Conformal test martingales for hypergraphical models

Abstract

In this work, we study applications of the Conformal Prediction machine learning framework to the questions of statistical data testing. This technique is also known as Conformal Test Martingales. Earlier works on this topic used it to detect deviations from exchangeability assumptions (such as change points). Here we move to test popular hypergraphical models. We adopt and compare two versions of Conformal Testing Martingales. First: testing the data against exchangeability assumption, but using the elements of hypergraphical model for setting its parameters. Second: combining Conformal Testing Martingale with Hypergraphical On-Line Compression Models. The latter is an extension of the Conformal Prediction technique beyond exchangeability.

We show how these approaches help to accelerate the detection of data deviation from i.i.d. by making use of the knowledge about relations between the features embedded into a hypergraphical model.