Normalizing Flows Tutorial, Part 1: Distributions and Determinants

If you are a machine learning practitioner working on generative modeling, Bayesian deep learning, or deep reinforcement learning, normalizing flows are a handy technique to have in your algorithmic toolkit. Normalizing flows transform simple densities (like Gaussians) into rich complex distributions that can be used for generative models, RL, and variational inference. TensorFlow has a nice set of functions that make it easy to build flows and train them to suit real-world data. This tutorial comes in two parts: Part 1: Distributions and Determinants. In this post, I explain how invertible transformations of densities can be used to implement more complex densities, and how these transformations can be chained together to form a "normalizing flow". Part 2: Modern Normalizing Flows: In a follow-up post, I survey recent techniques developed by researchers to learn normalizing flows, and explain how a slew of modern generative modeling techniques -- autoregressive models, MAF, IAF, NICE, Real-NVP, Parallel-Wavenet -- are all related to each other. This series is written for an audience with a rudimentary understanding of linear algebra, probability, neural networks, and TensorFlow. Knowledge of recent advances in Deep Learning, generative models will be helpful in understanding the motivations and context underlying these techniques, but they are not necessary.