Discovering Multiple Constraints that are Frequently Approximately Satisfied

TL;DR

This paper introduces methods to learn products of linear constraints in high-dimensional data, modeling data probability based on the likelihood of constraint violations, especially when constraints are frequently approximately satisfied.

Contribution

It proposes three novel methods for learning products of constraints using heavy-tailed distributions to model violations in high-dimensional data.

Findings

Effective modeling of high-dimensional data with multiple constraints

Three new algorithms for learning constraint products

Improved understanding of constraint satisfaction in data

Abstract

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.