• Speaker: Jonathan Scarlett, National University of Singapore
• Title: Beyond Sparsity: Compressive Sensing with (Deep) Generative Modeling Assumptions
• Date: 09/02/2021
• Time: 4:30 AM - 5:30 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

The problem of estimating an unknown vector from linear measurements has a long history in statistics, machine learning, and signal processing. Classical studies focus on the "n >> p" regime (#measurements >> #parameters), and more recent studies handle the "n << p" regime by exploiting low-dimensional structure such as sparsity or low-rankness. Such variants are commonly known as compressive sensing. In this talk, I will overview recent methods that move beyond these simple notions of structure, and instead assume that the underlying vector is well-modeled by a generative model (e.g., produced by deep learning methods such as GANs). I will highlight algorithmic works that demonstrated up to 5-10x savings in the number of measurements over sparsity-based methods, and then move on to our theoretical work characterizing the order-optimal sample complexity in terms of quantities such as (i) the Lipschitz constant of the model, or (ii) the depth/width in a neural network model. I will also briefly highlight some recent results on non-linear observation models.

• Speaker: Russell Luke, University of Göttingen
• Title: Structured (In)Feasibility: Nonmonotone Operator Splitting in Nonlinear Spaces
• Date: 09/16/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

The success of operator splitting techniques for convex optimization has led to an explosion of methods for solving large-scale and nonconvex optimization problems via convex relaxation. This success is at the cost of overlooking direct approaches to operator splitting that embrace some of the more inconvenient aspects of many model problems, namely nonconvexity, nonsmoothness and infeasibility. I will introduce some of the tools we have developed for handling these issues, and present sketches of the basic results we can obtain. The formalism is in general metric spaces, but most applications have their basis in Euclidean spaces. Along the way I will try to point out connections to other areas of intense interest, such as optimal mass transport.

• Speaker: Michael Perlmutter, UCLA
• Title: Neural Networks on (Directed) Graphs
• Date: 09/30/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)

The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. These methods extend convolutions to graphs either in the spatial domain as a localized averaging operator or in the spectral domain via the eigendecomposition of a suitable Laplacian. However, most popular GNNs have two limitations. i) The filters used in these networks are essentially low-pass filters (i.e. averaging operators). This leads to the so called ``oversmoothing problem'' and the loss of high-frequency information. ii) If the graph is directed, as is the case in many applications including citation, website, and traffic networks, these networks are unable to effectively encode directional information. In this talk, discuss how we can overcome these limitations via i) the graph scattering transform, which uses band-pass filters rather than low-pass, and ii) MagNet, a network designed for directed graphs based on a complex Hermitian matrix known as the magnetic Laplacian.

• Speaker: Edgar Dobriban, University of Pennsylvania
• Title: Asymptotic perspectives on sketching
• Date: 10/14/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Sketching and random projection methods are a powerful set of techniques to speed up computations in numerical linear algebra, statistics, machine learning, optimization and data science. In this talk, we will discuss some of our works on developing a "big data" asymptotic perspective on sketching in the fundamental problems of linear regression and principal component analysis. This can lead to remarkably clean and elegant mathematical results, which yield powerful insights into the performance of various sketching methods. To highlight one, orthogonal sketches such as the Subsampled Randomized Hadamard Transform are provably better than iid sketches such as Gaussian sketching. This is obtained by using deep recent tools from asymptotic random matrix theory and free probability, including asymptotically liberating sequences (Anderson & Farrell, 2014). This is based on joint works with Jonathan Lacotte, Sifan Liu, Mert Pilanci, David P. Woodruff, and Fan Yang.

• Speaker: Rongrong Wang, Michigan State University
• Title: Sigma Delta quantization on images, manifolds, and graphs
• Date: 10/28/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

In digital signal processing, quantization is the step of converting a signal's real-valued samples into a finite string of bits. As the first step in digital processing, it plays a crucial role in determining the information conversion rate and the reconstruction accuracy. Compared to non-adaptive quantizers, the adaptive ones are known to be more efficient in quantizing bandlimited signals, especially when the bit-budget is small (e.g.,1 bit) and noises are present. However, adaptive quantizers are currently only designed for 1D functions/signals. In this talk, I will discuss challenges in extending it to high dimensions and present our proposed solutions. Specifically, we design new adaptive quantization schemes to quantize images/videos as well as functions defined on 2D surface manifolds and general graphs, which are common objects in signal processing and machine learning. Mathematically, we start from the 1D Sigma-Delta quantization, extend them to high-dimensions and build suitable decoders. The discussed theory would be useful in natural image acquisition, medical imaging, 3D printing, and graph embedding.

• Speaker: Sjoerd Dirksen, Utrecht University
• Title: TBA
• Date: 11/11/2021
• Time: 4:30 AM - 5:30 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

TBA

• Speaker: Alexandra Carpentier, Otto von Guericke Universität Magdeburg
• Title: TBA
• Date: 11/25/2021
• Time: 4:30 AM - 5:30 AM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

TBA