Plug-in martingales for testing exchangeability on-line

TL;DR

This paper introduces a new method for online testing of data exchangeability using martingales, which is more flexible and effective on complex datasets than existing techniques.

Contribution

The paper extends existing exchangeability martingale techniques and demonstrates their effectiveness in online testing scenarios, especially on challenging datasets.

Findings

The new method performs well on USPS dataset.

It outperforms previous techniques on Statlog Satellite data.

Existing methods are sufficient for simple datasets but less effective on complex data.

Abstract

A standard assumption in machine learning is the exchangeability of data, which is equivalent to assuming that the examples are generated from the same probability distribution independently. This paper is devoted to testing the assumption of exchangeability on-line: the examples arrive one by one, and after receiving each example we would like to have a valid measure of the degree to which the assumption of exchangeability has been falsified. Such measures are provided by exchangeability martingales. We extend known techniques for constructing exchangeability martingales and show that our new method is competitive with the martingales introduced before. Finally we investigate the performance of our testing method on two benchmark datasets, USPS and Statlog Satellite data; for the former, the known techniques give satisfactory results, but for the latter our new more flexible method becomes necessary.