Benjamin Cox

John-Joseph Brady, Benjamin Cox, Yunpeng Li et al.

State-space models (SSMs) are a widely used tool in time series analysis. In the complex systems that arise from real-world data, it is common to employ particle filtering (PF), an efficient Monte Carlo method for estimating the hidden state corresponding to a sequence of observations. Applying particle filtering requires specifying both the parametric form and the parameters of the system, which are often unknown and must be estimated. Gradient-based optimisation techniques cannot be applied directly to standard particle filters, as the filters themselves are not differentiable. However, several recently proposed methods modify the resampling step to make particle filtering differentiable. In this paper, we present an implementation of several such differentiable particle filters (DPFs) with a unified API built on the popular PyTorch framework. Our implementation makes these algorithms easily accessible to a broader research community and facilitates straightforward comparison between them. We validate our framework by reproducing experiments from several existing studies and demonstrate how DPFs can be applied to address several common challenges with state space modelling.

Benjamin Cox, Santiago Segarra, Victor Elvira

State-space models are a popular statistical framework for analysing sequential data. Within this framework, particle filters are often used to perform inference on non-linear state-space models. We introduce a new method, StateMixNN, that uses a pair of neural networks to learn the proposal distribution and transition distribution of a particle filter. Both distributions are approximated using multivariate Gaussian mixtures. The component means and covariances of these mixtures are learnt as outputs of learned functions. Our method is trained targeting the log-likelihood, thereby requiring only the observation series, and combines the interpretability of state-space models with the flexibility and approximation power of artificial neural networks. The proposed method significantly improves recovery of the hidden state in comparison with the state-of-the-art, showing greater improvement in highly non-linear scenarios.