Sparse Markov Models for High-Dimensional Inference

Consider a sample of size n of a finite order Markov chain. In this full generality, we can only estimate the parameters of the Markov chain (the order d and the transition probabilities) in the regime d=O(log (n)), limiting the practical application of these chains to small orders only. In this talk, we will discuss a way to overcome this constraint in a large subclass of Markov chains, namely  the Mixture of Transition Distribution (MTD) models. In our main result, we will show that it is possible to select a priori the portion of the past that is relevant for the transition probabilities of a MTD, allowing the estimation of the model parameters even in the regime d=O(n). The practical performance of our estimation procedure will be illustrated through simulations.

This is a joint work with Daniel Y. Takahashi (Brain Institute/UFRN).