# Adaptive joint distribution learning

arXiv: https://arxiv.org/abs/2110.04829 · HTML: https://mlsanity.com/paper/2110.04829/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 10 Oct 2021.

## Builds on (most cited first, 8 of 8)

- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Non-parametric Models for Non-negative Functions](https://mlsanity.com/paper/2007.03926/) (2020)
- [A Rigorous Theory of Conditional Mean Embeddings](https://mlsanity.com/paper/1912.00671/) (2019)
- [Kernel Conditional Density Operators](https://mlsanity.com/paper/1905.11255/) (2019)
- [A New Parametrization of Correlation Matrices](https://mlsanity.com/paper/2012.02395/) (2020)
- [A Note on Optimizing Distributions using Kernel Mean Embeddings](https://mlsanity.com/paper/2106.09994/) (2021)
- [Constrained Polynomial Likelihood](https://mlsanity.com/paper/1910.14009/) (2019)

## Built on by (most cited first, 2 of 2)

- [Kernel Density Machines](https://mlsanity.com/paper/2504.21419/) (2025)
- [Kernel-Based Nonparametric Tests For Shape Constraints](https://mlsanity.com/paper/2510.16745/) (2025)

## Abstract (arXiv)

We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym derivative, which we estimate from sample sizes of up to several millions, alleviating the inherent limitations of RKHS modeling. Well-defined normalized and positive conditional distributions are natural by-products to our approach. Our proposal is fast to compute and accommodates learning problems ranging from prediction to classification. Our theoretical findings are supplemented by favorable numerical results.