Time Series Structure Discovery via Probabilistic Program Synthesis

There is a widespread need for techniques that can discover structure from time series data. Recently introduced techniques such as Automatic Bayesian Covariance Discovery (ABCD) provide a way to find structure within a single time series by searching through a space of covariance kernels that is generated using a simple grammar. While ABCD can identify a broad class of temporal patterns, it is difficult to extend and can be brittle in practice. This paper shows how to extend ABCD by formulating it in terms of probabilistic program synthesis. The key technical ideas are to (i) represent models using abstract syntax trees for a domain-specific probabilistic language, and (ii) represent the time series model prior, likelihood, and search strategy using probabilistic programs in a sufficiently expressive language. The final probabilistic program is written in under 70 lines of probabilistic code in Venture. The paper demonstrates an application to time series clustering that involves a non-parametric extension to ABCD, experiments for interpolation and extrapolation on real-world econometric data, and improvements in accuracy over both non-parametric and standard regression baselines.