Transformation Autoregressive Networks

The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods can be categorized into either using: a) autoregressive models to estimate the conditional factors of the chain rule, $p(x_{i}\, |\, x_{i-1}, \ldots)$; or b) non-linear transformations of variables of a simple base distribution. To better study the characteristics of these categories we propose multiple methods for each category. For example we propose RNN based transformations to model non-Markovian transformation of variables. Further, through a comprehensive study over both real world and synthetic data, we show for that jointly leveraging transformations of variables and autoregressive conditional models, results in a considerable improvement in performance. We illustrate the use of our models in outlier detection and image modeling. Finally we introduce a novel data driven framework for learning a family of distributions.