Computable inference for hidden Markov models via duality
speaker: Matteo Ruggiero (University of Torino and Collegio Carlo Alberto)abstract: We review some recent advances on the use of duality for solving certain nonlinear filtering problems on uncountable state spaces. Specifically, the goal is to estimate the law of a hidden signal that evolves as a diffusion process, given observations collected at discrete times whose emission distribution is modulated by the signal. The existence of a certain type of dual process for a reversible signal, together with other assumptions on the emission distribution, is shown to lead to a closed-form expression for the filtering, prediction and smoothing distributions, the three main quantities of interest on the signal, and for the likelihood of the observations. Our sufficient conditions cover the cases of Ornstein-Uhlenbeck, Cox-Ingersoll-Ross and K-dimensional Wright-Fisher diffusions, and are then extended to nonparametric signals given by Fleming-Viot and Dawson-Watanabe measure-valued diffusions. Our results imply that only a finite computational effort is required to evaluate the quantities of interest, making the associated recursive filters computable, and suggest some efficient approximations that are shown to outperform particle filtering methods.
timetable:
Mon 1 Apr, 17:00 - 18:00, Aula Dini
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