The Statistics Seminar speaker for Wednesday, April 21, 2021, is Lucas Janson. Janson is an assistant professor in the department of statistics and an affiliate in computer science at Harvard University. He works on high-dimensional inference and statistical machine learning, and recently received the NSF CAREER Award. Dr. Janson received his Ph.D. in statistics from Stanford University in 2017 and was advised by Emmanuel Candès.
Talk: Floodgate: inference for model-free variable importance
Zoom details will be shared via email
Abstract: Many modern applications seek to understand the relationship between an outcome variable Y and a covariate X in the presence of confounding variables Z = (Z_1,...,Z_p). Although much attention has been paid to testing whether Y depends on X given Z, in this paper we seek to go beyond testing by inferring the strength of that dependence. We first define our estimand, the minimum mean squared error (mMSE) gap, which quantifies the conditional relationship between Y and X in a way that is deterministic, model-free, interpretable, and sensitive to nonlinearities and interactions. We then propose a new inferential approach called floodgate that can leverage any regression function chosen by the user (including those fitted by state-of-the-art machine learning algorithms or derived from qualitative domain knowledge) to construct asymptotic confidence bounds, and we apply it to the mMSE gap. In addition to proving floodgate’s asymptotic validity, we rigorously quantify its accuracy (distance from confidence bound to estimand) and robustness. We demonstrate floodgate’s performance in a series of simulations and apply it to data from the UK Biobank to infer the strengths of dependence of platelet count on various groups of genetic mutations. This is joint work with my PhD student Lu Zhang, and the associated paper can be found at https://arxiv.org/abs/2007.01283.