# Conditional Distribution Quantization in Machine Learning

arXiv: https://arxiv.org/abs/2502.07151 · HTML: https://mlsanity.com/paper/2502.07151/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 22 of 22)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles](https://mlsanity.com/paper/1606.07839/) (2016)
- [Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/1809.09087/) (2018)
- [On the Posterior Distribution in Denoising: Application to Uncertainty Quantification](https://mlsanity.com/paper/2309.13598/) (2023)
- [Confident Multiple Choice Learning](https://mlsanity.com/paper/1706.03475/) (2017)
- [On the expressivity of bi-Lipschitz normalizing flows](https://mlsanity.com/paper/2107.07232/) (2021)
- [Uncertainty Quantification via Neural Posterior Principal Components](https://mlsanity.com/paper/2309.15533/) (2023)
- [Resilient Multiple Choice Learning: A learned scoring scheme with application to audio scene analysis](https://mlsanity.com/paper/2311.01052/) (2023)
- [Annealed Multiple Choice Learning: Overcoming limitations of Winner-takes-all with annealing](https://mlsanity.com/paper/2407.15580/) (2024)
- [Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows](https://mlsanity.com/paper/2305.18910/) (2023)
- [Winner-takes-all learners are geometry-aware conditional density estimators](https://mlsanity.com/paper/2406.04706/) (2024)
- [pcaGAN: Improving Posterior-Sampling cGANs via Principal Component Regularization](https://mlsanity.com/paper/2411.00605/) (2024)

## Abstract (arXiv)

Conditional expectation mathbbE(Y mid X) often fails to capture the complexity of multimodal conditional distributions L(Y mid X). To address this, we propose using n-point conditional quantizations--functional mappings of X that are learnable via gradient descent--to approximate L(Y mid X). This approach adapts Competitive Learning Vector Quantization (CLVQ), tailored for conditional distributions. It goes beyond single-valued predictions by providing multiple representative points that better reflect multimodal structures. It enables the approximation of the true conditional law in the Wasserstein distance. The resulting framework is theoretically grounded and useful for uncertainty quantification and multimodal data generation tasks. For example, in computer vision inpainting tasks, multiple plausible reconstructions may exist for the same partially observed input image X. We demonstrate the effectiveness of our approach through experiments on synthetic and real-world datasets.