Archive for the ‘Supplementary Math’ Category

Formulating the PCA

Today I have thought about how one can formulate the Principal Component Analysis (PCA) method. In particular I want to reformulate PCA as a solution for a regression problem. The idea of reformulation PCA as a solution for some regression problem is useful in Sparse PCA , in which a L_1 regularization term is inserted into a ridge regression formula to enforce spareness of the coefficients (i.e. elastic net). There are at least two equivalent ways to motivate PCA. In this post I will first give a formulation of PCA based on orthogonal projection, and then discuss a regression-type reformulation of PCA.

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Nonparametric Bayesian Seminar 1 : Notes

(mục đích chính là viết ra để khỏi quên nên sẽ  lộn xộn. Không có hình vẽ)

Paper: Introduction to Nonparametric Bayesian Models (Naonori Ueda, Takeshi Yamada)

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Bounding probability of an event

1.

– If  A \Rightarrow B then Pr(A) \leq Pr(B).

– If A \Rightarrow B and A \Rightarrow C then Pr(A) \leq \frac{1}{2}(Pr(B) +Pr(C)).

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