Sequential Monte Carlo Learning for Time Series Structure Discovery
Feras A. Saad Brian J. Patton Matthew D. Hoffman Rif A. Saurous Vikash K. Mansinghka
This paper presents a new approach to automatically discovering accurate
models of complex time series data. Working within a Bayesian nonparametric
prior over a symbolic space of Gaussian process time series models, we present
a novel structure learning algorithm that integrates sequential Monte Carlo
(SMC) and involutive MCMC for highly effective posterior inference. Our method
can be used both in "online" settings, where new data is incorporated
sequentially in time, and in "offline" settings, by using nested subsets of
historical data to anneal the posterior. Empirical measurements on real-world
time series show that our method can deliver 10x--100x runtime speedups over
previous MCMC and greedy-search structure learning algorithms targeting the
same model family. We use our method to perform the first large-scale
evaluation of Gaussian process time series structure learning on a prominent
benchmark of 1,428 econometric datasets. The results show that our method
discovers sensible models that deliver more accurate point forecasts and
interval forecasts over multiple horizons as compared to widely used
statistical and neural baselines that struggle on this challenging data.