  Understanding the dependencies among features of a dataset is at the core of
most unsupervised learning tasks. However, a majority of generative modeling
approaches are focused solely on the joint distribution $p(x)$ and utilize
models where it is intractable to obtain the conditional distribution of some
arbitrary subset of features $x_u$ given the rest of the observed covariates
$x_o$: $p(x_u \mid x_o)$. Traditional conditional approaches provide a model
for a fixed set of covariates conditioned on another fixed set of observed
covariates. Instead, in this work we develop a model that is capable of
yielding all conditional distributions $p(x_u \mid x_o)$ (for arbitrary $x_u$)
via tractable conditional likelihoods. We propose a novel extension of (change
of variables based) flow generative models, arbitrary conditioning flow models
(AC-Flow), that can be conditioned on arbitrary subsets of observed covariates,
which was previously infeasible. We apply AC-Flow to the imputation of
features, and also develop a unified platform for both multiple and single
imputation by introducing an auxiliary objective that provides a principled
single "best guess" for flow models. Extensive empirical evaluations show that
our models achieve state-of-the-art performance in both single and multiple
imputation across image inpainting and feature imputation in synthetic and
real-world datasets. Code is available at https://github.com/lupalab/ACFlow.
