Learning Markov chains with variable memory length from noisy output

Abstract

The problem of modeling complicated data sequences, such as DNA or speech, often arises in practice. Most of the algorithms select a hypothesis from within a model class assuming that the observed sequence is the direct output of the underlying generation process. In this paper we consider the case when the output passes through a memoryless noisy channel before observation. In particular, we show that in the class of Markov chains with variable memory length, learning is affected by factors, which, despite being super-polynomial, are still small in some practical cases. Markov models with variable memory length, or probabilistic finite suffix automata, were introduced in learning theory by Ron, Singer and Tishby who also described a polynomial time learning algorithm. We present a modification of the algorithm which uses a noise-corrupted sample and has knowledge of the noise structure. The same algorithm is still viable if the noise is not known exactly but a good estimation is available. Finally, some experimental results are presented for removing noise from corrupted English text, and to measure how the performance of the learning algorithm is affected by the size of the noisy sample and the noise rate.