  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.
