  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: \textit{a})
autoregressive models to estimate the conditional factors of the chain rule,
$p(x_{i}\, |\, x_{i-1}, \ldots)$; or \textit{b}) non-linear transformations of
variables of a simple base distribution. Based on the study of the
characteristics of these categories, we propose multiple novel methods for each
category. For example we proposed RNN based transformations to model
non-Markovian dependencies. 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.

Machine Learning