Floodgate: inference for model-free variable importance

by   Lu Zhang, et al.

Many modern applications seek to understand the relationship between an outcome variable Y and a covariate X in the presence of a (possibly high-dimensional) confounding variable Z. 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 (allowing, e.g., it to be fitted by a state-of-the-art machine learning algorithm or be 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.


POT-flavored estimator of Pickands dependence function

This work proposes an estimator with both Peak-Over-Threshold and Block-...

High-Dimensional Inference Based on the Leave-One-Covariate-Out LASSO Path

We propose a new measure of variable importance in high-dimensional regr...

A Stratification Approach to Partial Dependence for Codependent Variables

Model interpretability is important to machine learning practitioners, a...

Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach

We propose a model-free framework for sensitivity analysis of individual...

Optimal Sampling Density for Nonparametric Regression

We propose a novel active learning strategy for regression, which is mod...

Ecological Regression with Partial Identification

We study a partially identified linear contextual effects model for ecol...