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
$\mathcal {C}$
into two subsets
$\mathcal {C}^{(i)},i=1,2$
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
$\theta$
. We construct a prediction function
$\psi$
to the data set
$\mathcal {C}$
by combining prediction functions
$\psi _{i},i=1,2$
each of which is constructed on
$\mathcal {C}^{(i)}$
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.