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Spectral Methods Recap: Applications in Gaussian Mixture Models & Hidden Markov Models

Learn about extending Hidden Markov Models, Gaussian mixtures through clustering, and applications of spectral methods. Explore Partially Observed Markov Decision Processes and Predictive State Representations. Discover stochastic bandits in a low-rank subspace.

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Spectral Methods Recap: Applications in Gaussian Mixture Models & Hidden Markov Models

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  1. Lecture 6 CMS 165 Spectral Methods: Tensor methods

  2. Recap: PCA on Gaussian Mixtures Can obtain span(A). But what about columns of A?

  3. Learning Gaussian mixtures through clustering

  4. Hidden Markov Models Source: slides from Daniel Hsu

  5. Discrete Hidden Markov Models

  6. Lots of other applications of spectral methods • Extending HMMs to Partially observed Markov decision processes (POMDP) and Predictive state representations (PSR): passive vs active. • POMDP: Action based on each observation and can influence Markovian evolution of hidden state • PSR: No explicit Markovian assumption on hidden state. Directly predicts future (tests) based on past observations and actions (For linear PSR, similar to spectral updates in HMM) • Stochastic bandits in a low rank subspace (ask TA Sahin about it)

  7. References • Monograph on spectral learning on matrices and tensors (preprint available on Piazza) • Slides from MLSS: available on http://tensorlab.cms.caltech.edu/users/anima/

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