Inria（法国国家信息与自动化研究所）；PSL Research University（巴黎文理研究大学）；University College London（伦敦大学学院）；Inria Lille - Nord Europe（法国国家信息与自动化研究所里尔-北欧分部）；Inria London（法国国家信息与自动化研究所伦敦分部）
Théophile Cantelobre, Carlo Ciliberto, Benjamin Guedj, Alessandro Rudi
Sequential Bayesian Filtering aims to estimate the current state distribution of a Hidden Markov Model, given the past observations. The problem is well-known to be intractable for most application domains, except in notable cases such as the tabular setting or for linear dynamical systems with gaussian noise. In this work, we propose a new class of filters based on Gaussian PSD Models, which offer several advantages in terms of density approximation and computational efficiency. We show that filtering can be efficiently performed in closed form when transitions and observations are Gaussian PSD Models. When the transition and observations are approximated by Gaussian PSD Models, we show that our proposed estimator enjoys strong theoretical guarantees, with estimation error that depends on the quality of the approximation and is adaptive to the regularity of the transition probabilities. In particular, we identify regimes in which our proposed filter attains a TV $ε$-error with memory and computational complexity of $O(ε^{-1})$ and $O(ε^{-3/2})$ respectively, including the offline learning step, in contrast to the $O(ε^{-2})$ complexity of sampling methods such as particle filtering.
KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics
ETH Zürich（苏黎世联邦理工学院）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Eindhoven University of Technology（埃因霍温理工大学）；Phillips Research（飞利浦研究院）；Weizmann Institute of Science（魏茨曼科学研究所）
