Classification via Minimum Incremental Coding Length (MICL)

We present a simple new criterion for classification, based on principles from lossy data compression. The criterion assigns a test sample to the class that uses the min- imum number of additional bits to code the test sample, subject to an allowable distortion. We prove asymptotic optimality of this criterion for Gaussian data and analyze its relationships to classical classifiers. Theoretical results provide new insights into relationships among popular classifiers such as MAP and RDA, as well as unsupervised clustering methods based on lossy compression [13]. Mini- mizing the lossy coding length induces a regularization effect which stabilizes the (implicit) density estimate in a small-sample setting.