$$ \newcommand{\dint}{\mathrm{d}} \newcommand{\vphi}{\boldsymbol{\phi}} \newcommand{\vpi}{\boldsymbol{\pi}} \newcommand{\vpsi}{\boldsymbol{\psi}} \newcommand{\vomg}{\boldsymbol{\omega}} \newcommand{\vsigma}{\boldsymbol{\sigma}} \newcommand{\vzeta}{\boldsymbol{\zeta}} \renewcommand{\vx}{\mathbf{x}} \renewcommand{\vy}{\mathbf{y}} \renewcommand{\vz}{\mathbf{z}} \renewcommand{\vh}{\mathbf{h}} \renewcommand{\b}{\mathbf} \renewcommand{\vec}{\mathrm{vec}} \newcommand{\vecemph}{\mathrm{vec}} \newcommand{\mvn}{\mathcal{MN}} \newcommand{\G}{\mathcal{G}} \newcommand{\M}{\mathcal{M}} \newcommand{\N}{\mathcal{N}} \newcommand{\S}{\mathcal{S}} \newcommand{\I}{\mathcal{I}} \newcommand{\diag}[1]{\mathrm{diag}(#1)} \newcommand{\diagemph}[1]{\mathrm{diag}(#1)} \newcommand{\tr}[1]{\text{tr}(#1)} \renewcommand{\C}{\mathbb{C}} \renewcommand{\R}{\mathbb{R}} \renewcommand{\E}{\mathbb{E}} \newcommand{\D}{\mathcal{D}} \newcommand{\inner}[1]{\langle #1 \rangle} \newcommand{\innerbig}[1]{\left \langle #1 \right \rangle} \newcommand{\abs}[1]{\lvert #1 \rvert} \newcommand{\norm}[1]{\lVert #1 \rVert} \newcommand{\two}{\mathrm{II}} \newcommand{\GL}{\mathrm{GL}} \newcommand{\Id}{\mathrm{Id}} \newcommand{\grad}[1]{\mathrm{grad} \, #1} \newcommand{\gradat}[2]{\mathrm{grad} \, #1 \, \vert_{#2}} \newcommand{\Hess}[1]{\mathrm{Hess} \, #1} \newcommand{\T}{\text{T}} \newcommand{\dim}[1]{\mathrm{dim} \, #1} \newcommand{\partder}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\rank}[1]{\mathrm{rank} \, #1} \newcommand{\inv}1 \newcommand{\map}{\text{MAP}} \newcommand{\L}{\mathcal{L}} \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator*{\argmin}{arg\,min} $$

Minkowski's, Dirichlet's, and Two Squares Theorem

Application of Minkowski's Theorem in geometry problems, Dirichlet's Approximation Theorem, and Two Squares Theorem.

Posted on July 24, 2018

Reduced Betti number of sphere: Mayer-Vietoris Theorem

A proof of reduced homology of sphere with Mayer-Vietoris sequence.

Posted on July 23, 2018

Brouwer's Fixed Point Theorem: A Proof with Reduced Homology

A proof of special case (ball) of Brouwer's Fixed Point Theorem with Reduced Homology.

Posted on July 18, 2018

Natural Gradient Descent

Intuition and derivation of natural gradient descent.

Posted on March 14, 2018

Fisher Information Matrix

An introduction and intuition of Fisher Information Matrix.

Posted on March 11, 2018

Introduction to Annealed Importance Sampling

An introduction and implementation of Annealed Importance Sampling (AIS).

Posted on December 23, 2017

Gibbs Sampler for LDA

Implementation of Gibbs Sampler for the inference of Latent Dirichlet Allocation (LDA)

Posted on September 7, 2017

Boundary Seeking GAN

Training GAN by moving the generated samples to the decision boundary.

Posted on March 7, 2017

Least Squares GAN

2017 is the year GAN loss its logarithm. First, it was Wasserstein GAN, and now, it's LSGAN's turn.

Posted on March 2, 2017

CoGAN: Learning joint distribution with GAN

Original GAN and Conditional GAN are for learning marginal and conditional distribution of data respectively. But how can we extend them to learn joint distribution instead?

Posted on February 18, 2017