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Lecture 6 CMS 165

Lecture 6 CMS 165. Spectral Methods: Tensor methods. Recap: PCA on Gaussian Mixtures. Can obtain span(A). But what about columns of A?. Learning Gaussian mixtures through clustering. Hidden Markov Models. Source: slides from Daniel Hsu. Discrete Hidden Markov Models.

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Lecture 6 CMS 165

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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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