Blind Construction of Optimal Nonlinear Recursive Predictors for Discrete Sequences
This work addresses the challenge of predicting discrete sequences for applications in fields like time series analysis or data compression, though it appears incremental as it builds on existing hidden Markov model approaches.
The paper tackles the problem of nonlinear prediction of discrete random sequences with minimal structural assumptions by constructing optimal predictors as hidden Markov models and introducing the CSSR algorithm to approximate them from data. The method is shown to deliver results superior to variable-length Markov models and at least comparable to cross-validated hidden Markov models in simulations.
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.