# Bottleneck Conditional Density Estimation

arXiv: https://arxiv.org/abs/1611.08568 · HTML: https://mlsanity.com/paper/1611.08568/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2016.

## Built on by (most cited first, 5 of 5)

- [Testing for the Markov Property in Time Series via Deep Conditional Generative Learning](https://mlsanity.com/paper/2305.19244/) (2023)
- [Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow](https://mlsanity.com/paper/2203.08617/) (2022)
- [Quantile Off-Policy Evaluation via Deep Conditional Generative Learning](https://mlsanity.com/paper/2212.14466/) (2022)
- [Conditional Density Estimation with Histogram Trees](https://mlsanity.com/paper/2410.11449/) (2024)
- [Semi-Supervised Few-Shot Classification with Deep Invertible Hybrid Models](https://mlsanity.com/paper/2105.10644/) (2021)

## Abstract (arXiv)

We introduce a new framework for training deep generative models 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. Crucially, we propose a new hybrid training method that blends the conditional generative model with a joint generative model. Hybrid blending is the key to effective training of the BCDE, which avoids overfitting and provides a novel mechanism for leveraging unlabeled data. We show that our hybrid training procedure enables models to achieve competitive results in the MNIST quadrant prediction task in the fully-supervised setting, and sets new benchmarks in the semi-supervised regime for MNIST, SVHN, and CelebA.