Mixed Membership Models for Time Series
نویسندگان
چکیده
20.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 20.1.1 State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 20.1.2 Latent Dirichlet Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 20.1.3 Bayesian Nonparametric Mixed Membership Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 Hierarchical Dirichlet Process Topic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 Beta-Bernoulli Process Topic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 20.2 Mixed Membership in Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 20.2.1 Markov Switching Processes as a Mixed Membership Model . . . . . . . . . . . . . . . . . . . . . . . . 426 Hidden Markov Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 Switching VAR Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 20.2.2 Hierarchical Dirichlet Process HMMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 20.2.3 A Collection of Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 20.3 Related Bayesian and Bayesian Nonparametric Time Series Models . . . . . . . . . . . . . . . . . . . . . . . . . 434 20.3.1 Non-Homogeneous Mixed Membership Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Time-Varying Topic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Time-Dependent Bayesian Nonparametric Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 20.3.2 Hidden-Markov-Based Bayesian Nonparametric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 20.3.3 Bayesian Mixtures of Autoregressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 20.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
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