Efficient Learning of Deep State Space Models via Importance Smoothing

Latent state space systems are ubiquitous in statistical modelling, arising naturally when time series are observed through noisy measurements. However, training deep state space models (DSSMs) at scale remains difficult. Two largely distinct strategies have emerged for training DSSMs. The first, auto-encoding DSSMs, trains generative models by optimising a variational lower bound. The second backpropagates through the outputs of classical sequential Monte Carlo (SMC) algorithms. Such approaches can train DSSMs for both discriminative and generative tasks, but their inherently sequential forward passes scale poorly on modern hardware. We propose \emph{parallel variational Monte Carlo} (PVMC), a new training method that bridges these paradigms and robustly trains DSSMs for both discriminative and generative tasks. Across a set of benchmark experiments, PVMC matches or exceeds state-of-the-art performance while training $10\times$ faster than the fastest competing SMC-based approach.

State space models are a powerful tool for modelling systems that evolve in time. They express the behaviour of a system that is under study over a length of time with two separate models. A model for the evolution of the system's internal properties, and a model for how the internal properties are expressed in the measurements that we take. This naturally mimics the structure of many models employed across science and finance. There are two broad types of goals in modelling such systems, generative and discriminative. Discriminative modelers try to estimate the system properties from a set of measurements. Generative modellers try to design their model so that it can be used to generate fake measurements that appear as if they had come from the actual system. Previous work in learning state space models in a deep learning context are either fast but only capable at generative modelling or slow. Our method makes use of modern parallel computation to learn discriminative models 10 times faster than previous approaches. We also show it has benefits over previous approaches in generative tasks whilst maintaining a good run time.