Stochastics and Statistics Seminar

Abstract: When we run a complex algorithm on real data, it is standard to use a holdout set, or a cross-validation strategy, to evaluate its behavior and performance. When we do so, are we learning information about the algorithm itself, or only about the particular fitted model(s) that this particular data set produced? In this talk, we will establish fundamental hardness results on the problem of empirically evaluating properties of a black-box algorithm, such as its stability and its average…

Abstract:  In statistical inference problems, we are typically given a limited number of samples from some underlying distribution, and we wish to estimate some property of that distribution, under a given measure of risk. We are usually interested in characterizing and achieving the best possible risk as a function of the number of available samples. Thus, it is often implicitly assumed that samples are co-located, and that communication bandwidth as well as computational power are not a bottleneck, essentially making the number…

Abstract:  We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. By integrating concepts and tools from cross-validation and differential privacy, we develop a test statistic that is asymptotically normal even in high-dimensional settings, and allows for arbitrarily many ties in the population mean vector. The key technical ingredient is a central limit theorem for globally dependent data characterized…