Stochastic Gradient MCMC for Nonlinear State Space Models
This work addresses scalability issues in time series modeling for applications like finance, though it is incremental as it builds on existing stochastic gradient MCMC frameworks.
The authors tackled the challenge of scaling Bayesian inference for nonlinear, non-Gaussian state space models to long time series by extending stochastic gradient MCMC with particle methods, achieving improved computational efficiency and handling particle degeneracy in evaluations on synthetic and financial data.
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with time, as in the linear case, but particle filters additionally suffer from increasing particle degeneracy with longer series. Stochastic gradient MCMC methods have been developed to scale Bayesian inference for finite-state hidden Markov models and linear SSMs using buffered stochastic gradient estimates to account for temporal dependencies. We extend these stochastic gradient estimators to nonlinear SSMs using particle methods. We present error bounds that account for both buffering error and particle error in the case of nonlinear SSMs that are log-concave in the latent process. We evaluate our proposed particle buffered stochastic gradient using stochastic gradient MCMC for inference on both long sequential synthetic and minute-resolution financial returns data, demonstrating the importance of this class of methods.