Equivalent Definitions of the (Best) Lipschitz Constant
A quick note on the equivalent (dual?) definitions of the Lipschitz constant.
VAE learning on MNIST using Keras.
Projections of Probability Distributions and the Reparameterization Trick
A brief review of M-projection, I-projection, REINFORCE, and the Reparameterization Trick.
Restricted Boltzmann Machine and Contrastive Divergence
RBM training with CD from scratch on MNIST data.
Linear Regression as Conditional Random Field
Classical linear regression simply uses a linear Gaussian model (CRF).
Gibbs Sampling in Pairwise Markov Networks
Discrete pairwise Markov networks are pretty straightforward to work with analytically. Let's use the canonical overcomplete representation, where the sufficient statistics functions are indicator functions …
Kernel => RKHS + Feature Map
Given a kernel function, find the Reproducing Kernel Hilbert Space and the feature map it defines.
Separating Hyerplane Example
What it takes to separate an affine and a convex set.
A relative notion of set interior.
Geometric Interpretations of First-Order Taylor Approximation
Geometric views from the output space, input space, and graph space.
Joint vs. Marginal Expectation
They're pretty much the same.
Polar Decomposition Example
A small numeric example illustrating polar decomposition.
Eigendecomposition as Change of Basis
An operator has a particularly simple matrix description in its eigenbasis.
Change of Basis
How to encode a linear operator in a different matrix.
The Matrix of a Linear Map
Matrices are descriptions of linear maps.
Example of a Polynomial Basis
Example basis of a function space.