What is the difference between ZCA whitening and PCA whitening?
Let your (centered) data be stored in a $n\times d$ matrix $\mathbf X$ with $d$ features (variables) in columns and $n$ data points in rows. Let the covariance matrix $\mathbf C=\mathbf X^\top \mathbf X/n$ have eigenvectors in columns of $\mathbf E$ and eigenvalues on the diagonal of $\mathbf D$, so that $\mathbf C = \mathbf E \mathbf D \mathbf E^\top$. Then what you call "normal" PCA whitening tr
Python as a statistics workbench
Lots of people use a main tool like Excel or another spreadsheet, SPSS, Stata, or R for their statistics needs. They might turn to some specific package for very special needs, but a lot of things can be done with a simple spreadsheet or a general stats package or stats programming environment. I've always liked Python as a programming language, and for simple needs, it's easy to write a short pro
PyMC for nonparametric clustering: Dirichlet process to estimate Gaussian mixture's parameters fails to cluster
Problem setup One of the first toy problems I wanted to apply PyMC to is nonparametric clustering: given some data, model it as a Gaussian mixture, and learn the number of clusters and each cluster's mean and covariance. Most of what I know about this method comes from video lectures by Michael Jordan and Yee Whye Teh, circa 2007 (before sparsity became the rage), and the last couple of days' read
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Why do we use Gaussian distributions in Variational Autoencoder?
What causes the elbow shape of the loss curve?
How to generate the posterior predictive distribution for hierarchal model in PYMC3
Posterior Predictive Check (PPC) for a Bayesian linear regression model: Edward's result is pretty different from PyMC3's?
Binary version of Probabilistic Matrix Factorization in pymc?
Scatterplot with contour/heat overlay