Bounded Rationality (Posts about autoregressive)

PixelCNN

Brian Keng — Mon, 22 Jul 2019 11:11:09 GMT

It's been a long time coming but I'm finally getting this post out! I read this paper a couple of years ago and wanted to really understand it because it was state of the art at the time (still pretty close even now). As usual though, once I started down the variational autoencoder line of posts, there was always yet another VAE paper to look into so I never got around to looking at this one.

This post is all about a proper probabilistic generative model called Pixel Convolutional Neural Networks or PixelCNN. It was originally proposed as a side contribution of Pixel Recurrent Neural Networks in [1] and later expanded upon in [2,3] (and I'm sure many other papers). The real cool thing about it is that it's (a) probabilistic, and (b) autoregressive. It's still counter-intuitive to me that you can generate images one pixel at at time, but I'm jumping ahead of myself here. We'll go over some background material, the method, and my painstaking attempts at an implementation (and what I learned from it). Let's get started!

Importance Sampling and Estimating Marginal Likelihood in Variational Autoencoders

Brian Keng — Wed, 06 Feb 2019 12:20:11 GMT

It took a while but I'm back! This post is kind of a digression (which seems to happen a lot) along my journey of learning more about probabilistic generative models. There's so much in ML that you can't help learning a lot of random things along the way. That's why it's interesting, right?

Today's topic is importance sampling. It's a really old idea that you may have learned in a statistics class (I didn't) but somehow is useful in deep learning, what's old is new right? How this is relevant to the discussion is that when we have a large latent variable model (e.g. a variational autoencoder), we want to be able to efficiently estimate the marginal likelihood given data. The marginal likelihood is kind of taken for granted in the experiments of some VAE papers when comparing different models. I was curious how it was actually computed and it took me down this rabbit hole. Turns out it's actually pretty interesting! As usual, I'll have a mix of background material, examples, math and code to build some intuition around this topic. Enjoy!

Variational Autoencoders with Inverse Autoregressive Flows

Brian Keng — Tue, 19 Dec 2017 13:47:38 GMT

In this post, I'm going to be describing a really cool idea about how to improve variational autoencoders using inverse autoregressive flows. The main idea is that we can generate more powerful posterior distributions compared to a more basic isotropic Gaussian by applying a series of invertible transformations. This, in theory, will allow your variational autoencoder to fit better by concentrating the stochastic samples around a closer approximation to the true posterior. The math works out so nicely while the results are kind of marginal 1. As usual, I'll go through some intuition, some math, and have an implementation with few experiments I ran. Enjoy!

Autoregressive Autoencoders

Brian Keng — Sat, 14 Oct 2017 14:02:15 GMT

You might think that I'd be bored with autoencoders by now but I still find them extremely interesting! In this post, I'm going to be explaining a cute little idea that I came across in the paper MADE: Masked Autoencoder for Distribution Estimation. Traditional autoencoders are great because they can perform unsupervised learning by mapping an input to a latent representation. However, one drawback is that they don't have a solid probabilistic basis (of course there are other variants of autoencoders that do, see previous posts here, here, and here). By using what the authors define as the autoregressive property, we can transform the traditional autoencoder approach into a fully probabilistic model with very little modification! As usual, I'll provide some intuition, math and an implementation.