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Tag: probabilistic pca

  • Automatic Relevance Determination for Probabilistic PCA

    In this note I flesh out the computations for Section 12.2.3 of Bishop’s Pattern Recognition and Machine Learning, where he uses automatic relevance to determine the dimensionality of the principal subspace in probabilistic PCA. The principal subspace describing the data is spanned by the columns $\ww_1, \dots, \ww_M$ of $\WW$. The proper Bayesian way to…

  • Maximum likelihood PCA

    These are my derivations of the maximum likelihood estimates of the parameters of probabilistic PCA as described in section 12.2.1 of Bishop, and with some hints from (Tipping and Bishop 1999). Once we have determined the maximum likelihood estimate of $\mu$ and plugged it in, we have (Bishop 12.44)$$ L = \ln p(X|W, \mu, \sigma^2)…