Understand Fourier Transform of Images

We’ve covered Fourier Transform in [1] and [2] while we use only examples of 1D. In this post we are going to see what 2D Fourier Transform looks like. First, we look at a 2D image with one direction sinusoid waves (left) and its Fourier Transform (right). I added coordinates to help you understand the …

Revisit Gaussian kernel

This post is mainly about Gaussian kernel (aka radial basis function kernel), a commonly used technique in machine learning. We’ve touched the concept of Gaussian kernel in [1] and [2] but with less details.  Definition of Gaussian Kernel The intuitive understanding of a kernel is that it maps points in a data space, where those …

Optimization with discrete random variables

In this post, I’m going to talk about common techniques that enable us to optimize a loss function w.r.t. discrete random variables. I may go off on a tangent on various models (e.g., variational auto-encoder and reinforcement learning) because these techniques come from many different areas so please bear with me. We start from variational …