# Discovering Multiple Constraints that are Frequently Approximately Satisfied

arXiv: https://arxiv.org/abs/1301.2278 · HTML: https://mlsanity.com/paper/1301.2278/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2013.

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

- [Product of Gaussian Mixture Diffusion Models](https://mlsanity.com/paper/2310.12653/) (2023)
- [Back to Square One: Superhuman Performance in Chutes and Ladders Through Deep Neural Networks and Tree Search](https://mlsanity.com/paper/2104.00698/) (2021)

## Abstract (arXiv)

Some high-dimensional data.sets can be modelled by assuming that there are many different linear constraints, each of which is Frequently Approximately Satisfied (FAS) by the data. The probability of a data vector under the model is then proportional to the product of the probabilities of its constraint violations. We describe three methods of learning products of constraints using a heavy-tailed probability distribution for the violations.