Seminar on Statistics and Data Science

Many modern statistical procedures are randomized in the sense that the output is a random function of data. For example, many procedures employ data splitting, which randomly divides the dataset into disjoint parts for separate purposes. Despite their flexibility and popularity, data splitting and other constructions of randomized procedures have obvious drawbacks. First, two analyses of the same dataset may lead to different results due to the extra randomness introduced. Second, randomized procedures typically lose statistical power because the entire sample is not fully utilized. \[ \] To address these drawbacks, in this talk, I will study how to properly combine the results from multiple realizations (such as through multiple data splits) of a randomized procedure. I will introduce rank-transformed subsampling as a general method for delivering large sample inference of the combined result under minimal assumptions. I will illustrate the method with three applications: (1) a “hunt-and-test” procedure for detecting cancer subtypes using high-dimensional gene expression data, (2) testing the hypothesis of no direct effect in a sequentially randomized trial and (3) calibrating cross-fit “double machine learning” confidence intervals. For these problems, our method is able to derandomize and improve power. Moreover, in contrast to existing approaches for combining p-values, our method enjoys type-I error control that asymptotically approaches the nominal level. This new development opens up the possibility of designing procedures that explicitly randomize and derandomize: extra randomness is introduced to make the problem easier before being marginalized out. \[ \] This talk is based on joint work with Prof. Rajen Shah. \[ \] Bio: Richard Guo is a research associate in the Statistical Laboratory at the University of Cambridge, mentored by Prof. Rajen Shah. Previously, he was the Richard M. Karp Research Fellow in the 2022 causality program at the Simons Institute for the Theory of Computing. He received his PhD in Statistics from University of Washington in 2021, advised by Thomas Richardson. His research interests include graphical models, causal inference, semiparametric methods and replicability of data analysis. Dr. Guo will start as a tenure-track assistant professor in Biostatistics at the University of Washington in 2024.

Many datasets for modern machine learning consist of high dimensional observations that are generated from some low dimensional latent variables. While recent advances in deep learning allow us to sample from distributions of almost arbitrary complexity, the recovery of the ground truth latent variable is still challenging even in simple settings. We study this problem through the lens of identifiability, i.e., when can we, at least theoretically, hope to recover the latent structure up to certain symmetries? We will present a general identifiability result for interventional data and a contrastive algorithm to find the latent variables. In the second part, we study the robustness of identifiability results to misspecification as one challenge for practical applications of representation learning. This talk is based on joined work with Goutham Rajendran, Elan Rosenfeld, Bryon Aragam, Bernhard Schölkopf, and Pradeep Ravikumar. Bio: Simon Buchholz received his PhD in mathematics from the University of Bonn where he was advised by Stefan Mueller. Currently he is a Postdoctoral Researcher with Bernhard Schölkopf in the department for Empirical Inference at the Max Planck Institute for Intelligent Systems in Tübingen where he works on problems in causal representation learning.