  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 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.
