Model change detection with application to machine learning

Abstract: Model change detection is studied, in which there are two sets of samples that are independently and identically distributed (i.i.d.) according to a pre-change probabilistic model with parameter $\theta$, and a post-change model with parameter $\theta'$, respectively. The goal is to detect whether the change in the model is significant, i.e., whether the difference between the pre-change parameter and the post-change parameter $|\theta-\theta'|_2$ is larger than a pre-determined threshold $\rho$. The problem is considered in a Neyman-Pearson setting, where the goal is to maximize the probability of detection under a false alarm constraint. Since the generalized likelihood ratio test (GLRT) is difficult to compute in this problem, we construct an empirical difference test (EDT), which approximates the GLRT and has low computational complexity. Moreover, we provide an approximation method to set the threshold of the EDT to meet the false alarm constraint. Experiments with linear regression and logistic regression are conducted to validate the proposed algorithms.