  A novel framework has recently been proposed for designing the molecular
structure of chemical compounds with a desired chemical property, where design
of novel drugs is an important topic in bioinformatics and chemo-informatics.
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. A set of graph theoretical
descriptors in the feature function plays a key role to derive a compact
formulation of such an MILP. To improve the learning performance of prediction
functions in the framework maintaining the compactness of the MILP, this paper
utilizes the product of two of those descriptors as a new descriptor and then
designs a method of reducing the number of descriptors. The results of our
computational experiments suggest that the proposed method improved the
learning performance for many chemical properties and can infer a chemical
structure with up to 50 non-hydrogen atoms.
