  In many contexts it is extremely costly to perform enough high quality
experimental measurements to accurately parameterize a predictive quantitative
model. However, it is often much easier to carry out large numbers of
experiments that indicate whether each sample is above or below a given
threshold. Can many such categorical or "coarse" measurements be combined with
a much smaller number of high resolution or "fine" measurements to yield
accurate models? Here, we demonstrate an intuitive strategy, inspired by
statistical physics, wherein the coarse measurements are used to identify the
salient features of the data, while the fine measurements determine the
relative importance of these features. A linear model is inferred from the fine
measurements, augmented by a quadratic term that captures the correlation
structure of the coarse data. We illustrate our strategy by considering the
problems of predicting the antimalarial potency and aqueous solubility of small
organic molecules from their 2D molecular structure.
