# Sampling from Arbitrary Functions via PSD Models

arXiv: https://arxiv.org/abs/2110.10527 · HTML: https://mlsanity.com/paper/2110.10527/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 20 Oct 2021.

## Builds on (most cited first, 7 of 7)

- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017)
- [Non-parametric Models for Non-negative Functions](https://mlsanity.com/paper/2007.03926/) (2020)
- [PSD Representations for Effective Probability Models](https://mlsanity.com/paper/2106.16116/) (2021)
- [Globally Convergent Newton Methods for Ill-conditioned Generalized Self-concordant Losses](https://mlsanity.com/paper/1907.01771/) (2019)

## Built on by (most cited first, 8 of 8)

- [Squared Neural Families: A New Class of Tractable Density Models](https://mlsanity.com/paper/2305.13552/) (2023)
- [Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimation](https://mlsanity.com/paper/2303.03237/) (2023)
- [Approximation of optimization problems with constraints through kernel Sum-Of-Squares](https://mlsanity.com/paper/2301.06339/) (2023)
- [Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models](https://mlsanity.com/paper/2303.17109/) (2023)
- [Squared families: Searching beyond regular probability models](https://mlsanity.com/paper/2503.21128/) (2025)
- [Kernelised Normalising Flows](https://mlsanity.com/paper/2307.14839/) (2023)
- [Closed-form Filtering for Non-linear Systems](https://mlsanity.com/paper/2402.09796/) (2024)
- [Asymptotically Optimal Change Detection for Unnormalized Pre- and Post-Change Distributions](https://mlsanity.com/paper/2410.14615/) (2024)

## Abstract (arXiv)

In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through evaluations of the density, current methods either scale badly with the dimension or require very involved implementations. Instead, we take a two-step approach by first modeling the probability distribution and then sampling from that model. We use the recently introduced class of positive semi-definite (PSD) models, which have been shown to be efficient for approximating probability densities. We show that these models can approximate a large class of densities concisely using few evaluations, and present a simple algorithm to effectively sample from these models. We also present preliminary empirical results to illustrate our assertions.