The Document as an Ergodic Markov Chain

Abstract

In recent years, statistical language models are being proposed as alternative to the vector space model. Viewing documents as language samples introduces the issue of defining a joint probability distribution over the terms. The present paper models a document as the result of a Markov process. It argues that this process is ergodic, which is theoretically plausible, and easy to verify in practice. The theoretical result is that the joint distribution can be easily obtained. This can also be applied for search resolutions other than the document level. We verified this in an experiment on query expansion demonstrating both the validity and the practicability of the method. This holds a promise for general language models.