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hi, i'm matthew

and I'm interested in everything.

Written by Matthew Russell who follows Jesus, studies machine learning at the University of Kentucky, and interns at NASA. Get to know him or check out his projects on GitHub.

Disentangling VAEs, KL Divergence, and Mutual Information

September 24, 2020
#probability#math#machine-learning#jointvae

I’ve recently been reading about the JointVAE model proposed by Emilien Dupont in the paper Learning Disentangled Joint Continuous and Discrete Representations. The paper builds on the development of variational autoencoders (VAEs). As a quick overview, autoencoders are neural networks that take an input, generate some “secret” representation of it, then try to use that “secret” code to reconstruct the input. If it can do that well, then we have found a secret code that summarizes the important…

Markov Chain Monte Carlo Sampling

September 23, 2020
#probability#math

One of my courses recently introduced Markov Chain Monte Carlo (MCMC) sampling, which has a lot of applications. I’d like to dive into those applications in a future post, but for now let’s take a quick look at Metropolis-Hastings MCMC. A Brief Prologue Let’s say we have a probability distribution function (within a mulplicative constant) that is very complex. We have an equation, but maybe it is impossible to integrate. Somehow, we’d like to draw samples from this distribution to estimate…

Belief Propagation

September 16, 2020
#probability#math

Let’s say that you and I are roommates, and I notice you’ve been gone the last two Friday nights. This is not necessarily unusual, and sometimes your Friday night excursion is a date. However, you don’t communicate well, so I have no idea if you had a date or not. As you prepare to go out for the third Friday in a row, I wonder if this Friday you have a date. You won’t spill the beans, but I have a mind-reading superpower — *pause for dramatic effect* — math 🔥. I make an educated guess that if…