Blind construction of optimal nonlinear recursive predictors for discrete sequences
Cosma Rohilla Shalizi, Kristina Lisa Shalizi · 2004
We present a new method for nonlinear predic-tion of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such pro-cesses, 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 re-liability of CSSR, its data requirements, and its performance in simulations. Finally, we compare our approach to existing methods using variable-length Markov models and cross-validated hid-den Markov models, and show theoretically and experimentally that our method delivers results superior to the former and at least comparable to the latter. 1