# MCD: Marginal Contrastive Discrimination for conditional density estimation

arXiv: https://arxiv.org/abs/2206.01592 · HTML: https://mlsanity.com/paper/2206.01592/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 58 references that are in the map.
- First posted on arXiv 3 Jun 2022.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [Learning Representations by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/1906.00910/) (2019)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [A Survey on Contrastive Self-supervised Learning](https://mlsanity.com/paper/2011.00362/) (2020)
- [fastai: A Layered API for Deep Learning](https://mlsanity.com/paper/2002.04688/) (2020)
- [Decoupled Contrastive Learning](https://mlsanity.com/paper/2110.06848/) (2021)
- [Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks](https://mlsanity.com/paper/1903.00954/) (2019)
- [Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimation](https://mlsanity.com/paper/1704.08095/) (2017)
- [Conditional Density Estimation Tools in Python and R with Applications to Photometric Redshifts and Likelihood-Free Cosmological Inference](https://mlsanity.com/paper/1908.11523/) (2019)
- [Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas](https://mlsanity.com/paper/1503.03305/) (2015)
- [The Kernel Mixture Network: A Nonparametric Method for Conditional Density Estimation of Continuous Random Variables](https://mlsanity.com/paper/1705.07111/) (2017)
- [RFCDE: Random Forests for Conditional Density Estimation](https://mlsanity.com/paper/1804.05753/) (2018)
- [Fast multivariate empirical cumulative distribution function with connection to kernel density estimation](https://mlsanity.com/paper/2005.03246/) (2020)

## Abstract (arXiv)

We consider the problem of conditional density estimation, which is a major topic of interest in the fields of statistical and machine learning. Our method, called Marginal Contrastive Discrimination, MCD, reformulates the conditional density function into two factors, the marginal density function of the target variable and a ratio of density functions which can be estimated through binary classification. Like noise-contrastive methods, MCD can leverage state-of-the-art supervised learning techniques to perform conditional density estimation, including neural networks. Our benchmark reveals that our method significantly outperforms in practice existing methods on most density models and regression datasets.