Automatic Construction and Natural-Language Description of Nonparametric Regression Models

This paper presents the beginnings of an automatic statistician, focusing on regression problems. Our system explores an open-ended space of possible statistical models to discover a good explanation of the data, and then produces a detailed report with figures and natural-language text. Our approach treats unknown functions nonparametrically using Gaussian processes, which has two important consequences. First, Gaussian processes model functions in terms of high-level properties (e.g. smoothness, trends, periodicity, changepoints). Taken together with the compositional structure of our language of models, this allows us to automatically describe functions through a decomposition into additive parts. Second, the use of flexible nonparametric models and a rich language for composing them in an open-ended manner also results in state-of-the-art extrapolation performance evaluated over 13 real time series data sets from various domains.