Function Trees: Transparent Machine Learning

A fundamental exercise in machine learning is the approximation of a function of several to many variables given values of the function, often contaminated with noise, at observed joint values of the input variables. The result can then be used to estimate unknown function values given corresponding inputs. The goal is to accurately estimate the underlying (non noisy) outcome values since the noise is by definition unpredictable. To the extent that this is successful the estimated function may, in addition, be used to try to understand underlying phenomena giving rise to the data. Even when prediction accuracy is the dominate concern, being able to comprehend the way in which the input variables are jointly combining to produce predictions may lead to important sanity checks on the validity of the function estimate. Besides accuracy, the success of this latter exercise requires that the structure of the function estimate be represented in a comprehensible form.