Fitting Rank Order Data in the Age of Context

Abstract

Rank order data are pervasive in science and in our daily lived experience. With the advent of high performance computing and the commensurate increase in available data, the opportunity to capture the overall distribution of values by means of nonparametric curve fitting enables the identification of exceptional points in large datasets. With a rank order structure, these distributions may exhibit a “knee” delineating a threshold between exceptional points and those of the baseline. Given an accurate characterization of the distribution of prediction scores, including careful identification of the knee, we have previously shown that predictive performance can be significantly improved by leveraging this “context”. This paper examines the nonparametric characterization of such distributions. Locally weighted regression (LOESS) is a widely used nonparametric approach to curve fitting. Here, we revisit the assumptions behind the selection of kernel functions for nonparametric curve fitting of biological and biomedical data exhibiting rare or exceptional instances. We propose a new linear asymmetric kernel function and compare it to the commonly used tricube kernel used in LOESS. We evaluate its ability to fit rank order data in the domain of protein-protein interaction prediction. The proposed linear kernel significantly improved predictive performance $(p < 0.001$) of two state-of-the-art predictors and promises to be widely applicable in related machine learning pipelines and nonparametric regression tasks.