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Recitation 10/8
Mixture Models, PCA
Slides borrowed from Prof. Seyoung Kim, Ryan Tibshirani. Thanks!
Law of Total Probability
Recitation 10/8 Mixture Models, PCA Slides borrowed from Prof. - - PowerPoint PPT Presentation
Recitation 10/8 Mixture Models, PCA Slides borrowed from Prof. - - PowerPoint PPT Presentation
Recitation 10/8 Mixture Models, PCA Slides borrowed from Prof. Seyoung Kim, Ryan Tibshirani. Thanks! Law of Total Probability Completely Observed Data Bishop Page 431 Since z uses a 1-of-K representation, we have What if we do not know
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Since z uses a 1-of-K representation, we have
Completely Observed Data
Bishop Page 431
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What if we do not know ?
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Example 2-d data points coming from K = 2 Gaussian distributions
K=2 1-d Gaussian distributions: <x, y> pairs
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Example 2-d data points coming from K = 2 Gaussian distributions
K=2 1-d Gaussian distributions: <x, y> pairs
Initialize
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Example 2-d data points coming from K = 2 Gaussian distributions
Initialize iteration t =1
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Example 2-d data points coming from K = 2 Gaussian distributions
Initialize iteration t =1 2 4 7 0.953 0.047
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Example 2-d data points coming from K = 2 Gaussian distributions
Initialize iteration t =1 2 4 7 0.953 0.047
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PCA
Principal components are a sequence of projections of the data, mutually uncorrelated and ordered in variance.
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Assume X is a normalized Nxp data matrix for N samples and p features Assume data is normalized. ⇐> each column of X is normalized. Variance of projected data where S = <- Want to maximize this over v
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The proportion of variance explained is a nice way to quantify how much structure is being captured