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.

翻译：状态空间模型通过潜在随机过程为复杂时间序列建模提供了灵活框架。非线性、非高斯状态空间模型的推断常采用粒子方法，但这类方法难以扩展到长时间序列。其挑战性体现在两方面：一方面计算复杂度随时间线性增长（与线性情形类似），另一方面粒子滤波会随着序列增长出现更严重的粒子退化问题。针对有限状态隐马尔可夫模型和线性状态空间模型的贝叶斯推断，已有研究者开发了基于缓冲随机梯度估计的随机梯度MCMC方法以处理时间依赖性。我们通过粒子方法将这些随机梯度估计器推广至非线性状态空间模型。针对在潜在过程上满足对数凹性的非线性状态空间模型，我们给出了同时考虑缓冲误差和粒子误差的误差界。通过将所提出的粒子缓冲随机梯度与随机梯度MCMC方法结合，我们在长序列合成数据与分钟级金融收益率数据上进行了推断实验，验证了这类方法的重要性。