Blind Construction of Optimal Nonlinear Recursive Predictors for Discrete Sequences

TL;DR

This paper introduces CSSR, an algorithm for constructing optimal nonlinear predictors of discrete sequences using hidden Markov models, demonstrating superior or comparable performance to existing methods.

Contribution

The paper presents a new method and algorithm for optimal nonlinear prediction of discrete sequences, with theoretical guarantees and empirical validation.

Findings

CSSR effectively reconstructs predictors from data.

The method outperforms variable-length Markov models.

CSSR achieves comparable results to hidden Markov models.

Abstract

We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then describe an algorithm, CSSR (Causal-State Splitting Reconstruction), which approximates the ideal predictor from data. We discuss the reliability of CSSR, its data requirements, and its performance in simulations. Finally, we compare our approach to existing methods using variablelength Markov models and cross-validated hidden Markov models, and show theoretically and experimentally that our method delivers results superior to the former and at least comparable to the latter.