Past Events › Stochastics and Statistics Seminar Series

Abstract: This talk will introduce a precise high-dimensional asymptotic theory for AdaBoost on separable data, taking both statistical and computational perspectives. We will consider the common modern setting where the number of features p and the sample size n are both large and comparable, and in particular, look at scenarios where the data is asymptotically separable. Under a class of statistical models, we will provide an (asymptotically) exact analysis of the max-min-L1-margin and the min-L1-norm interpolant. In turn, this will characterize the…

Abstract: Sorted L1 regularization has been incorporated into many methods for solving high-dimensional statistical estimation problems, including the SLOPE estimator in linear regression. In this talk, we study how this relatively new regularization technique improves variable selection by characterizing the optimal SLOPE trade-off between the false discovery proportion (FDP) and true positive proportion (TPP) or, equivalently, between measures of type I and type II error. Additionally, we show that on any problem instance, SLOPE with a certain regularization sequence outperforms the Lasso,…

Abstract:  Classical statistical inference relies on numerous tools from probability theory to study the properties of estimators. However, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk, we extend universal limit theorems beyond the classical setting. Firstly, we consider distributionally \structured" and dependent random object i.e random objects whose distribution are invariant under the action of an amenable group. We…

Abstract: One of the main reasons behind the success of high-dimensional statistics and modern machine learning in taming the curse of dimensionality is that many classes of high-dimensional distributions are surprisingly well-behaved and, when viewed correctly, exhibit a simple structure. This emergent simplicity is in the center of the theory of “high-dimensional phenomena”, and is manifested in principles such as “Gaussian-like behavior” (objects of interest often inherit the properties of the Gaussian measure), “dimension-free behavior” (expressed in inequalities which do…

Abstract: The sample complexity of an interactive learning problem, such as multi-armed bandits or reinforcement learning, is the number of interactions with nature required to output an answer (e.g., a recommended arm or policy) that is approximately close to optimal with high probability. While minimax guarantees can be useful rules of thumb to gauge the difficulty of a problem class, algorithms optimized for this worst-case metric often fail to adapt to “easy” instances where fewer samples suffice. In this talk, I…

Abstract: Reinforcement learning (RL), which is frequently modeled as sequential learning and decision making in the face of uncertainty, is garnering growing interest in recent years due to its remarkable success in practice. In contemporary RL applications, it is increasingly more common to encounter environments with prohibitively large state and action space, thus imposing stringent requirements on the sample efficiency of the RL algorithms in use. Despite the empirical success, however, the theoretical underpinnings for many popular RL algorithms remain…

Abstract: Motivated by applications such as particle tracking, network de-anonymization, and computer vision, a recent thread of research is devoted to statistical models of assignment problems, in which the data are random weight graphs correlated with the latent permutation. In contrast to problems such as planted clique or stochastic block model, the major difference here is the lack of low-rank structures, which brings forth new challenges in both statistical analysis and algorithm design.   In the first half of the…

Matrix completion is the study of recovering an underlying matrix from a sparse subset of noisy observations. Traditionally, it is assumed that the entries of the matrix are “missing completely atrandom” (MCAR), i.e., each entry is revealed at random, independent of everything else, with uniform probability. This is likely unrealistic due to the presence of “latent confounders”, i.e., unobserved factors that determine both the entries of the underlying matrix and the missingness pattern in the observed matrix.  In general, these…