An Algorithm for Pattern Discovery in Time Series

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dc.creatorShalizi, Cosma Rohilla
dc.creatorShalizi, Kristina Lisa
dc.creatorCrutchfield, James P.
dc.date2002-10-29
dc.date2002-11-27
dc.date.accessioned2026-07-07T03:18:57Z
dc.date.available2026-07-07T03:18:57Z
dc.descriptionWe 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.
dc.description26 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
dc.identifierhttps://arxiv.org/abs/cs/0210025
dc.identifierhttp://arxiv.org/abs/cs/0210025
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/31324
dc.subjectMachine Learning
dc.subjectComputation and Language
dc.subjectI.2.6;H.1.1;E.4
dc.titleAn Algorithm for Pattern Discovery in Time Series
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