Neural Autoregressive Flows

by   Chin-Wei Huang, et al.

Normalizing flows and autoregressive models have been successfully combined to produce state-of-the-art results in density estimation, via Masked Autoregressive Flows (MAF), and to accelerate state-of-the-art WaveNet-based speech synthesis to 20x faster than real-time, via Inverse Autoregressive Flows (IAF). We unify and generalize these approaches, replacing the (conditionally) affine univariate transformations of MAF/IAF with a more general class of invertible univariate transformations expressed as monotonic neural networks. We demonstrate that the proposed neural autoregressive flows (NAF) are universal approximators for continuous probability distributions, and their greater expressivity allows them to better capture multimodal target distributions. Experimentally, NAF yields state-of-the-art performance on a suite of density estimation tasks and outperforms IAF in variational autoencoders trained on binarized MNIST.


page 2

page 7


Unconstrained Monotonic Neural Networks

Monotonic neural networks have recently been proposed as a way to define...

LogitBoost autoregressive networks

Multivariate binary distributions can be decomposed into products of uni...

Gaussianization Flows

Iterative Gaussianization is a fixed-point iteration procedure that can ...

HCNAF: Hyper-Conditioned Neural Autoregressive Flow and its Application for Probabilistic Occupancy Map Forecasting

We introduce Hyper-Conditioned Neural Autoregressive Flow (HCNAF); a pow...

Autoregressive Quantile Flows for Predictive Uncertainty Estimation

Numerous applications of machine learning involve predicting flexible pr...

Sum-of-Squares Polynomial Flow

Triangular map is a recent construct in probability theory that allows o...

AUTM Flow: Atomic Unrestricted Time Machine for Monotonic Normalizing Flows

Nonlinear monotone transformations are used extensively in normalizing f...