Abstract: We examine consistency of the Gibbs posterior for dynamical systems using a classical idea in dynamical systems called the thermodynamic formalism in tracking dynamical systems. We state a variation formulation under which there is a unique posterior distribution of parameters as well as hidden states using using classic ideas from dynamical systems such as pressure and joinings. We use an example of consistency of hidden Markov with infinite lags as an application of our theory. We develop a geometric framework that characterizes…

Abstract:  Can learning theory, as we know it today, form a theoretical basis for neural networks. I will try to discuss this question in light of two new results -- one positive and one negative. Based on joint work with Roy Frostig, Vineet Gupta and Yoram Singer, and with Vitaly Feldman Biography: Amit Daniely is an Assistant Professor at the Hebrew University in Jerusalem, and a research scientist at Google Research, Tel-Aviv. Prior to that, he was a research scientist at Google Research, Mountain-View. Even…

Abstract: Markov chain Monte Carlo methods provide consistent approximations of integrals as the number of iterations goes to infinity. However, these estimators are generally biased after any fixed number of iterations, which complicates both parallel computation. In this talk I will explain how to remove this burn-in  bias by using couplings of Markov chains and a telescopic sum argument, inspired by Glynn & Rhee (2014). The resulting unbiased estimators can be computed independently in parallel, and averaged. I will present…

Abstract:  Deep Learning, thanks mostly to Convolutional architectures, has recently transformed computer vision and speech recognition. Their ability to encode geometric stability priors, while offering enough expressive power, is at the core of their success. In such settings, geometric stability is expressed in terms of local deformations, and it is enforced thanks to localized convolutional operators that separate the estimation into scales. Many problems across applied sciences, from particle physics to recommender systems, are formulated in terms of signals defined over…

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…