Composing Biases by Using CP to Decompose Minimal Functional Dependencies for Acquiring Complex Formulae

Ramiz Gindullin, Nicolas Beldiceanu, Jovial Cheukam-Ngouonou, Rémi Douence, Claude-Guy Quimper

Abstract:

Given a table with a minimal set of input columns that functionally determines an output column, we introduce a method that tries to gradually decompose the corresponding minimal functional dependency (mfd) to acquire a formula expressing the output column in terms of the input columns. A
first key element of the method is to create sub-problems
that are easier to solve than the original formula acquisition
problem, either because it learns formulae with fewer inputs
parameters, or as it focuses on formulae of a particular class,
such as Boolean formulae; as a result, the acquired formulae
can mix different learning biases such as polynomials, conditionals or Boolean expressions. A second key feature of
the method is that it can be applied recursively to find formulae that combine polynomial, conditional or Boolean subterms in a nested manner. The method was tested on data for
eight families of combinatorial objects; new conjectures were
found that were previously unattainable. The method often
creates conjectures that combine several formulae into one
with a limited number of automatically found Boolean terms