Jun Liu is a Professor of Statistics at Harvard University. For more information and for a list of publications and research interests, visit Liu's webpage.
Title: "Detecting Relationships Via Slicing and Inverse Modeling"
Abstract: I will discuss a few recent results from my group exploring the utility of inverse modeling in detecting nonlinear relationships. Our investigations bring together ideas from the naive Bayes modeling, Fisher’s linear discriminant analysis, and the sliced inverse regression for dimension reductions. These ideas center around the strategies related to ``slicing” (aka, discretization) of the response variable. In one direction, we optimally slice one variable (or the response) to maximize a score function based on the likelihood‐ratio statistic. Our test statistic, called generalized R‐square or G2, gives rise to a relationship measure taking values in [0,1] and can be viewed as a direct extension of the standard R‐square. We can also fully "Bayesianize" the procedure to arrive at a Bayesian version of G2. The G2 statistic is compared with some popular measures such as Distance Correlation, Pearson Correlation, Maximal Information Criterion, etc., on many simulated examples, and found superior for detecting highly nonlinear and non‐smooth relationships. We will also discuss some theoretical properties of sliced inverse regression in high dimensions.