Molecular Design Based on Integer Programming and Splitting Data Sets by Hyperplanes

A novel framework for designing the molecular structure of chemical compounds with a desired chemical property has recently been proposed. The framework infers a desired chemical graph by solving a mixed integer linear program (MILP) that simulates the computation process of two functions: a feature function defined by a two-layered model on chemical graphs and a prediction function constructed by a machine learning method. To improve the learning performance of prediction functions in the framework, we design a method that splits a given data set <tex-math notation="LaTeX">C</tex-math> into two subsets <tex-math notation="LaTeX">C⁽ⁱ⁾,i=1,2</tex-math> by a hyperplane in a chemical space so that most compounds in the first (resp., second) subset have observed values lower (resp., higher) than a threshold <tex-math notation="LaTeX">θ</tex-math> . We construct a prediction function <tex-math notation="LaTeX">ψ</tex-math> to the data set <tex-math notation="LaTeX">C</tex-math> by combining prediction functions <tex-math notation="LaTeX">ψ ᵢ,i=1,2</tex-math> each of which is constructed on <tex-math notation="LaTeX">C⁽ⁱ⁾</tex-math> independently. The results of our computational experiments suggest that the proposed method improved the learning performance for several chemical properties to which a good prediction function has been difficult to construct.