Model interpretation through lower-dimensional posterior summarization

Abstract: Nonparametric regression models have recently surged in their power and popularity, accompanying the trend of increasing dataset size and complexity. While these models have proven their predictive ability in empirical settings, they are often difficult to interpret and do not address the underlying inferential goals of the analyst or decision maker. In this paper, we propose a modular two-stage approach for creating parsimonious, interpretable summaries of complex models which allow freedom in the choice of modeling technique and the inferential target. In the first stage a flexible model is fit which is believed to be as accurate as possible. In the second stage, lower-dimensional summaries are constructed by projecting draws from the distribution onto simpler structures. These summaries naturally come with valid Bayesian uncertainty estimates. Further, since we use the data only once to move from prior to posterior, these uncertainty estimates remain valid across multiple summaries and after iteratively refining a summary. We apply our method and demonstrate its strengths across a range of simulated and real datasets. Code to reproduce the examples shown is avaiable at github.com/spencerwoody/ghost