Abstract:   The goal of compressed sensing is to estimate a vector from an under-determined system of noisy linear measurements, by making use of prior knowledge in the relevant domain. For most results in the literature, the structure is represented by sparsity in a well-chosen basis. We show how to achieve guarantees similar to standard compressed sensing but without employing sparsity at all. Instead, we assume that the unknown vectors lie near the range of a generative model, e.g. a GAN…

Abstract:  A formidable challenge in designing sequential treatments is to  determine when and in which context it is best to deliver treatments.  Consider treatment for individuals struggling with chronic health conditions.  Operationally designing the sequential treatments involves the construction of decision rules that input current context of an individual and output a recommended treatment.   That is, the treatment is adapted to the individual's context; the context may include  current health status, current level of social support and current level of adherence…

Abstract: I will give a broad overview of human genetic variation, polygenic traits, association studies, heritability estimation and risk prediction. I will focus on the dual correlation structures of linkage disequilibrium and population structure, discussing how these both confound and enable the various analyses we perform. I will highlight an important open problem on the failure of polygenic risk prediction to generalize across diverse ancestries. Biography: Alex Bloemendal is a computational scientist at the Broad Institute of MIT and Harvard…

Abstract:  Many modern statistical estimation problems rely on imposing additional structure in order to reduce the statistical complexity and provide interpretability. Unfortunately, these structures often are combinatorial in nature and result in computationally challenging problems. In parallel, the combinatorial optimization community has placed significant effort in developing algorithms that can approximately solve such optimization problems in a computationally efficient manner. The focus of this talk is to expand upon ideas that arise in combinatorial optimization and connect those algorithms and…

Abstract:  In a number of problems, we are presented with positive and unlabelled data, referred to as presence-only responses. The application I present today involves studying the relationship between protein sequence and function and presence-only data arises since for many experiments it is impossible to obtain a large set of negative (non-functional) sequences. Furthermore, if the number of variables is large and the goal is variable selection (as in this case), a number of statistical and computational challenges arise due…

Abstract: In this talk, I will revisit the recently established theoretical guarantees for the convergence of the Langevin Monte Carlo algorithm of sampling from a smooth and (strongly) log-concave density. I will discuss the existing results when the accuracy of sampling is measured in the Wasserstein distance and provide further insights on relations between, on the one hand, the Langevin Monte Carlo for sampling and, on the other hand, the gradient descent for optimization. I will also present non-asymptotic guarantees for the accuracy…

Abstract: It is becoming increasingly clear that implicit regularization afforded by the optimization algorithms play a central role in machine learning, and especially so when using large, deep, neural networks. We have a good understanding of the implicit regularization afforded by stochastic approximation algorithms, such as SGD, and as I will review, we understand and can characterize the implicit bias of different algorithms, and can design algorithms with specific biases. But in this talk I will focus on implicit biases of…

Abstract: Finding an efficient test for a testing problem is often linked to the problem of estimating a given function of the data. When this function is not smooth, it is necessary to approximate it cleverly in order to build good tests. In this talk, we will discuss two specific testing problems in Gaussian mixtures models. In both, the aim is to test the proportion of null means. The aforementioned link between sharp approximation rates of non-smooth objects and minimax testing…

Abstract: : Many problems in signal/image processing, and computer vision amount to estimating a signal, image, or tri-dimensional structure/scene from corrupted measurements. A particularly challenging form of measurement corruption are latent transformations of the underlying signal to be recovered. Many such transformations can be described as a group acting on the object to be recovered. Examples include the Simulatenous Localization and Mapping (SLaM) problem in Robotics and Computer Vision, where pictures of a scene are obtained from different positions andorientations;…