Significance tests of feature relevance for a black-box learner

Dr. Ben Dai an Assistant Professor in the Department of Statistics at The Chinese University of Hong Kong. His primary research interests include statistical consistency, theory-driven machine learning methods, theoretical foundation of machine learning, black-box significance testing, statistical computing and software development.

An exciting recent development is the uptake of deep neural networks in many scientific fields, where the main objective is outcome prediction with a black-box nature.  Significance testing is promising to address the black-box issue and  explore novel scientific insights and interpretations of the  decision-making process based on a deep learning model. However, testing for a neural network poses a challenge because of its black-box nature  and unknown limiting distributions of parameter estimates while existing methods require strong assumptions or excessive computation. In this  article, we derive one-split and two-split tests relaxing the  assumptions and computational complexity of existing black-box tests and extending to examine the significance of a collection of features of  interest in a dataset of possibly a complex type, such as an image. The  one-split test estimates and evaluates a black-box model based on  estimation and inference subsets through sample splitting and data  perturbation. The two-split test further splits the inference subset  into two but requires no perturbation. Also, we develop their combined  versions by aggregating the p -values based on repeated sample  splitting. By deflating the bias-sd-ratio, we establish asymptotic null  distributions of the test statistics and the consistency in terms of  Type 2 error. Numerically, we demonstrate the utility of the proposed  tests on seven simulated examples and six real datasets. Accompanying  this article is our python library dnn-inference  (https://dnn-inference.readthedocs.io/en/latest/) that implements the  proposed tests.