Partial structure learning by subset walsh transform

Estimation of distribution algorithms (EDAs) use structure learning to build a statistical model of good solutions discovered so far, in an effort to discover better solutions. The non-zero coefficients of the Walsh transform produce a hypergraph representation of structure of a binary fitness function; however, computation of all Walsh coefficients requires exhaustive evaluation of the search space. In this paper, we propose a stochastic method of determining Walsh coefficients for hyperedges contained within the selected subset of the variables (complete local structure). This method also detects parts of hyperedges which cut the boundary of the selected variable set (partial structure), which may be used to incrementally build an approximation of the problem hypergraph.