A statistical approach to learning constraints

A constraint-based model represents knowledge about a domain by a set of constraints, which must be satisfied by solutions in that domain. These models may be used for reasoning, decision making and optimisation. Unfortunately, modelling itself is a hard and error-prone task that requires expertise. The automation of this process is often referred to as constraint acquisition and has been pursued for over 20 years. Methods typically learn constraints by testing candidates against a dataset of solutions and non-solutions, and often use some form of machine learning to decide which should be learned. However, few methods are robust under errors in the data, some cannot handle large sets of candidates, and most are computationally expensive even for small problems. We describe a statistical approach based on sequential analysis that is robust, fast and scalable to large biases. Its correctness depends on an assumption that does not always hold but which is, we show using Bayesian analysis, reasonable in practice.