Hidden Markov Models and Dynamical SystemsSIAM, 1 ian. 2008 - 144 pagini This text provides an introduction to hidden Markov models (HMMs) for the dynamical systems community. It is a valuable text for third or fourth year undergraduates studying engineering, mathematics, or science that includes work in probability, linear algebra and differential equations. The book presents algorithms for using HMMs, and it explains the derivation of those algorithms. It presents Kalman filtering as the extension to a continuous state space of a basic HMM algorithm. The book concludes with an application to biomedical signals. This text is distinctive for providing essential introductory material as well as presenting enough of the theory behind the basic algorithms so that the reader can use it as a guide to developing their own variants. |
Cuprins
Basic Algorithms | 19 |
Variants and Generalizations | 47 |
Performance Bounds and a Toy Problem | 73 |
Obstructive Sleep Apnea | 97 |
Formulas for Matrices and Gaussians | 117 |
Notation | 125 |
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Termeni și expresii frecvente
argmax backward algorithm Baum-Welch algorithm Bayes Bayesian calculate Chapter characterize component conditional distribution conditional probability conditionally independent convergence cross entropy decoded define denote derive described discrete dynamical systems eigenvalue EM algorithm entropy rate equations ergodic estimate extended Kalman filter Figure forecast formula forward algorithm function F Gibbs inequality given HMMs implement integrating inverse covariance iterations Kolmogorov-Sinai entropy laser linear log likelihood Lorenz system low pass heart Lyapunov exponent Markov model matrix maximize minutes model parameters noise terms normal notation observation models observation sequence observation y(t Obstructive Sleep Apnea oscillations partition pass heart rate plot probability density procedure Python quantization random variable records recursion reestimation relative entropy respiration sample Section sequence ending sequence of observations simulated step stochastic process training data trajectory values vector Viterbi algorithm µa(t μβ ΣΤ ᎧᎾ