Existence of Large Sublattices Isomorphic to Boolean Algebra in a Candidate Lattice

Abstract

Algebraic machine learning has emerged as a way to overcome the need to generate a (potentially exponential) lattice of all candidates (as, for example, in the case of Boolean algebra). In this paper, it is proven that for a random training sample generated by the Bernoulli sequence, the probability that a large sublattice will arise in the lattice of candidates isomorphic to Boolean algebra will tend to unity as the sample size increases.