Noise Contrastive Estimation
Noise contrastive estimation (NCE) is a method to estimate high dimensional data distributions. It converts a generative learning problem to a discriminative learning one. Parameters of the distribution are learned by doing a classification between data and noise. In this post, we introduce NCE in detail, in the setting...
Automate Your Routines with Task Scheduler
If you are using the windows operating system, do you know you can use the Task Scheduler application to run tasks at specific time? In this post I will show you how to do this. We’ll also look at how to mute and unmute computer, play music, and open...
Visualizing the Double Dual
We provide a picture for visualizing the concept of double dual in linear algebra and functional analysis. We show that, every vector in a vector space $V$ naturally corresponds to a function that maps functionals on $V$ to numbers, namely evaluation of functionals on that vector. Conversely, thanks to...
Deformation Retractions are 「Continuous」 Retractions
In this post we discuss retractions and deformation retractions in algebraic topology. Positive as well as negative examples are presented to illustrate the two concepts.
Generative Models: from Noise to Data
In this post I give an introduction to several generative models in deep learning literature, including adversarial networks (GANs), variational autoencoder (VAE) and flow models. I also derive the formula for evaluating flow densities on generated samples.
Building a website with Jekyll and GitHub Pages
An overview of the Jekyll framework, instructions about hosting your website on GitHub Pages, and a comparison among different options for writing technical blogs.