulent dynamical systems can satisfy the requirements of the mathematical structures for the proposed efficient data assimilation scheme. The new data assimilation scheme is then applied to the Sabra shell model, which is a conceptual model for nonlinear turbulence. The goal is to recover the unobserved shell velocities across different spatial scales. It is shown that the new data assimilation scheme is skillful in capturing the nonlinear features of turbulence including the intermittency and extreme events in both the chaotic and the turbulent dynamical regimes. It is also shown that the new data assimilation scheme is more accurate and computationally cheaper than the standard ensemble Kalman filter and nudging data assimilation schemes for assimilating the Sabra shell model with partial observations. This is joint work with Nan Chen and Yuchen Li. . 

March 2
Zoom
Katy Craig
University of California, Santa Barbara Graph Clustering Dynamics: From Spectral to Mean Shift
Clustering algorithms based on mean shift or spectral methods on graphs are ubiquitous in data analysis. However, in practice, these two types of algorithms are treated as conceptually disjoint: mean shift clusters based on the density of a dataset, while spectral methods allow for clustering based on geometry. In joint work with Nicolás García Trillos and Dejan Slepcev, we define a new notion of FokkerPlanck equation on graph and use this to introduce an algorithm that interpolates between mean shift and spectral approaches, enabling it to cluster based on both the density and geometry of a dataset. We illustrate the benefits of this approach in numerical examples and contrast it with Coifman and Lafon’s wellknown method of diffusion maps, which can also be thought of as a FokkerPlanck equation on a graph, though one that degenerates in the zero diffusion limit. 

March 16
Hybrid in Shaffer 301 and on Zoom
Clément Royer
University ParisDauphine Numerical optimization methods with complexity guarantees for nonconvex data science
Nonconvex optimization problems have attracted significant attention from the data science community. Those formulations arise not only in deep learning, but also in data analysis and robust statistics. As a result, these instances come with a great amount of structure, that can be leveraged for optimization purposes. For such problems, the optimization landscape is often completely characterized by means of the first and secondorder derivatives. Consequently, the development of optimization routines based on those derivatives has become an important area of research, wherein the theoretical efficiency of a method is typically measured by deriving complexity bounds, or convergence rates. Such guarantees quantify the effort required to reach an approximate solution, and are often used to compare optimization schemes. On the other hand, approaches that achieve the best theoretical results tend to depart from standard optimization frameworks, and may even by outperformed by textbook algorithms in practice. In this talk, we revisit popular numerical optimization frameworks to equip them with complexity guarantees while maintaining their practical appeal, as evidenced on certain data science problems. The first part of the talk concerns nonlinear conjugate gradient methods. Through a careful complexity analysis, we are able to identify a regime in which nonlinear conjugate gradient achieves a better complexity than gradient descent on nonconvex problems. Our experiments on nonconvex robust regression suggest that this regime is actually met in practice, thus partially explaining the superior performance of nonlinear conjugate gradient on these instances. In the second part of the talk, we study NewtonConjugate Gradient techniques, and describe a framework equipped with the bestknown complexity guarantees for nonconvex optimization that hews close to the classical algorithm, and illustrate the practical impact of enforcing these guarantees. We then propose a variant of this method tailored to specific nonconvex optimization landscapes, for which even stronger results can be derived. Finally, if time permits, we will also discuss nonconvex problems arising in the development of neural network architectures, and the guarantees that can be sought for on such instances. 

April 6
Recording pwd: DSS@JHU0406
Hybrid in Shaffer 301 and on Zoom
Matthew Levine
Caltech A Framework for Machine Learning of Model Error in Dynamical Systems
The development of datainformed predictive models for dynamical systems is of widespread interest in many disciplines. Here, we present a unifying framework for blending mechanistic and machinelearning approaches for identifying dynamical systems from data. This framework is agnostic to the chosen machine learning model parameterization, and casts the problem in both continuous and discretetime. We will also show recent developments that allow these methods to learn from noisy, partial observations. We first study model error from the learning theory perspective, defining the excess risk and generalization error. For a linear model of the error used to learn about ergodic dynamical systems, both excess risk and generalization error are bounded by terms that diminish with the squareroot of T (the length of the training trajectory data). In our numerical examples, we first study an idealized, fullyobserved Lorenz system with model error, and demonstrate that hybrid methods substantially outperform solely datadriven and solely mechanisticapproaches. Then, we present recent results for modeling partially observed Lorenz dynamics that leverages both data assimilation and neural differential equations. Joint work with Andrew Stuart. 

April 13
Recording pwd: DSS@JHU0413
Hybrid in Shaffer 301 and on Zoom
Salar Fattahi
University of Michigan Convergence of Subgradient Method in Factorized Models: Small Initialization, Noisy Measurements, and Overparameterization
Factorized models, from lowrank matrix recovery to deep neural networks, play a central role in many modern machine learning problems. Despite their widespread applications, problems based factorized models are difficult to solve in their worst case due to their inherent nonconvexitya fact noted as early as the 1980s. Our talk is inspired by the recent observations in the optimization and machine learning community that, despite their nonconvexity, many realistic and practical instances of factorized models are far from their worst case scenarios. We study a natural nonconvex and nonsmooth formulation of two prototypical factorized models, namely lowrank matrix factorization and deep linear regression, where the goal is to recover a lowdimensional model from a limited number of measurements, a subset of which may be grossly corrupted with noise. We study a scenario where the dimension of the true solution is unknown and overestimated instead. The overestimation of the dimension gives rise to an overparameterized model in which there are more degrees of freedom than needed. Such overparameterization may lead to overfitting, or adversely affect the performance of the algorithm. We prove that a simple subgradient method (SubGM) with small initialization is agnostic to both overparameterization and noise in the measurements. In particular, we provide the first unifying framework for analyzing the behavior of subgradient method under different noise models, showing that it converges to the true solution, even under arbitrarily large and arbitrarily dense noise values, andperhaps surprisinglyeven if the globally optimal solutions do not correspond to the ground truth. Finally, we study the effect of depth on the local landscape of the factorized models, showing that deeper models enjoy a flatter landscape around ground truth. 

April 20
Hybrid in Shaffer 1 and on Zoom
Terry Lyons
University of Oxford Rough paths and streamed data  current challenges
The mathematics of rough paths began as an approach to extending calculus to address the interactions between highly oscillatory streams. The methods come from geometry of Chen and the analysis of Young. A key step involved is the representation of unparameterized paths as elements of the tensor algebra. Today this representation or feature set is having a significant impact on the data science of streamed data. 

April 27 Recording pwd: DSS@JHU0427
Hybrid in Shaffer 301 and on Zoom
Amarjit Budhiraja
University of North Carolina at Chapel Hill Numerical Approaches for Computing Quasistationary Distributions
Markov processes with absorbing states occur frequently in epidemiology, statistical physics, population biology, and other areas. Quasistationary distributions (QSD) are the basic mathematical object used to describe the longtime behavior of such Markov processes on nonabsorption events. Just as stationary distributions of ergodic Markov processes make the law of the Markov process, initialized at that distribution, invariant at all times, quasistationary distributions are probability measures that leave the conditional law of the Markov process, on the event of nonabsorption, invariant. In this talk I will present a couple of numerical approaches for approximating QSD for Markov processes. These approaches use ideas from reinforced random walks, interacting particle systems, and stochastic approximations. The talk is based on joint work with Adam Waterbury. 

Organizers: Mauro Maggioni, Fei Lu, MarieJose Kuffner, and Christian Kümmerle. Contacts us if you would like to meet with the speakers. 
The Data Science seminar will be held on ZOOM at at 3:004:00pm EST on Wednesdays. Meeting ID: 936 4120 5752 Passcode: 507989 
September 15
Shiqian Ma
UC Davis Riemannian Optimization for Projection Robust Optimal Transport
The optimal transport problem is known to suffer the curse of dimensionality. A recently proposed approach to mitigate the curse of dimensionality is to project the sampled data from the high dimensional probability distribution onto a lowerdimensional subspace, and then compute the optimal transport between the projected data. However, this approach requires solving a maxmin problem over the Stiefel manifold, which is very challenging in practice. In this talk, we propose a Riemannian block coordinate descent (RBCD) method to solve this problem. We analyze the complexity of arithmetic operations for RBCD to obtain an $\epsilon$stationary point, and show that it significantly improves the corresponding complexity of existing methods. Numerical results on both synthetic and real datasets demonstrate that our method is more efficient than existing methods, especially when the number of sampled data is very large. If time permits, we will also talk about the projection robust Wasserstein barycenter problem. 

October 13
Yuxin Chen
Princeton University Inference and Uncertainty Quantification for LowRank Models
Many highdimensional problems involve reconstruction of a lowrank matrix from incomplete and corrupted observations. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of the obtained lowrank estimates, and how to construct valid yet short confidence intervals for the unknown lowrank matrix. In this talk, I will discuss how to perform inference and uncertainty quantification for two examples of lowrank models: (1) noisy matrix completion, and (2) heteroskedastic PCA with Missing Data. For both problems, we identify statistically efficient estimators that admit nonasymptotic distributional characterizations, which in turn enable optimal construction of confidence intervals for, say, the unseen entries of the lowrank matrix of interest. Our inferential procedures do not rely on sample splitting, thus avoiding unnecessary loss of data efficiency. All this is accomplished by a powerful leaveoneout analysis framework that originated from probability and random matrix theory. The first part of my talk is based on joint work with Cong Ma, Yuling Yan and Jianqing Fan, while the second part is based on joint work with Yuling Yan and Jianqing Fan. 

October 20
Grigorios A. Pavliotis
Imperial College University Optimal Langevin Samplers
Sampling from a probability distribution in a high dimensional spaces is a standard problem in computational statistical mechanics, Bayesian statistics and other applications. A standard approach for doing this is by constructing an appropriate Markov process that is ergodic with respect to the measure from which we wish to sample. In this talk we will present a class of sampling schemes based on Langevintype stochastic differential equations. We will show, in particular, nonreversible Langevin samplers, i.e. stochastic dynamics that do not satisfy detailed balance, have, in general, better properties than their reversible counterparts, in the sense of accelerating convergence to equilibrium and of reducing the asymptotic variance. Numerical schemes for such nonreversible samplers will be discussed and the connection with nonequilibrium statistical mechanics will be made. 

October 27, Hybrid: Hodson 316
Thomas Fai
Brandeis University Coarsegrained stochastic model of myosindriven vesicles into dendritic spines
We model vesicle transport into dendritic spines, which are micronsized structures located at the postsynapses of neurons characterized by their thin necks and bulbous heads. Recent highresolution 3D images show that spine morphologies are highly diverse. To study the influence of geometry on transport, our model reduces the fluid dynamics of vesicle motion to two essential parameters representing the system geometry and elasticity. Upon including competing molecular motor species that push and pull on vesicles, the model exhibits multiple steady states that neurons could exploit in order to control the strength of synapses. Moreover, the small numbers of motors lead to random switching between these steady states. We describe a method that incorporates stochasticity into the model to predict the probability and mean time of translocation as a function of spine geometry. 

Nov. 3
Arnaud Doucet
University of Oxford & DeepMind Diffusion Schrodinger Bridge with Applications to ScoreBased Generative Modeling
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE), Song et al. (2021) demonstrate how the time inhomogeneous drift of the associated reversetime SDE may be estimated using scorematching. A limitation of this approach is that the forwardtime SDE must be run for a sufficiently long time for the final distribution to be approximately Gaussian. In contrast, solving the Schrodinger Bridge problem (SB), i.e. an entropyregularized optimal transport problem on path spaces, yields diffusions which generate samples from the data distribution in finite time. We present Diffusion SB (DSB), an original approximation of the Iterative Proportional Fitting (IPF) procedure to solve the SB problem, and provide theoretical analysis along with generative modeling experiments. The first DSB iteration recovers the methodology proposed by Song et al. (2021), with the flexibility of using shorter time intervals, as subsequent DSB iterations reduce the discrepancy between the finaltime marginal of the forward (resp. backward) SDE with respect to the prior (resp. data) distribution. Beyond generative modeling, DSB offers a widely applicable computational optimal transport tool as the continuous statespace analogue of the popular Sinkhorn algorithm (Cuturi, 2013). This is joint work with Valentin De Bortoli, James Thornton and Jeremy Heng. 

Nov 10, Hybrid: Hodson 316
Paris Perdikaris
University of Pennsylvania Learning to solve parametric PDEs with deep operator networks
Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is dramatically amplified when different scenarios need to be investigated, for example corresponding to different initial or boundary conditions, different inputs, etc. In this work we introduce physicsinformed DeepONets; a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired inputoutput training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a new paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering. 

Special time 4pm, Dec. 1
Madeleine Udell
Cornell University Detecting equivalence between iterative algorithms for optimization
When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor twist on an existing method? In this talk, we present a framework for reasoning about equivalence between a broad class of iterative algorithms, with a focus on algorithms designed for convex optimization. We propose several notions of what it means for two algorithms to be equivalent, and provide computationally tractable means to detect equivalence. Our main definition, oracle equivalence, states that two algorithms are equivalent if they result in the same sequence of calls to the function oracles (for suitable initialization). Borrowing from control theory, we use statespace realizations to represent algorithms and characterize algorithm equivalence via transfer functions. Our framework can also identify and characterize some algorithm transformations including permutations of the update equations, repetition of the iteration, and conjugation of some of the function oracles in the algorithm. A software package named Linnaeus implements the framework and makes it easy to find other iterative algorithms that are equivalent to an input algorithm. More broadly, this framework and software advances the goal of making mathematics searchable. This is based on joint work with Shipu Zhao and Laurent Lessard. 

Organizers: Mauro Maggioni, Fei Lu, Sui Tang, Felix (Xiaofeng) Ye, and Ming Zhong. Contacts us if you would like to meet with the speakers. 
The Data Science seminar will be held at Maryland Hall 309 at 3:004:00pm on Wednesdays, unless otherwise specified. 
Postponed, date TBD
David F. Anderson
University of Wisconsin Network structure and dynamics for biochemical reaction networks
Models of cellular processes are often represented with networks that describe the interactions between the constituent molecules. The mathematical study of how dynamical properties of a system relate to graphical properties of its associated network often goes by the name "reaction network theory". In this talk, I will connect some of the classical results of reaction network theory, including the Deficiency Zero Theorem and its analog in the stochastic setting, with some current results at the interface of synthetic biology and mathematics. Topics will include: (i) a characterization of when a stochastic model will admit a timedependent distribution that is a product of Poissons and (ii) designing reaction networks that admit a particular (marginal) stationary distribution. 

Cancelled due to COVID 19.
Eitan Tadmor
University of Maryland Emergent Behavior in Collective Dynamics
A fascinating aspect of collective dynamics is the selforganization of smallscales and their emergence as higherorder patterns  clusters, flocks, tissues, parties. The emergence of different patterns can be described in terms of few fundamental ''rules of interactions''. I will discuss recent results of the largetime, largecrowd dynamics, driven by anticipation that tend to align the crowd, while other pairwise interactions keep the crowd together and prevent overcrowding. In particular, I address the question how shortrange interactions lead to the emergence of longrange patterns, comparing different rules of interactions based on geometric vs. topological neighborhoods. 

Cancelled due to COVID 19. April 8
Paris Perdikaris
University of Pennsylvania 

Cancelled due to COVID 19.
April 22
Evelyn Lunasin
U.S. Naval Academy TBD
TBD. 

Organizers: Mauro Maggioni, Fei Lu, Sui Tang, Felix (Xiaofeng) Ye, and Ming Zhong. Contacts us if you would like to meet with the speakers. 
The Data Science seminar will be held at Maryland Hall 109 at 3:004:00pm on Wednesdays, unless otherwise specified. 
Sep. 11th
Tingran Gao
University of Chicago MultiRepresentation Manifold Learning on Fibre Bundles
Fibre bundles serve as a natural geometric setting for many learning problems involving nonscalar pairwise interactions. Modeled on a fixed principal bundle, different irreducible representations of the structural group induce many associated vector bundles, encoding rich geometric information for the fibre bundle as well as the underlying base manifold. An intuitive example for such a learning paradigm is phase synchronizationthe problem of recovering angles from noisy pairwise relative phase measurementswhich is prototypical for a large class of imaging problems in cryogenic electron microscopy (cryoEM) image analysis. We propose a novel nonconvex optimization formulation for this problem, and develop a simple yet efficient twostage algorithm that, for the first time, guarantees strong recovery for the phases with high probability. We demonstrate applications of this multirepresentation methodology that improve denoising and clustering results for cryoEM images. This algorithmic framework also extends naturally to general synchronization problems over other compact Lie groups, with a wide spectrum of potential applications. This talk is based on three joint work with Prof. Zhizhen Zhao from UIUC:
Tingran Gao and Zhizhen Zhao, MultiFrequency Phase Synchronization, Proceedings of the 36th International Conference on Machine Learning, PMLR 97:2132  2141, 2019 Tingran Gao, Yifeng Fan, and Zhizhen Zhao, Representation Theoretic Patterns in MultiFrequency Class Averaging for ThreeDimensional CryoElectron Microscopy, arXiv:1906.01082. (2019) Yifeng Fan, Tingran Gao, and Zhizhen Zhao, Unsupervised CoLearning on GManifolds Across Irreducible Representations, arXiv:1906.02707. (2019) 

Sep. 25th, 2019
Anna Little
Michigan State University
Robust Statistical Procedures for Clustering in High Dimensions
This talk addresses multiple topics related to robust statistical procedures for clustering in high dimensions, including pathbased spectral clustering (a new method), classical multidimensional scaling (an old method), and clustering in signal processing. Pathbased spectral clustering is a novel approach which combines a data driven metric with graphbased clustering. Using a data driven metric allows for fast algorithms and strong theoretical guarantees when clusters concentrate around lowdimensional sets. Another approach to highdimensional clustering is classical multidimensional scaling (CMDS), a dimension reduction technique widely popular across disciplines due to its simplicity and generality. CMDS followed by a simple clustering algorithm can exactly recover all cluster labels with high probability when the signal to noise ratio is high enough. However, scaling conditions become increasingly restrictive as the ambient dimension increases, illustrating the need for robust unbiasing procedures in high dimensions. Clustering in signal processing is the final topic; in this context each data point corresponds to a corrupted signal. The classic multireference alignment problem is generalized to include random dilation in addition to random translation and additive noise, and a wavelet based approach is used to define an unbiased representation of the target signal(s) which is robust to high frequency perturbations. 

Oct. 2nd, 2019
Jinqiao Duan
Illinois Institute of Technology Data Science Plus Dynamical Systems: What Can We Learn?
Observational datasets are abundant. Dynamical systems are mathematical models in engineering, medicine and science. Data are noisy and dynamical systems are often under random fluctuations (either Gaussian or nonGaussian noise). The interactions between data science and dynamical systems are becoming exciting. On the one hand, dynamical systems tools are valuable to extract information from datasets. On the other hand, data science techniques are indispensable for understanding dynamical behaviors with observational data. I will present recent progress on extracting information like the most probable transition pathways, mean residence time, and escape probability from datasets, and on estimating system states and parameters with help of datasets. In addition to highlighting the underlying dynamical systems structures, such as stochastic flows, slow manifolds and dimension reduction, I will outline several mathematical issues at the foundation of relevant machine learning approaches. Relevant papers
The OnsagerMachlup function as Lagrangian for the most probable path of a jumpdiffusion process. Discovering mean residence time and escape probability from data of stochastic dynamical systems. Effective Filtering Analysis for NonGaussian Dynamic Systems. Dynamical inference for transitions in stochastic systems with alphastable Levy noise. More on arXiv. 

Oct. 9th, 2019
Guang Lin
Purdue University Uncertainty Quantification and Machine Learning of the Physical Laws Hidden Behind the Noisy Data
In this talk, we will present three new datadriven, machinelearning based methods for Learning of the physical laws Hidden Behind the noisy data and quantifying the uncertainties in machine learning. First, I will present a new datadriven paradigm on how to quantify the structural uncertainty (modelform uncertainty) and learn the physical laws hidden behind the noisy data in the complex systems governed by partial differential equations. The key idea is to identify the terms in the underlying equations and to approximate the coefficients of the terms with error bars using Bayesian machine learning algorithms on the available noisy measurement. In particular, Bayesian sparse feature selection and parameter estimation are performed. Numerical experiments show the robustness of the learning algorithms with respect to noisy data and size, and its ability to learn various candidate equations with error bars to represent the quantified uncertainty. Second, I will introduce a fastprobabilistic convolutional encoderdecoder network named ConvPDEUQ for predicting the solutions of heterogeneous elliptic partial differential equations on varied domains. Unlike other approaches, ConvPDEUQ can quantify the uncertainties in deeplearningbased prediction and allow training to be scaled to the large data sets. Finally, to predict material failure and fracture propagation, we will present a new deep neural network named PeriNet. 

Note date and place: Nov. 7th, 1:302:30pm, Whitehead 304 AMS seminar
Jonathan Mattingly
Duke University Computational methods for Quantifying Gerrymandering and other computational statistical mechanics problems
I will describe some of the interesting problems which have arisen around the problem of understanding Gerrymandering. It is a high sampling dimensional problem. I will talk about some basic MCMC schemes and some extensions to both interesting global moves as well as some other generalizations. I will also take a moment to frame the problem and state some open questions. 

Nov. 13th, 2019
Le Song
Georgia Institute of Technology Learning Augmented Design of Algorithms
Algorithms are stepbystep instructions designed by humans to solve a problem. However, many data analytics problems are intrinsically hard and complex, making the design of effective algorithms very challenging. Domain experts have to perform extensive research, experiment with many trialanderrors, and carefully craft some approximation or heuristic schemes in order to design effective algorithms. Previous algorithm design paradigms seldom systematically exploit a common trait of realworld algorithms: instances of the same type of problem are solved again and again on a regular basis using the algorithm, maintaining the same problem structure, but differing mainly in their data. In this talk, I will explain two examples of using learning to augment algorithm design (combinatorial optimization and sparse recovery). The new design paradigm will delegate some difficult design choices in an algorithm to a nonlinear learning model, and use data to figure out the best model/algorithm. I will show that the learned augmented design leads to interesting and effective new algorithms. 

Dec. 4th, 2019
Matthew Zahr
University of Notre Dame
Integrating computational physics and numerical optimization to address challenges in computational science, engineering, and medicine
Optimization problems governed by partial differential equations are ubiquitous in modern science, engineering, and mathematics. They play a central role in optimal design and control of multiphysics systems, data assimilation, and inverse problems. However, as the complexity of the underlying PDE increases, efficient and robust methods to accurately compute the objective function and its gradient become paramount. To this end, I will present a globally highorder discretization of PDEs and their quantities of interest and the corresponding fully discrete adjoint method for use in a gradientbased PDEconstrained optimization setting. The framework is applied to solve a several of optimization problems including the design of energetically optimal flapping motions, the design of energy harvesting mechanisms, and data assimilation to dramatically enhance the resolution of magnetic resonance images. In addition, I will demonstrate that the role of optimization in computational physics extends well beyond these traditional design and control problems. I will introduce a new method for the discovery and highorder accurate resolution of shock waves in compressible flows using PDEconstrained optimization techniques. The key feature of this method is an optimization formulation that aims to align discontinuous features of the solution basis with discontinuities in the solution. The method is demonstrated on a number of one and twodimensional transonic and supersonic flow problems. In all cases, the framework tracks the discontinuity closely with curved mesh elements and provides accurate solutions on extremely coarse meshes. References
An adjoint method for a highorder discretization of deforming domain conservation laws for optimization of flow problems. An optimizationbased approach for highorder accurate discretization of conservation laws with discontinuous solutions. Highorder, linearly stable, partitioned solvers for general multiphysics problems based on implicitexplicit RungeKutta schemes. 

Organizers: Mauro Maggioni, Fei Lu, Sui Tang, Felix (Xiaofeng) Ye, and Ming Zhong. Contacts us if you would like to meet with the speakers. 
The Data Science seminar is merging with the CIS seminar , and it will be in either Mergenthaler 11 or in Clark Hall 316, throughout the semester, on Johns Hopkins Homewood campus this map). As the merging of the two seminar series takes place in Spring 2019, the the schedule of the CIS seminar will remain available and takes precedence over the one below for CIS speakers. 
Jan. 29th
Hamed Pirsiavash
UMBC Clark Hall Room 12:151:15pm 

Feb. 5th, 2019
Ted Satterthwaite
UPenn Clark Hall Room 12:151:15pm 

Feb. 12th, 2019
Yanxun Xu
Johns Hopkins University Clark Hall Room 110, 1pm2pm (light lunch served at 12:30pm) Bayesian Estimation of Sparse Spiked Covariance Matrices in High Dimensions
Abstract: We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is equipped with a novel matrix spikeandslab LASSO prior, which is a continuous shrinkage prior for modeling jointly sparse matrices. We establish the rateoptimal posterior contraction for the covariance matrix with respect to the operator norm as well as that for the principal subspace with respect to the projection operator norm loss. We also study the posterior contraction rate of the principal subspace with respect to the twotoinfinity norm loss, a novel loss function measuring the distance between subspaces that is able to capture elementwise eigenvector perturbations. We show that the posterior contraction rate with respect to the twotoinfinity norm loss is tighter than that with respect to the routinely used projection operator norm loss under certain lowrank and bounded coherence conditions. In addition, a point estimator for the principal subspace is proposed with the rateoptimal risk bound with respect to the projection operator norm loss. These results are based on a collection of concentration and large deviation inequalities for the matrix spikeandslab LASSO prior. The numerical performance of the proposed methodology is assessed through synthetic examples and the analysis of a realworld face data example. 

April 10, Special time: 3:004:00, location: Shaffer 100
Nan Chen
University of WisconsinMadison Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Nonlinear Turbulent Dynamical Systems
Abstract: A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly nonGaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the realtime data assimilation and prediction. This talk will include three applications of such conditional Gaussian framework. The first part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the second part, an efficient statistically accurate algorithm is developed that is able to solve a rich class of highdimensional FokkerPlanck equation with strong nonGaussian features and beat the curse of dimensions. In the last part of this talk, a physicsconstrained nonlinear stochastic model is developed, and is applied to predicting the MaddenJulian oscillation indices with strongly nonGaussian intermittent features. Related papers:


May 31st, Special time: 3:004:00, location: Whitehead 304
Jinchao Feng
University of Massachusetts  Amherst Title: ModelForm Uncertainty Quantification for Predictive Modeling in Probabilistic Graphical Models
Abstract: Probabilistic Graphical Models (PGM) is an important class of methods for probabilistic modeling and inference, and constitutes the mathematical foundation of modeling uncertainty in Artificial Intelligence (AI). Its hierarchical structure allows us to bring together in a systematic way statistical and multiscale physical modeling, different types of data, incorporating in expert knowledge, correlations and causal relationships. However, due to multiscale modeling, learning from sparse data, and mechanisms without full knowledge, many predictive models will necessarily have diverse sources of uncertainty at different scales. On the other hand, traditional Uncertainty Quantification (UQ) methods mostly consider parametric approaches, e.g., by perturbing, tuning, or inferring the model parameters, which are not suitable for the aforementioned models. For this type of modelform (epistemic) uncertainty we develop a new informationtheoretic, nonparametric approach for UQ. We develop new modelform UQ indices that can handle both parametric and nonparametric PGMs, as well as small and large model/parameter perturbations in a single, unified mathematical framework and provide an envelope of model predictions for our quantities of interests (QoIs). Moreover, we propose a modelform Sensitivity Index, which allows us to rank the impact of each component of the PGM, and provide a systematic methodology to close the experiment  model  simulation  prediction loop and improve the computational model iteratively based on our new UQ and SA methods. Related papers:


Organizers: Mauro Maggioni, Fei Lu. Contacts us if you would like to meet with the speakers. 
The data seminar will take place on Wednesdays at 3pm, in Shaeffer 304, during the semester, on Johns Hopkins Homewood campus this map). 
October 10
Jianfeng Lu
Duke Title: Solving largescale leading eigenvalue problem
Abstract: The leading eigenvalue problems arise in many applications. When the dimension of the matrix is super huge, such as for applications in quantum manybody problems, conventional algorithms become impractical due to computational and memory complexity. In this talk, we will describe some recent works on new algorithms for the leading eigenvalue problems based on randomized and coordinatewise methods (joint work with Yingzhou Li and Zhe Wang). 

November 6, Special time: 4:005:00, location: Gilman 277
Mohammad Farazmand
Department of Mechanical Engineering, MIT Title: Extreme Events: Dynamics, Prediction and Mitigation
Abstract: A wide range of natural and engineering systems exhibit extreme events, i.e., spontaneous intermittent behavior manifested through sporadic bursts in the time series of their observables. Examples include ocean rogue waves, intermittency in turbulence and extreme weather patterns. Because of their undesirable impact on the system or the surrounding environment, the realtime prediction and mitigation of extreme events is of great interest. In this talk, I discuss some recent advances in the quantification and prediction of extreme events. In particular, I introduce a variational method that disentangles the mechanisms underpinning the formation of extreme events. This in turn enables the datadriven, realtime prediction of the extreme events. I demonstrate the application of this method with several examples including the prediction of ocean rogue waves and the intermittent energy dissipation bursts in turbulent fluid flows. 

November 7
Kevin Lin
School of Mathematical Science, University of Arizona Title: MoriZwanzig formalism and discretetime modeling of chaotic
dynamics
Abstract: Nonlinear dynamic phenomena often require a large number of dynamical variables to model, only a small fraction of which are of direct interest. Reduced models that use only the relevant dynamical variables can be very useful in such situations, both for computational efficiency and insights into the dynamics. Recent work has shown that the NARMAX (Nonlinear AutoRegressive MovingAverage with eXogenous inputs) representation of stochastic processes provides an effective basis for parametric model reduction in a number of concrete settings [ChorinLu PNAS 2015]. In this talk, I will review some of these developments, then explain how the NARMAX method can be seen as a special case of a general theoretical framework for model reduction due to Mori and Zwanzig. These ideas will be illustrated on a prototypical model of spatiotemporal chaos. Related papers:
Preprint available upon request (please write to feilu@math.jhu.edu) Databased stochastic model reduction for the KuramotoSivashinsky equation Comparison of continuous and discretetime databased modeling for hypoelliptic systems 

December 5
Clarence Rowley
Princeton University Title: Structure, stability, and simplicity in complex fluid flows
Abstract: Fluid flows can be extraordinarily complex, and even turbulent, yet often there is structure lying within the apparent complexity. Understanding this structure can help explain observed physical phenomena, and can help with the design of control strategies in situations where one would like to change the natural state of a flow. This talk addresses techniques for obtaining simple, approximate models for fluid flows, using data from simulations or experiments. We discuss a number of methods, including balanced truncation, linear stability theory, and dynamic mode decomposition, and apply them to several flows with complex behavior, including a transitional channel flow, a jet in crossflow, and a Tjunction in a pipe. 

December 10, Special time: 12:001:00, location: Shaffer 304
Marina Meila
Department of Statistics, University of Washington Title: Unsupervised Validation for Unsupervised Learning
Abstract: Scientific research involves finding patterns in data, formulating hypotheses, and validating them with new observations. Machine learning is many times faster than humans at finding patterns, yet the task of validating these as "significant" is still left to the human expert or to further experiment. In this talk I will present a few instances in which unsupervised machine learning tasks can be augmented with data driven validation. In the case of clustering, I will demonstrate a new framework of "proving" that a clustering is approximately correct, that does not require a user to know anything about the data distribution. This framework has some similarities to PAC bounds in supervised learning; unlike PAC bounds, the bounds for clustering can be calculated exactly and can be of direct practical utility. In the case of nonlinear dimension reduction by manifold learning, I will present a way around the following problem. It is widely recognized that the low dimensional embeddings obtained with manifold learning algorithms distort the geometric properties of the original data, like distances and angles. These algorithm dependent distortions make it unsafe to pipeline the output of a manifold learning algorithm into other data analysis algorithms, limiting the use of these techniques in engineering and the sciences. Our contribution is a statistically founded methodology to estimate and then cancel out the distortions introduced by any embedding algorithm, thus effectively preserving the distances in the original data. This method is based on augmenting the output of a manifold learning algorithm with "the pushforward Riemannian metric", i.e. with additional metric information that allows it to reconstruct the original geometry. Joint work with Dominique PerraultJoncas, James McQueen, Jacob VanderPlas, Grace Telford, Yuchia Chen, Samson Koelle 

Organizers: Mauro Maggioni, Fei Lu. Contacts us if you would like to meet with the speakers. 
The data seminar will take place on Wednesdays at 3pm, in Shaeffer 304, during the semester, on Johns Hopkins Homewood campus this map). 
Special Time: 11am and Location: Krieger 413; January 25th
Xiaofeng (Felix) Ye
University of Washington Title: Stochastic dynamics: Markov chains and random transformations
Abstract: The theory of stochastic dynamics has two different mathematical representations: stochastic processes and random dynamical system (RDS). RDS actually is a more refined mathematical description of the reality; it provides not only stochastic trajectories following one initial condition, but also describes how the entire phase space, with all initial conditions, changes with time. Stochastic processes represent the stochastic movements of individual systems. RDS, however, describes the motions of many systems that experience a common deterministic law that is changing with time due to extrinsic noises, which represent a fluctuating environment or complex external singles. The RDS is often a good framework to study a quite counterintuitive phenomenon called noiseinduced synchronization: the stochastic motions of noninteracting systems under a common noise synchronize; their trajectories become close to each other, while individual one remains stochastic. I first established some elementary contradistinctions between Markov chain theory and RDS descriptions of a stochastic dynamical system under discrete time, discrete state (dtds) setting. It was shown that a given Markov chain is compatible with many possible RDS, and I particularly studied the corresponding RDS with maximum metric entropy. I then proved the sufficient and necessary conditions for synchronization in general dtdsRDS and in dtdsRDS with maximum metric entropy. The work is based on the observation that under certain mild conditions, the forward probability in a hidden Markov model exhibits synchronization, which yields an efficient estimation with subsequences. Here I developed a minibatch gradient descent algorithm for parameter inference in the hidden Markov model. I first efficiently estimated the rate of synchronization, which was proven as the gap of top Lyapunov exponents, and then fully utilized it to approximate the length of subsequences in the minibatch algorithm. I theoretically validated the algorithm and numerically demonstrated the effectiveness. 
January 31st
Tom Goldstein
University of Maryland Title: Principled nonconvex optimization for deep learning and phase retrieval
Abstract: This talk looks at two classes of nonconvex problems. First, we discuss phase retrieval problems, and present a new formulation, called PhaseMax, that reduces this class of nonconvex problems into a convex linear program. Then, we turn our attention to more complex nonconvex problems that arise in deep learning. We'll explore the nonconvex structure of deep networks using a range of visualization methods. Finally, we discuss a class of principled algorithms for training "binarized" neural networks, and show that these algorithms have theoretical properties that enable them to overcome the nonconvexities present in neural loss functions. 
February 21st
Dimitris Giannakis
NYU Title:Datadriven modeling of vector fields and differential forms by spectral exterior calculus
Abstract: We discuss a datadriven framework for exterior calculus on manifolds. This framework is based on a representations of vector fields, differential forms, and operators acting on these objects in frames (overcomplete bases) for L^2 and higherorder Sobolev spaces built entirely from the eigenvalues and eigenfunctions of the Laplacian of functions. Using this approach, we represent vector fields either as linear combinations of frame elements, or as operators on functions via matrices. In addition, we construct a Galerkin approximation scheme for the eigenvalue problem for the LaplacedeRham operator on 1forms, and establish its spectral convergence. We present applications of this scheme to a variety of examples involving data sampled on smooth manifolds and the Lorenz 63 fractal attractor. This work is in collaboration with Tyrus Berry. 
March 14th
Edriss Titi
Texas A&M University, and The Weizmann Institute of Science Title: Data Assimilation and Feedback Control Algorithm for Dissipative Evolution Models Employing Coarse Mesh Observables
Abstract: One of the main characteristics of infinitedimensional dissipative evolution equations, such as the NavierStokes equations and reactiondiffusion systems, is that their longtime dynamics is determined by finitely many parameters  finite number of determining modes, nodes, volume elements and other determining interpolants. In this talk I will show how to explore this finitedimensional feature of the longtime behavior of infinitedimensional dissipative systems to design finitedimensional feedback control for stabilizing their solutions. Notably, it is observed that this very same approach can be implemented for designing data assimilation algorithms of weather prediction based on discrete measurements. In addition, and if time allows, I will also show that the longtime dynamics of the NavierStokes equations can be imbedded in an infinitedimensional dynamical system that is induced by an ordinary differential equations, named {\it determining form}, which is governed by a globally Lipschitz vector field.Remarkably, as a result of this machinery I will eventually show that the global dynamics of the NavierStokes equations is be determining by only one parameter that is governed by an ODE. The NavierStokes equations are used as an illustrative example, and all the above mentioned results equally hold to other dissipative evolution PDEs, in particular to various dissipative reactiondiffusion systems and geophysical models. This is a joint work with A. Azouani, H. Bessaih, A. Farhat, C. Foias, M. Jolly, R. Kravchenko, E. Lunasin and E. Olson 
March 28th
Rama Chellappa
University of Maryland, College Park Title: Learning Along the Edge of Deep Networks
Abstract: While Deep Convolutional Neural Networks (DCNNs) have achieved impressive results on many detection and classification tasks (for example, unconstrained face detection, verification and recognition), it is still unclear why they perform so well and how to properly design them. It is widely recognized that while training deep networks, an abundance of training samples is required. These training samples need to be lossless, perfectly labeled, and spanning various classes in a balanced way. The generalization performance of designed networks and their robustness to adversarial examples needs to be improved too. In this talk, we analyze each of these individual conditions to understand their effects on the performance of deep networks and present mitigation strategies when the ideal conditions are not met. First, we investigate the relationship between the performance of a convolutional neural network (CNN), its depth, and the size of its training set and present performance bounds on CNNs with respect to the network parameters and the size of the available training dataset. Next, we consider the task of adaptively finding optimal training subsets which will be iteratively presented to the DCNN. We present convex optimization methods, based on an objective criterion and a quantitative measure of the current performance of the classifier, to efficiently identify informative samples to train on. Then we present DefenseGAN, a new strategy that leverages the expressive capability of generative models to defend DCNNs against adversarial attacks. The DefenseGAN can be used with any classification model and does not modify the classifier structure or training procedure. It can also be used as a defense against any attack as it does not assume knowledge of the process for generating the adversarial examples. An approach for training a DCNN using compressed data will also be presented by employing the GAN framework. Finally, to address generalization to unlabeled test data and robustness to adversarial samples, we propose an approach that leverages unsupervised data to bring the source and target distributions closer in a learned joint feature space. This is accomplished by inducing a symbiotic relationship between the learned embedding and a generative adversarial network. We demonstrate the impact of the analyses discussed above on a variety of reconstruction and classification problems. 
April 18th
PierreEmmanuel Jabin
University of Maryland, College Park Title: Complexity of some models of interacting biological neurons
Abstract: We study some models of for the dynamics of large groups of biological neurons: Those typically consist of large coupled systems of ODE's or SDE's, usually implementing some simple form of integrate and fire. The main question that we wish to address concerns the behavior of such networks as the number of neurons increases. Many particle systems (as they are used in physics, or multiagent systems in general) naturally come to mind, as it is well known in such cases that propagation of chaos (i.e. the almost independence of each agent) can lead to a reduction in complexity through the direct calculation of various macroscopic densities. However the system under consideration here can be seen as multiagent system with positive reinforcement so that correlations between neurons never vanish. In an ongoing work with D. Poyato, we first study the case where neurons are essentially fully connected. We show that in spite of this simple topology, the networks may exhibit different measures of complexity which can be characterized through the type of initial connections between neurons. Related papers:
On the simulation of large populations of neurons Dynamics of sparsely connected networks of excitatory and inhibitory spiking networks Meanfield theory of irregularly spiking neuronal populations and working memory in recurrent cortical networks The mean field equation for the Kuramoto model on graph sequences with nonLipschitz limit 
Organizers: Mauro Maggioni, Fei Lu, Stefano Vigogna. Contacts us if you would like to meet with the speakers. 
The data seminar will take place on Wednesdays at 3pm, in Hodson Hall 203, during the semester, on Johns Hopkins Homewood campus this map). 
September 13th
Yannis Kevrekidis
Bloomberg distinguished Professor, ChemBE, Johns Hopkins University Title: No equations, no variables, no parameters, no space, no time: Data and the computational modeling of complex/multiscale systems
Abstract: Obtaining predictive dynamical equations from data lies at the heart of science and engineering modeling, and is the linchpin of our technology. In mathematical modeling one typically progresses from observations of the world (and some serious thinking!) first to equations for a model, and then to the analysis of the model to make predictions. Good mathematical models give good predictions (and inaccurate ones do not)  but the computational tools for analyzing them are the same: algorithms that are typically based on closed form equations. While the skeleton of the process remains the same, today we witness the development of mathematical techniques that operate directly on observations data, and appear to circumvent the serious thinking that goes into selecting variables and parameters and deriving accurate equations. The process then may appear to the user a little like making predictions by "looking in a crystal ball". Yet the "serious thinking" is still there and uses the same and some new mathematics: it goes into building algorithms that "jump directly" from data to the analysis of the model (which is now not available in closed form) so as to make predictions. Our work here presents a couple of efforts that illustrate this ``new path from data to predictions. It really is the same old path, but it is travelled by new means. 
September 20th
Carey Priebe
Professor, Applied Mathematics and Statistics, Johns Hopkins University Semiparametric spectral modeling of the Drosophila connectome
We present semiparametric spectral modeling of the complete larval Drosophila mushroom body connectome. Motivated by a thorough exploratory data analysis of the network via Gaussian mixture modeling (GMM) in the adjacency spectral embedding (ASE) representation space, we introduce the latent structure model (LSM) for network modeling and inference. LSM is a generalization of the stochastic block model (SBM) and a special case of the random dot product graph (RDPG) latent position model, and is amenable to semiparametric GMM in the ASE representation space. The resulting connectome code derived via semiparametric GMM composed with ASE captures latent connectome structure and elucidates biologically relevant neuronal properties. Related papers:
The complete connectome of a learning and memory center in an insect brain A consistent adjacency spectral embedding for stochastic blockmodel graphs A limit theorem for scaled eigenvectors of random dot product graphs Limit theorems for eigenvectors of the normalized Laplacian for random graphs 
September 27
John Benedetto
Professor, Department of Mathematics, University of Maryland, College Park and Norbert Wiener Center Frames  two case studies: ambiguity and uncertainty
The theory of frames is an essential concept for dealing with signal representation in noisy environments. We shall examine the theory in the settings of the narrow band ambiguity function and of quantum information theory. For the ambiguity function, best possible estimates are derived for applicable constant amplitude zero autocorrelation (CAZAC) sequences using Weil's solution of the Riemann hypothesis for finite fields. In extending the theory to the vectorvalued case modelling multisensor environments, the definition of the ambiguity function is characterized by means of group frames. For the uncertainty principle, Andrew Gleason's measure theoretic theorem, establishing the transition from the lattice interpretation of quantum mechanics to Born's probabilistic interpretation, is generalized in terms of frames to deal with uncertainty principle inequalities beyond Heisenberg's. My collaborators are Travis Andrews, Robert Benedetto, Jeffrey Donatelli, Paul Koprowski, and Joseph Woodworth. Related papers:
Superresolution by means of Beurling minimal extrapolation Generalized Fourier frames in terms of balayage Uncertainty principles and weighted norm inequalities A frame reconstruction algorithm with applications to magnetric resonance imaging Frame multiplication theory and a vectorvalued DFT and ambiguity functions 
October 4th
Nathan Kutz
Robert Bolles and Yasuko Endo Professor, Applied Mathematics, University of Washington Datadriven discovery of governing equations and physical laws
The emergence of data methods for the sciences in the last decade has been enabled by the plummeting costs of sensors, computational power, and data storage. Such vast quantities of data afford us new opportunities for datadriven discovery, which has been referred to as the 4th paradigm of scientific discovery. We demonstrate that we can use emerging, largescale timeseries data from modern sensors to directly construct, in an adaptive manner, governing equations, even nonlinear dynamics, that best model the system measured using modern regression techniques. Recent innovations also allow for handling multiscale physics phenomenon and control protocols in an adaptive and robust way. The overall architecture is equationfree in that the dynamics and control protocols are discovered directly from data acquired from sensors. The theory developed is demonstrated on a number of canonical example problems from physics, biology and engineering. 
October 11th
Fei Lu
Assistant Professor, Department of Mathematics, Johns Hopkins University Data assimilation with stochastic model reduction
In weather and climate prediction, data assimilation combines data with dynamical models to make prediction, using ensemble of solutions to represent the uncertainty. Due to limited computational resources, reduced models are needed and coarsegrid models are often used, and the effects of the subgrid scales are left to be taken into account. A major challenge is to account for the memory effects due to coarse graining while capturing the key statisticaldynamical properties. We propose to use nonlinear autoregression moving average (NARMA) type models to account for the memory effects, and demonstrate by examples that the resulting NARMA type stochastic reduced models can capture the key statistical and dynamical properties and therefore can improve the performance of ensemble prediction in data assimilation. The examples include the Lorenz 96 system (which is a simplified model of the atmosphere) and the KuramotoSivashinsky equation of spatiotemporally chaotic dynamics. 
October 18th
Roy Lederman
Postdoc, Program in Applied and Computational Mathematics, Princeton University HyperMolecules in CryoElectron Microscopy (cryoEM)
CryoEM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson for developing cryoelectron microscopy for the highresolution structure determination of biomolecules in solution". Cryoelectron microscopes produce a large number of very noisy twodimensional projection images of individual frozen molecules. Unlike related tomography methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. Unlike other structure determination methods, such as xray crystallography and nuclear magnetic resonance (NMR), cryoEM produces measurements of individual molecules and not ensembles of molecules. Therefore, cryoEM could potentially be used to study mixtures of different conformations of molecules. While current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryoEM. I will discuss the hypermolecules approach to continuous heterogeneity, and the numerical tools and analysis methods that we are developing in order to recover such hypermolecules. 
October 25th
John Harlim
Professor, Department of Mathematics, The Pennsylvania State University Nonparametric modeling for prediction and data assimilation
I will discuss a nonparametric modeling approach for forecasting stochastic dynamical systems on smooth manifolds embedded in Euclidean space. This approach allows one to evolve the probability distribution of nontrivial dynamical systems with an equationfree modeling. In the second part of this talk, I will discuss a nonparametric estimation of likelihood functions using datadriven basis functions and the theory of kernel embeddings of conditional distributions developed in the machine learning community. I will demonstrate how to use this likelihood function to estimate biased modeling error in assimilating cloudy satellite brightness temperaturelike quantities. 
November 8th
Eitan Tadmor
Distinguished University Professor, Department of Mathematics, Institute for Physical Science & Technology, Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland Title: Emergent behavior in selforganized dynamics: from consensus to hydrodynamic flocking
Abstract: We discuss several first and secondorder models encountered in opinion and flocking dynamics. The models are driven by different rules of engagement, which quantify how each member interacts with its immediate neighbors. We highlight the role of geometric vs. topological neighborhoods and distinguish between local and global interactions, while addressing the following two related questions. (i) How local rules of interaction lead, over time, to the emergence of consensus; and (ii) How the flocking behavior of large crowds captured by their hydrodynamic description. Related papers:
Kinetic descriptions a mathematical bridge to better understand the world Mathematical aspects of selforganized dynamics: consensus, emergence of leaders, and social hydrodynamics Heterophilious dynamics enhances consensus From particle to kinetic and hydrodynamic descriptions of flocking 
November 15th
Tyrus Berry
Research Associate, Department of Mathematical Science, George Mason University What geometries can we learn from data?
In the field of manifold learning, the foundational theoretical results of Coifman and Lafon (Diffusion Maps, 2006) showed that for data sampled near an embedded manifold, certain graph Laplacian constructions are consistent estimators of the LaplaceBeltrami operator on the underlying manifold. Since these operators determine the Riemannian metric, they completely describe the geometry of the manifold (as inherited from the embedding). It was later shown that different kernel functions could be used to recover any desired geometry, at least in terms of pointwise estimation of the associated LaplaceBeltrami operator. In this talk I will first briefly review the above results and then introduce new results on the spectral convergence of these graph Laplacians. These results reveal that not all geometries are accessible in the stronger spectral sense. However, when the data set is sampled from a smooth density, there is a natural conformally invariant geometry which is accessible on all compact manifolds, and even on a large class of noncompact manifolds. Moreover, the kernel which estimates this geometry has a very natural construction which we call Continuous kNearest Neighbors (CkNN). 
November 29th
Yingzhou Li
Phillip Griffiths Research Assistant Professor, Department of Mathematics, Duke University Kernel functions and their fast evaluations
Kernel matrices are popular in machine learning and scientific computing, but they are limited by their quadratic complexity in both construction and storage. It is wellknown that as one varies the kernel parameter, e.g., the width parameter in radial basis function kernels, the kernel matrix changes from a smooth lowrank kernel to a diagonallydominant and then fullydiagonal kernel. Lowrank approximation methods have been widelystudied, mostly in the first case, to reduce the memory storage and the cost of computing matrixvector products. Here, we use ideas from scientific computing to propose an extension of these methods to situations where the matrix is not wellapproximated by a lowrank matrix. In particular, we construct an efficient block lowrank approximation method  which we call the Block Basis Factorization  and we show that it has O(n) complexity in both time and memory. Our method works for a wide range of kernel parameters, extending the domain of applicability of lowrank approximation methods, and our empirical results demonstrate the stability (small standard deviation in error) and superiority over current stateofart kernel approximation algorithms. Related papers:
Structured Block Basis Factorization for Scalable Kernel Matrix On the numerical rank of radial basis function kernel matrices in high dimension 
December 6th
HauTieng Wu
Associate Professor, Department of Mathematics, Duke University Some Data Analysis Tools Inspired by Medical Challenges Fetal ECG as an example
We discuss a particular interest in medicine extracting hidden dynamics from a single observed time series composed of multiple oscillatory signals, which could be viewed as a singlechannel blind source separation problem. This problem is common nowadays due to the popular mobile health monitoring devices, and is made challenging by the structure of the signal which consists of nonsinusoidal oscillations with time varying amplitude/frequency, and by the heteroscedastic nature of the noise. Inspired by the fetal electrocardiogram (ECG) signal analysis from the single lead maternal abdominal ECG signal, in this talk I will discuss some new data analysis tools, including the cepstrumbased nonlineartype timefrequency analysis and fiberbundle based manifold learning technique. In addition to showing the results in fetal ECG analysis, I will also show how the approach could be applied to simultaneously extract the instantaneous heart/respiratory rate from a PPG signal during exercise. If time permits, the clinical trial results will be discussed.Abstract: Some Data Analysis Tools Inspired by Medical Challenges Fetal ECG as an example Related papers:

December 20th
Valeriya Naumova
Senior research scientist, Section for Computing and Software, Simula Research Laboratory (Simula) Multiparameter regularisation for solving unmixing problems in signal
processing: theoretical and practical aspects
Motivated by reallife applications in signal processing and image analysis, where the quantity of interest is generated by several sources to be accurately modelled and separated, as well as by recent advances in sparse regularisation theory and optimisation, we present a theoretical and algorithmic framework for optimal support recovery in inverse problems of unmixing type by means of multipenalty regularisation. While multipenalty regularisation is not a novel technique [1], we aim at providing precise reconstruction guarantees and methods for adaptive regularisation parameter choice. We consider and analyse a regularisation functional composed of a datafidelity term, where signal and noise are additively mixed, a nonsmooth, convex, sparsity promoting term, and a convex penalty term to model the noise. We prove not only that the wellestablished theory for sparse recovery in the single parameter case can be translated to the multipenalty settings, but we also demonstrate the enhanced properties of multipenalty regularisation in terms of support identification compared to sole $\ell^1$minimisation. Extending the notion of Lasso path algorithm, we additionally propose an efficient procedure for an adaptive parameter choice in multipenalty regularisation, focusing on the recovery of the correct support of the solution. The approach essentially enables a fast construction of a tiling over the parameter space in such a way that each tile corresponds to a different sparsity pattern of the solution. Finally, we propose an iterative alternating algorithm based on simple iterative thresholding steps to perform the minimisation of the extended multipenalty functional, containing nonsmooth and nonconvex sparsity promoting term. To exemplify the robustness and effectiveness of the multipenalty framework, we provide an extensive numerical analysis of our method and compare it with stateoftheart singlepenalty algorithms for compressed sensing problems. This is joint work with Markus Grasmair [3, 4], Norwegian University of Science and Technology; Timo Klock [4], Simula Research Laboratory, and Johannes Maly and Steffen Peter [2], Technical University of Munich. Related papers:
Y. Meyer, Oscillating patterns in image processing and nonlinear evolution equations Minimization of multipenalty functionals by alternating iterative thresholding and optimal parameter choices Conditions on optimal support recovery in unmixing problems by means of multipenalty regularization Multiple parameter learning with regularization path algorithms 
Organizers: Mauro Maggioni, Wenjing Liao, Stefano Vigogna. Contacts us if you would like to meet with the speakers. 
The data seminar will take place on Wednesdays at 3pm, in Whitehead Hall 304, during the semester, on Johns Hopkins Homewood campus this map). 
February 8th
Kasso Okoudjou
Professor and Associate Chair, Department of Mathematics, University of Maryland, College Park https://www.math.umd.edu/~okoudjou/ Inductive and numerical approaches to the HRT conjecture
Given a nonzero square integrable function $g$ and $\Lambda=\{(a_k, b_k)\}_{k=1}^N \subset \Br^2$ let $G(g, \Lambda)=\{e^{2\pi i b_k \cdot}g(\cdot  a_k)\}_{k=1}^N.$ The HeilRamanathanTopiwala (HRT) Conjecture is the question of whether $G(g, \Lambda)$ is linearly independent. For the last two decades, very little progress has been made in settling the conjecture. In the first part of the talk, I will give an overview of the state of the conjecture. I will then describe recent inductive and numerical approaches to attack the conjecture. If time permits, I will present some new positive results in the special case where $g$ is realvalued. 
February 15th
Jerome Darbon
Assistant Professor, Applied Mathematics, Brown University https://www.brown.edu/academics/appliedmathematics/jeromedarbon On convex finitedimensional variational methods in imaging sciences,
and HamiltonJacobi equations
We consider standard finitedimensional variational models used in signal/image processing that consist in minimizing an energy involving a data fidelity term and a regularization term. We propose new remarks from a theoretical perspective which give a precise description on how the solutions of the optimization problem depend on the amount of smoothing effects and the data itself. The dependence of the minimal values of the energy is shown to be ruled by HamiltonJacobi equations, while the minimizers $u(x,t)$ for the observed images x and smoothing parameters $t$ are given by $ u(x,t)=x \nabla H(\nabla E(x,t))$ where $E(x,t)$ is the minimal value of the energy and $H$ is a Hamiltonian related to the data fidelity term. Various vanishing smoothing parameter results are derived illustrating the role played by the prior in such limits. Finally, we briefly present an efficient numerical numerical method for solving certain HamiltonJacobi equations in high dimension and some applications in optimal control. 
March 8th
Matthew Hirn
Assistant Professor, Department of Mathematics, Michigan State University https://matthewhirn.wordpress.com/ Learning many body physics via multiscale, multilayer machine learnining architectures
Deep learning algorithms are making their mark in machine learning, obtaining state of the art results across computer vision, natural language processing, auditory signal processing and more. A wavelet scattering transform has the general architecture of a convolutional neural network, but leverages structure within data by encoding multiscale, stable invariants relevant to the task at hand. This approach is particularly relevant to data generated by physical systems, as such data must respect underlying physical laws. We illustrate this point through many body physics, in which scattering transforms can be loosely interpreted as the machine learning version of a fast multipole method (FMM). Unlike FMMs, which efficiently simulate the physical system, the scattering transform learns the underlying physical kernel from given states of the system. The resulting learning algorithm obtains state of the art numerical results for the regression of molecular energies in quantum chemistry, obtaining errors on the order of more costly quantum mechanical approaches. 
March 29th
Jason Eisner
Professor, Department of Computer Science, Johns Hopkins University http://www.cs.jhu.edu/~jason/ Probabilistic Modeling of Natural Language
Natural language is a particular kind of timeseries data. By way of introduction, I will informally sketch some of the phenomena that occur in natural language data and the kinds of probabilistic models that are traditionally used to describe them (e.g., context free grammars, Chinese restaurant processes, graphical models, finitestate transducers, recurrent neural networks augmented with memory). Many of these are covered in my JHU fall course, EN.600.465 Natural Language Processing. As an illustrative example, I will then describe a new conditional probability model that combines LSTMs with finitestate transducers to predict one string from another. For example, such a model can convert between the past and present tenses of an unfamiliar verb. Such pairwise conditional distributions can be combined into graphical models that model the relationships among many strings. 
April 5th
Afonso Bandeira
Assistant Professor, Courant Institute of Mathematical Sciences, NYU http://www.cims.nyu.edu/~bandeira/ On Phase Transitions for Spiked Random Matrix and Tensor Models
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector (or low rank structure) is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences, where the goal is often to recover or detect the planted low rank structured. In this talk we discuss fundamental limitations of statistical methods to perform these tasks and methods that outperform PCA at it. Emphasis will be given to low rank structures arising in Synchronization problems. Time permitting, analogous results for spiked tensor models will also be discussed. Joint work with: Amelia Perry, Alex Wein, and Ankur Moitra. 
April 12th
Andrew Christlieb
MSU Foundation Professor (Department of Mathematics) and Department Chair (Department of Computational Mathematics, Science and Engineering), Michigan State University https://cmse.msu.edu/directory/faculty/andrewchristlieb/ A sublinear deterministic FFT for sparse high dimensional signals
In this talk we investigate the problems of efficient recover of sparse signals (sparsity=k) in a high dimensional setting. In particular, we are going to investigate efficient recovery of the k largest Fourier modes of a signal of size N^d, where N is the bandwidth and d is the dimension. Our objective is the development of a high dimensional sublinear FFT, d=100 or 1000, that can recover the signal in O(d k log k) time. The methodology is based on our one dimensional deterministic sparse FFT that is O(k log k). The original method is recursive and based on ratios of short FFTs of pares of subsampled signals. The same ratio test allows us to identify when there is a collision due to aliasing the subsampled signals. The recursive nature allows us to separate and identify frequencies that have collided. Key in the high dimensional setting is the introduction of a partial unwrapping method and a tilting method that can ensure that we avoid collisions in the high dimensional setting on subsampled grids. We present the method, some analysis and results for a range of tests in both the noisy and noiseless cases. 
April 26th
Wojciech Czaja
Professor, Department of Mathematics, University of Maryland, College Park https://www.math.umd.edu/~wojtek/ Solving Fredholm integrals from incomplete measurements
We present an algorithm to solve Fredholm integrals of the first kind with tensor product structures, from a limited number of measurements with the goal of using this method to accelerate Nuclear Magnetic Resonance (NMR) acquisition. This is done by incorporating compressive sampling type arguments to fill in the missing measurements using a priori knowledge of the structure of the data. In the first step, we recover a compressed data matrix from measurements that form a tight frame, and establish that these measurements satisfy the restricted isometry property (RIP). In the second step, we solve the zerothorder regularization minimization problem using the VenkataramananSongHuerlimann algorithm. We demonstrate the performance of this algorithm on simulated and real data and we compare it with other sampling techniques. Our theory applied to both 2D and multidimensional NMR. 
Organizers: Mauro Maggioni, Wenjing Liao, Stefano Vigogna. Contacts us if you would like to meet with the speakers. 
The data seminar will take place on Wednesdays at 3pm, in Krieger Hall 309, during the semester, on Johns Hopkins Homewood campus (building 39 at location F2/3 on this map). 
September 7th
Radu Balan
Professor, Department of Mathematics, University of Maryland, College Park http://www.math.umd.edu/~rvbalan/ Statistics of the Stability Bounds in the Phase Retrieval Problem
In this talk we present a localglobal Lipschitz analysis of the phase retrieval problem. Additionally we present tentative estimates of the tailbound for the distribution of the global Lipschitz constants. Specifically it is known that if the frame $\{f_1,\ldots,f_m\}$ for $C^n$ is phase retrievable then there are constants $a_0$ and $b_0$ so that for every $x,y\in C^n$: $a_0 xx^*yy^*_1^2 \leq \sum_{k=1}^m \langle x,f_k\rangle^2\langle y,f_k\rangle^2^2 \leq b_0 xx^*yy^*_1^2$. Assume $f_1,\ldots,f_m$ are independent realizations with entries from $CN(0,1)$. In this talk we establish estimates for the probability $P(a_0>a)$. 
September 21st
Charles Meneveau
Louis M. Sardella Professor of Mechanical Engineering, Johns Hopkins University http://pages.jh.edu/~cmeneve1/ Hydrodynamic turbulence in the era of big data: simulation, data, and analysis
In this talk, we review the classic problem of NavierStokes turbulence, the role numerical simulations have played in advancing the field, and the data challenges posed by these simulations. We describe the Johns Hopkins Turbulence Databases (JHTDB) and present some sample applications from the areas of velocity increment statistics and finite time Lyapunov exponents in isotropic turbulence and wall modeling for Large Eddy Simulations of wallbounded flows. Related papers:
A Web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES Largedeviation statistics of vorticity stretching in isotropic turbulence A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence 
Note date and place: September 23rd  2pm  Gilman 132
Ben Leimkuhler
Professor of Mathematics, University of Edinburgh http://kac.maths.ed.ac.uk/~bl/ From Molecular Dynamics to Large Scale Inference
Molecular models and data analytics problems give rise to very large systems of stochastic differential equations (SDEs) whose paths are designed to ergodically sample multimodal probability distributions. An important challenge for the numerical analyst (or the data scientist, for that matter) is the design of numerical procedures to generate these paths. One of the interesting ideas is to construct stochastic numerical methods with close attention to the error in the invariant measure. Another is to redesign the underlying stochastic dynamics to reduce bias or locally transform variables to enhance sampling efficiency. I will illustrate these ideas with various examples, including a geodesic integrator for constrained Langevin dynamics [1] and an ensemble sampling strategy for distributed inference [2]. 
September 28th
Rene Vidal
Professor of Biomedical Engineering, Computer Science, Mechanical Engineering, and Electrical and Computer Engineering, Johns Hopkins University http://cis.jhu.edu/~rvidal/ Global Optimality in Matrix and Tensor Factorization, Deep Learning, and Beyond
Matrix, tensor, and other factorization techniques are used in many applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the associated optimization problems are typically nonconvex due to a multilinear form or other convexity destroying transformation. Building on ideas from convex relaxations of matrix factorizations, in this talk I will present a very general framework which allows for the analysis of a wide range of nonconvex factorization problems  including matrix factorization, tensor factorization, and deep neural network training formulations. In particular, I will present sufficient conditions under which a local minimum of the nonconvex optimization problem is a global minimum and show that if the size of the factorized variables is large enough then from any initialization it is possible to find a global minimizer using a local descent algorithm. 
October 26th
Robert Pego
Professor, Department of Mathematical Sciences, Carnegie Mellon University http://www.math.cmu.edu/~bobpego/ Microdroplet instablity for incompressible distance between shapes
AbstractThe leastaction problem for geodesic distance on the 'manifold' of fluidblob shapes exhibits instability due to microdroplet formation.This reflects a striking connection between Arnold's leastaction principle for incompressible Euler flows and geodesic paths for Wasserstein distance. A connection with fluid mixture models via a variant of Brenier's relaxed leastaction principle for generalized Euler flows will be outlined also. This is joint work with JianGuo Liu and Dejan Slepcev. 
November 2nd
Dejan Slepcev
Associate Professor, Department of Mathematical Sciences, Carnegie Mellon University http://www.math.cmu.edu/~slepcev/ Variational problems on graphs and their continuum limits
We will discuss variational problems arising in machine learning and their limits as the number of data points goes to infinity. Consider point clouds obtained as random samples of an underlying "groundtruth" measure. Graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points. Many machine learning tasks, such as clustering and classification, can be posed as minimizing functionals on such graphs. We consider functionals involving graph cuts and graph laplacians and their limits as the number of data points goes to infinity. In particular we establish under what conditions the minimizers of discrete problems have a well defined continuum limit, and characterize the limit. The talk is primarily based on joint work with Nicolas Garcia Trillos, as well as on works with Xavier Bresson, Moritz Gerlach, Matthias Hein, Thomas Laurent, James von Brecht and Matt Thorpe. 
November 9th
Markos Katsoulakis
Professor, Department of Mathematics and Statistics http://people.math.umass.edu/~markos/ Scalable Information Inequalities for Uncertainty Quantification in high dimensional probabilistic models
In this this talk we discuss new scalable information bounds for quantities of interest of complex stochastic models. The scalability of inequalities allows us to (a) obtain uncertainty quantification bounds for quantities of interest in highdimensional systems and/or for long time stochastic dynamics; (b) assess the impact of large model perturbations such as in nonlinear response regimes in statistical mechanics; (c) address modelform uncertainty, i.e. compare different extended probabilistic models and corresponding quantities of interest. We demonstrate these tools in fast sensitivity screening of chemical reaction networks with a very large number of parameters, and towards obtaining robust and tight uncertainty quantification bounds for phase diagrams in statistical mechanics models. Related papers:
Scalable Information Inequalities for Uncertainty Quantification Accelerated Sensitivity Analysis in High Dimensional Stochastic Reaction Networks PathSpace Information Bounds for Uncertainty Quantification and Sensitivity Analysis of Stochastic Dynamics Pathspace variational inference for nonequilibrium coarsegrained systems Effects of correlated parameters and uncertainty in electronicstructurebased chemical kinetic modelling 
November 30th
Youssef Marzouk
Associate Professor of Aeronautics and Astronautics, Massachusetts Institute of Technology http://aeroastro.mit.edu/facultyresearch/facultylist/youssefmmarzouk Measure transport approaches for Bayesian computation
We will discuss how transport maps, i.e., deterministic couplings between probability measures, can enable useful new approaches to Bayesian computation. A first use involves a combination of optimal transport and Metropolis correction; here, we use continuous transportation to transform typical MCMC proposals into adapted nonGaussian proposals, both local and global. Second, we discuss a variational approach to Bayesian inference that constructs a deterministic transport map from a reference distribution to the posterior, without resorting to MCMC. Independent and unweighted samples can then be obtained by pushing forward reference samples through the map. Making either approach efficient in high dimensions, however, requires identifying and exploiting lowdimensional structure. We present new results relating the sparsity and decomposability of transports to the conditional independence structure of the target distribution. We also describe conditions, common in inverse problems, under which transport maps have a particular lowrank or nearidentity structure. In general, these properties of transports can yield more efficient algorithms. As a particular example, we derive new deterministic "online" algorithms for Bayesian inference in nonlinear and nonGaussian statespace models with static parameters. This is joint work with Daniele Bigoni, Matthew Parno, and Alessio Spantini. 
Note date and place: December 2nd  10am  Gilman 132
Alex Cloninger
Gibbs Assistant Professor and NSF Postdoctoral Fellow, Yale University http://users.math.yale.edu/~ac2528 Incorporation of Geometry into Learning Algorithms and Medicine
This talk focuses on two instances in which scientific fields outside mathematics benefit from incorporating the geometry of the data. In each instance, the applications area motivates the need for new mathematical approaches and algorithms, and leads to interesting new questions. (1) A method to determine and predict drug treatment effectiveness for patients based off their baseline information. This motivates building a function adapted diffusion operator high dimensional data X when the function F can only be evaluated on large subsets of X, and defining a localized filtration of F and estimation values of F at a finer scale than it is reliable naively. (2) The current empirical success of deep learning in imaging and medical applications, in which theory and understanding is lagging far behind.. By assuming the data lies near low dimensional manifolds and building local wavelet frames, we improve on existing theory that breaks down when the ambient dimension is large (the regime in which deep learning has seen the most success) 
December 7th
Ben Adcock
Assistant Professor, Simons Fraser University http://benadcock.org/ Sparse polynomial approximation of highdimensional functions
Many problems in scientific computing require the approximation of smooth, highdimensional functions from limited amounts of data. For instance, a common problem in uncertainty quantification involves identifying the parameter dependence of the output of a computational model. Complex physical systems require computational models with many parameters, resulting in multivariate functions of many variables. Although the amount of data may be large, the curse of dimensionality essentially prohibits collecting or processing enough data to reconstruct the unknown function using classical approximation techniques. In this talk, I will give an overview of the approximation of smooth, highdimensional functions by sparse polynomial expansions. I will focus on the recent application of techniques from compressed sensing to this problem, and demonstrate how such approaches theoretically overcome the curse of dimensionality. If time, I will also discuss a number of extensions, including dealing with corrupted and/or unstructured data, the effect of model error and incorporating additional information such as gradient data. I will also highlight several challenges and open problems. This is joint work with Casie Bao, Simone Brugiapaglia and Yi Sui (SFU). 