Title: Computational Imaging: Reconciling Physical and Learned Model
Abstract: Computational imaging is a rapidly growing area that seeks to enhance the capabilities of imaging instruments by viewing imaging as an inverse problem. There are currently two distinct approaches for designing computational imaging methods: model-based and learning-based. Model-based methods leverage analytical signal properties and often come with theoretical guarantees and insights. Learning-based methods leverage data-driven representations for best empirical performance through training on large datasets. This talk presents Regularization by Artifact Removal (RARE), as a framework for reconciling both viewpoints by providing a learning-based extension to the classical theory. RARE uses “artifact-removing deep neural nets” as mechanisms to infuse learned prior knowledge into an inverse problem while maintaining a clear separation between the prior and physics-based acquisition model. Our results indicate that RARE can achieve state-of-the-art performance in different computational imaging tasks, while also being amenable to rigorous theoretical analysis. We will focus on the applications of RARE in biomedical imaging, including magnetic resonance and tomographic imaging.
Biography: Ulugbek S. Kamilov is Assistant Professor and Director of Computational Imaging Group (CIG) at Washington University in St. Louis. He obtained the BSc and MSc degrees in Communication Systems, and the PhD degree in Electrical Engineering from EPFL, Switzerland, in 2008, 2011, and 2015, respectively. From 2015 to 2017, he was a Research Scientist at MERL, Cambridge, MA, USA. He is a recipient of the NSF CAREER Award in 2021 and the IEEE Signal Processing Society’s 2017 Best Paper Award. His Ph.D. thesis was selected as a finalist for the EPFL Doctorate Award in 2016. He has served as an Associate Editor of IEEE Transactions on Computational Imaging (2019-present), Biological Imaging (2020-present), and on IEEE Signal Processing Society’s Computational Imaging Technical Committee (2016-present). He was a plenary speaker at iTWIST 2018, has co-organized IMA Special Workshop on Computational Imaging in 2019, and is a program co-chair for SampTA 2021 and BASP 2022.
Title: Finding low-dimensional structure in messy data
Abstract: In order to draw inferences from large, high-dimensional datasets, we often seek simple structure that model the phenomena represented in those data. Low-rank linear structure is one of the most flexible and efficient such models, allowing efficient prediction, inference, and anomaly detection. However, classical techniques for learning low-rank models assume your data have only minor corruptions that are uniform over samples. Modern research in optimization has begun to develop new techniques to handle realistic messy data — where data are missing, have wide variations in quality, and/or are observed through nonlinear measurement systems.
In this talk we will focus on two problems. In the first, our data are heteroscedastic, ie, corrupted by one of several noise variances. This is common in problems like sensor networks or medical imaging, where different measurements of the same phenomenon are taken with different quality sensing (eg high or low radiation). In this context, learning the low-rank structure via PCA suffers from treating all data samples as if they are equally informative. We will discuss our theoretical results on weighted PCA and new algorithms for the non-convex probabilistic PCA formulation of this problem. In the second part of the talk we will extend the matrix completion problem to cases where the columns are points on low-dimensional nonlinear algebraic varieties. We discuss two optimization approaches to this problem, one kernelized algorithm and one that leverages existing LRMC techniques on a tensorized representation of the data. We also provide a formal mathematical justification for the success of our method and experimental results showing that the new approach outperforms existing state-of-the-art methods for matrix completion in many situations.
Biography: Laura Balzano is an associate professor in Electrical Engineering and Computer Science at the University of Michigan. She is recipient of the NSF Career Award, ARO Young Investigator Award, AFOSR Young Investigator Award, and faculty fellowships from Intel and 3M. She received the Vulcans Education Excellence Award at the University of Michigan. Her main research focus is on modeling with big, messy data — highly incomplete or corrupted data, uncalibrated data, and heterogeneous data — and its applications in a wide range of scientific problems. Her expertise is in statistical signal processing, matrix factorization, and optimization. Laura received a BS from Rice University, MS from the UCLA, and PhD from the University of Wisconsin in Electrical and Computer Engineering.
Abstract: The classical theory of nonlinear dynamics exhibits wonderfully rich and exotic structures. I would argue that as we move to an era of data driven dynamics it offers too many riches. Stated differently, if we only have finite data at our disposal we need a simpler theory of dynamics. I will present such a theory based on combinatorics and algebraic topology (no prerequisite understanding of algebraic topology is necessary). After describing the theory, I will discuss two directions of application. First, directly to the analysis of time series. Second to the analysis of dynamics of networks.
Biography: Konstantin Mischaikow obtained his Ph.D. in Mathematics in 1985 from the University of Wisconsin, Madison. He was a Postdoc in the Applied Math department at Brown. He has held positions in Mathematics at Michigan State University, Georgia Tech, and since 2006 at Rutgers University. His research interests include nonlinear dynamics, computational dynamics, and topological data analysis.
Title: Graph Ricci Flow and Applications in Network Analysis and Learning
Abstract: The notion of curvature describes how spaces are bent at each point and Ricci flow deforms the space such that curvature changes in a way analogous to the diffusion of heat. In this talk I will discuss some recent work in my group on discrete Ollivier Ricci curvature defined on graphs. Discrete curvature defined on an edge captures the local connectivity in the neighborhood. In general edges within a densely connected community have positive curvature while edges connecting different communities have negative curvature. By deforming edge weights with respect to curvature one can derive a Ricci flow metric which is robust to edge insertion/deletion. I will show applications of graph Ricci flow in graph analysis and learning, including network alignment, community detection and graph neural networks.
Biography: Professor Jie Gao is currently Professor in computer science, Rutgers University. She was on the faculty of Computer Science department at Stony Brook University from 2005-2019. She received B.Eng from the Special Class of the Gifted Young, University of Science and Technology of China in 1999, Ph.D in Computer Science from Stanford University in 2004 and a postdoc at Caltech from 2004-2005. She received the NSF career award in 2006, IMC best paper award and multiple Research Excellence Award in computer science department of Stony Brook. She is currently serving on the editorial board of ACM Transactions on Sensor Networks and International Journal of Computational Geometry and Applications. She published over 140 referred papers in computer networking and theoretical computer science fields, and has graduated over 16 Ph.D students.
Title: Black-box Optimization in Theory and in Practice
Abstract: In this talk, we will consider the problem of maximizing a black-box function via noisy and costly queries from a theoretical perspective (a lot of it) as well as applications (an exciting bit). We first motivate the problem by considering a wide variety of engineering design applications from the heuristic optimization of wireless networks to hardware acceleration to neural network architecture search.
In the second part of the talk, we consider the problem in a Bayesian framework with a Gaussian Process prior. In particular, a new algorithm for this problem is proposed, and high probability bounds on its simple and cumulative regret are established. The query point selection rule in most existing methods involves an exhaustive search over an increasingly fine sequence of uniform discretizations of the input space. The proposed algorithm, in contrast, adaptively refines the domain which leads to a lower computational complexity, particularly when the domain is a subset of a high dimensional Euclidean space. In addition to the computational gains, sufficient conditions are identified under which the regret bounds of the new algorithm improve upon the known results.
In the last part of the talk, we build on the intuition provided by our work in the Bayesian setting to consider the problem in a non-Bayesian setting where the objective function is assumed to have a smooth kernel representation. Most notably the proposed algorithm –augmenting the Gaussian Process surrogate with a local polynomial estimator— closes a significant gap to the (optimal) regret lower bound for a class of widely used and practically relevant Matern family of Kernels. This is joint work with my PhD student Shekhar Shubhanshu.
Biography: Dr. Javidi is a professor of electrical and computer engineering at University of California, San Diego. She received her MS and PhD degrees in Electrical Engineering and Computer Science as well as her MS in Applied Mathematics from the University of Michigan, Ann Arbor. Before joining UCSD, she was on the faculty of Electrical Engineering Department at the University of Washington, Seattle; In 2013-2014, she spent her sabbatical at Stanford University as a visiting faculty. Her area of research is at the intersection of stochastic control, information theory, and data science with notable contributions to the theory of information acquisition and active learning. At the University of California, San Diego, Tara is a founding co-director of the Center for Machine-Integrated Computing and Security, the principal investigator of Detect Drone Project as well as a faculty member of the member of the Centers of Information Theory and Applications (ITA), Halıcıoğlu Data Science Institute, Wireless Communications (CWC), Contextual Robotics Institute (CRI) and Networked Systems (CNS).