Parameterizing Hierarchical Particle Filters with Concept Drift for Time-varying Parameter Estimation

Models used in real-world applications can experience concept drift, where the deployment environment differs from the training environment due to previously unseen input data distributions or changes in the data generation process. Sequential Monte Carlo squared (SMC<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>) is a Bayesian algorithm which infers the distribution of both the states and parameters of non-linear, non-Gaussian state space models. A Sequential Monte Carlo (SMC) sampler operates on the static parameter space and samples the parameters with which a number of particle filters (PFs), tackle the dynamic state inference problem. PFs often do not consider the influence of concept drift on the parameters of interest. Models that consider drift will do so in a purely online context and can suffer from slow convergence. By formulating PFs as hierarchical models, with explicit dynamics to describe parameter evolution, the use of batch parameter estimation techniques like SMC<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is enabled. We demonstrate our approach by applying five concept drift models to an epidemiological disease model with time-varying transmission rates.