  Conditional density estimation (CDE) is the task of estimating the
probability of an event conditioned on some inputs. A neural network (NN) can
also be used to compute the output distribution for continuous-domain, which
can be viewed as an extension of regression task. Nevertheless, it is difficult
to explicitly approximate a distribution without knowing the information of its
general form a priori. In order to fit an arbitrary conditional distribution,
discretizing the continuous domain into bins is an effective strategy, as long
as we have sufficiently narrow bins and very large data. However, collecting
enough data is often hard to reach and falls far short of that ideal in many
circumstances, especially in multivariate CDE for the curse of dimensionality.
In this paper, we demonstrate the benefits of modeling free-form conditional
distributions using a deconvolution-based neural net framework, coping with
data deficiency problems in discretization. It has the advantage of being
flexible but also takes advantage of the hierarchical smoothness offered by the
deconvolution layers. We compare our method to a number of other
density-estimation approaches and show that our Deconvolutional Density Network
(DDN) outperforms the competing methods on many univariate and multivariate
tasks. The code of DDN is available at https://github.com/NBICLAB/DDN.
