Extrapolation is not the same as interpolation

Abstract

We propose a new machine learning formulation designed specifically for extrapolation. The textbook way to apply machine learning to drug design is to learn a univariate function that when a drug (structure) is input, the function outputs a real number (the activity): f(drug) \(\rightarrow\) activity. However, experience in real-world drug design suggests that this formulation of the drug design problem is not quite correct. Specifically, what one is really interested in is extrapolation: predicting the activity of new drugs with higher activity than any existing ones. Our new formulation for extrapolation is based on learning a bivariate function that predicts the difference in activities of two drugs F(drug1, drug2) \(\rightarrow\) difference in activity, followed by the use of ranking algorithms. This formulation is general and agnostic, suitable for finding samples with target values beyond the target value range of the training set. We applied the formulation to work with support vector machines , random forests , and Gradient Boosting Machines . We compared the formulation with standard regression on thousands of drug design datasets, gene expression datasets and material property datasets. The test set extrapolation metric was the identification of examples with greater values than the training set, and top-performing examples (within the top 10% of the whole dataset). On this metric our pairwise formulation vastly outperformed standard regression. Its proposed variations also showed a consistent outperformance. Its application in the stock selection problem further confirmed the advantage of this pairwise formulation.