Molecular Design Based on Integer Programming and Splitting Data Sets by Hyperplanes
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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 𝒞 into two subsets 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 θ. We construct a prediction function ψ to the data set 𝒞 by combining prediction functions ψ_i,i=1,2 each of which is constructed on 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.
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