Inverse Problem of Censored Markov Chain: Estimating Markov Chain Parameters from Censored Transition Data

Masahiro Kohjima, Takeshi Kurashima, Hiroyuki Toda

Abstract: Due to the difficulty of collecting comprehensive data sets (factors include limited GPS coverage and the existence of competitors), most transition data collected from, for example, people and automobiles, have been censored, and so record only the visits of known observable states (locations). In this paper, we tackle the problem of estimating Markov chain parameters from censored transition data. Our parameter estimation method utilizes the theory of the censored Markov chain, the Markov chain that has unobservable states. Our problem formulation can be seen as the inverse of existing studies that construct censored Markov chains from (original) Markov chains and unobservable states. We confirm the effectiveness of the proposal by experiments on synthetic and real data sets.