Bottleneck Conditional Density Estimation

We propose a neural network framework for high-dimensional conditional density estimation. The Bottleneck Conditional Density Estimator (BCDE) is a variant of the conditional variational autoencoder (CVAE) that employs layer(s) of stochastic variables as the bottleneck between the input x and target y, where both are high-dimensional. The key to effectively train BCDEs is the hybrid blending of the conditional generative model with a joint generative model that leverages unlabeled data to regularize the conditional model. We show that the BCDE significantly outperforms the CVAE in MNIST quadrant prediction benchmarks in the fully supervised case and establishes new benchmarks in the semi-supervised case.