2002/10/29 by Cosma Rohilla Shalizi, Shalizi, Cosma Rohilla, Kristina Lisa Shalizi +3 · 1 citation
Computer Science · #Algorithms and Data Compression #Blind Source Separation Techniques #Cellular Automata and Applications #Computation and Language (cs.CL) #E.4 #FOS: Computer and information sciences #H.1.1 #I.2.6 #Machine Learning (cs.LG) #cs.CL #cs.LG
paper · pdf · doi:10.48550/arxiv.cs/0210025
26 pages, 5 figures; 5 tables; http://www.santafe.edu/projects/CompMech Added discussion of algorithm parameters; improved treatment of convergence and time complexity; added comparison to older methods
openalex publication_date 2002/10/29 · arxiv created 2002/11/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new algorithm for discovering patterns in time series and other sequential data. We exhibit a reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior exhibited in the data -- the underlying process's causal states. Unlike conventional methods for fitting hidden Markov models (HMMs) to data, our algorithm makes no assumptions about the process's causal architecture (the number of hidden states and their transition structure), but rather infers it from the data. It starts with assumptions of minimal structure and introduces complexity only when the data demand it. Moreover, the causal states it infers have important predictive optimality properties that conventional HMM states lack. We introduce the algorithm, review the theory behind it, prove its asymptotic reliability, use large deviation theory to estimate its rate of convergence, and compare it to other algorithms which also construct HMMs from data. We also illustrate its behavior on an example process, and report selected numerical results from an implementation.