Significance tests of feature relevance for a black-box learner

Abstract

An exciting recent development is the uptake of deep learning in many scientific fields, where the objective is seeking novel scientific insights and discoveries. To interpret a learning outcome, researchers perform hypothesis testing for explainable features to advance scientific domain knowledge. In such a situation, testing for a blackbox learner poses a severe challenge because of intractable models, unknown limiting distributions of parameter estimates, and high computational constraints. In this article, we derive two consistent tests for the feature relevance of a blackbox learner. The first one evaluates a loss difference with perturbation on an inference sample, which is independent of an estimation sample used for parameter estimation in model fitting. The second further splits the inference sample into two but does not require data perturbation. Also, we develop their combined versions by aggregating the order statistics of the p-values based on repeated sample splitting. To estimate the splitting ratio and the perturbation size, we develop adaptive splitting schemes for suitably controlling the Type I error subject to computational constraints. By deflating the bias-sd-ratio, we establish asymptotic null distributions of the test statistics and their consistency in terms of statistical power. Our theoretical power analysis and simulations indicate that the one-split test is more powerful than the two-split test, though the latter is easier to apply for large datasets. Moreover, the combined tests are more stable while compensating for a power loss by repeated sample splitting. Numerically, we demonstrate the utility of the proposed tests on two benchmark examples. Accompanying this paper is our Python library dnn-inference (https://dnn-inference.readthedocs. io/en/latest/) that implements the proposed tests.

Local permutation tests for conditional independence

“…In these applications, the assumption of conditional independence offers significant representational and computational benefits, and helps disentangle causal relationships among variables in an efficient and tractable way. In a related vein, a problem of essential importance in statistical practice is that of variable selection (Dai et al, 2021;Williamson et al, 2021), which is concerned with selecting a parsimonious subset of features that are predictive of a response variable. In each of these settings, conditional independence tests are an essential tool to validate (or invalidate) critical modeling assumptions, and can lend additional credibility to the conclusions of our data analysis.…”