# Inference for machine learning under dependence

Recent interest has centered on uncertainty quantification for machine learning models. For the most part, this work has assumed independence of the observations. However, many of the most important problems arising across scientific fields, from genomics to climate science, involve systems where dependence cannot be ignored. In this talk, I will investigate inference on machine learning models in the presence of dependence.

In the first part of my talk, I will consider a common practice in the field of genomics in which researchers compute a correlation matrix between genes and threshold its elements in order to extract groups of independent genes. I will describe how to construct valid p-values associated with these discovered groups that properly account for the group selection process. While this is related to the literature on selective inference developed in the past decade, this work involves inference about the covariance matrix rather than the mean, and therefore requires an entirely new technical toolset. This same toolset can be applied to quantify the uncertainty associated with canonical correlation analysis after feature screening.

In the second part of my talk, I will turn to an important problem in the field of oceanography as it relates to climate science. Oceanographers have recently applied random forests to estimate carbon export production, a key quantity of interest, at a given location in the ocean; they then wish to sum the estimates across the world's oceans to obtain an estimate of global export production. While quantifying uncertainty associated with a single estimate is relatively straightforward, quantifying uncertainty of the summed estimates is not, due to their complex dependence structure. I will adapt the theory of V-statistics to this dependent data setting in order to establish a central limit theorem for the summed estimates, which can be used to quantify the uncertainty associated with global export production across the world's oceans.

This is joint work with my postdoctoral supervisors, Daniela Witten (University of Washington) and Jacob Bien (University of Southern California).