2023-04-11-bishop23a.md

title	abstract	section	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Recurrent Neural Networks and Universal Approximation of Bayesian Filters	We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and observation models. Instead, we formulate a generic recurrent neural network framework and seek to learn directly a recursive mapping from observational inputs to the desired estimator statistics. The main focus of this article is the approximation capabilities of this framework. We provide approximation error bounds for filtering in general non-compact domains. We also consider strong time-uniform approximation error bounds that guarantee good long-time performance. We discuss and illustrate a number of practical concerns and implications of these results.	Regular Papers	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	bishop23a	0	Recurrent Neural Networks and Universal Approximation of Bayesian Filters	6956	6967	6956-6967	6956	false	Bishop, Adrian N. and Bonilla, Edwin V.	given family Adrian N. Bishop given family Edwin V. Bonilla	2023-04-11		Proceedings of The 26th International Conference on Artificial Intelligence and Statistics	206	inproceedings	date-parts 2023 4 11	https://proceedings.mlr.press/v206/bishop23a/bishop23a.pdf