Bounded Rationality (Posts about autoencoders)

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!

Residual Networks

Brian Keng — Sun, 18 Feb 2018 18:55:13 GMT

Taking a small break from some of the heavier math, I thought I'd write a post (aka learn more about) a very popular neural network architecture called Residual Networks aka ResNet. This architecture is being very widely used because it's so simple yet so powerful at the same time. The architecture's performance is due its ability to add hundreds of layers (talk about deep learning!) without degrading performance or adding difficulty to training. I really like these types of robust advances where it doesn't require fiddling with all sorts of hyper-parameters to make it work. Anyways, I'll introduce the idea and show an implementation of ResNet on a few runs of a variational autoencoder that I put together on the CIFAR10 dataset.

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.

Semi-supervised Learning with Variational Autoencoders

Brian Keng — Mon, 11 Sep 2017 12:40:47 GMT

In this post, I'll be continuing on this variational autoencoder (VAE) line of exploration (previous posts: here and here) by writing about how to use variational autoencoders to do semi-supervised learning. In particular, I'll be explaining the technique used in "Semi-supervised Learning with Deep Generative Models" by Kingma et al. I'll be digging into the math (hopefully being more explicit than the paper), giving a bit more background on the variational lower bound, as well as my usual attempt at giving some more intuition. I've also put some notebooks on Github that compare the VAE methods with others such as PCA, CNNs, and pre-trained models. Enjoy!

A Variational Autoencoder on the SVHN dataset

Brian Keng — Thu, 13 Jul 2017 12:13:03 GMT

In this post, I'm going to share some notes on implementing a variational autoencoder (VAE) on the Street View House Numbers (SVHN) dataset. My last post on variational autoencoders showed a simple example on the MNIST dataset but because it was so simple I thought I might have missed some of the subtler points of VAEs -- boy was I right! The fact that I'm not really a computer vision guy nor a deep learning guy didn't help either. Through this exercise, I picked up some of the basics in the "craft" of computer vision/deep learning area; there are a lot of subtle points that are easy to gloss over if you're just reading someone else's tutorial. I'll share with you some of the details in the math (that I initially got wrong) and also some of the implementation notes along with a notebook that I used to train the VAE. Please check out my previous post on variational autoencoders to get some background.

Update 2017-08-09: I actually found a bug in my original code where I was only using a small subset of the data! I fixed it up in the notebooks and I've added some inline comments below to say what I've changed. For the most part, things have stayed the same but the generated images are a bit blurry because the dataset isn't so easy anymore.

Variational Autoencoders

Brian Keng — Tue, 30 May 2017 12:19:36 GMT

This post is going to talk about an incredibly interesting unsupervised learning method in machine learning called variational autoencoders. It's main claim to fame is in building generative models of complex distributions like handwritten digits, faces, and image segments among others. The really cool thing about this topic is that it has firm roots in probability but uses a function approximator (i.e. neural networks) to approximate an otherwise intractable problem. As usual, I'll try to start with some background and motivation, include a healthy does of math, and along the way try to convey some of the intuition of why it works. I've also annotated a basic example so you can see how the math relates to an actual implementation. I based much of this post on Carl Doersch's tutorial, which has a great explanation on this whole topic, so make sure you check that out too.