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

Conditional density estimation is the task of estimating the probability of an event, conditioned on some inputs. A neural network can be used to compute the output distribution explicitly. For such a task, there are many ways to represent a continuous-domain distribution using the output of a neural network, but each comes with its own limitations for what distributions it can accurately render. If the family of functions is too restrictive, it will not be appropriate for many datasets. In this paper, we demonstrate the benefits of modeling free-form distributions using deconvolution. It has the advantage of being flexible, but also takes advantage of the topological 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 artificial and real tasks, without committing to a restrictive parametric model.