Statistics and Data Science Seminar: Repro Samples Method for Addressing Irregular Inference Problems and for Unraveling Machine Learning Blackboxes

Co-sponsored by TRIADS

Abstract: Rapid data science developments and the desire to have interpretable AI require us to have innovative frameworks to tackle frequently seen, but highly non-trivial "irregular inference problems,’’ e.g., those in models involving discrete or non-numerical parameters and those involving non-numerical data, etc. This talk presents a novel, effective, and wide-reaching framework, called repro samples method, to conduct statistical inference for the irregular problems plus more.  We develop both theories to support our development and provide effective computing algorithms for problems in which explicit solutions are not available. The method is likelihood-free and is particularly effective for irregular inference problems. For commonly encountered irregular inference problems that involve discrete or nonnumerical parameters, we propose an effective three-step procedure to make inferences for all parameters and develop a unique matching scheme that turns the disadvantage of lacking theoretical tools to handle discrete/nonnumerical parameters into an advantage of improving computational efficiency.  The effectiveness of the proposed method is illustrated through case studies by solving two open problems in statistics: a) how to quantify the uncertainty in the estimation of the unknown number of components and make inference for the associated parameters in a normal mixture model; b) how to quantify the uncertainty in model estimation and construct confidence sets for the unknown true model, the regression coefficients, or both true model and coefficients jointly in high dimensional regression models. The method also has direct extensions to complex machine learning models, e.g., (ensemble) tree models, neural networks, graphical models, etc. It provides a new toolset to develop interpretable AI and to address the blackbox issues in complex machine learning models.

Bio: Min-ge Xie, PhD is a Distinguished Professor at Rutgers, The State University of New Jersey. He is the current Editor of The American Statistician and a co-founding Editor-in-Chief of The New England Journal of Statistics in Data Science. His research interests include theoretical foundations of statistical inference and data science, fusion learning, large sample theories, parametric and nonparametric methods. He also has served as the Director of the Rutgers Office of Statistical Consulting in the past 15 years. He is a fellow of ASA, IMS, and an elected member of ISI.

Host: Xuming He