Implicit Maximum a Posteriori Filtering via Adaptive Optimization
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Bayesian filtering, optimization, neural networks
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
TL;DR: We can define the Bayesian filtering problem as optimization over a time-varying objective, which makes it possible to define implicit filters based on optimization that perform well.
Abstract: Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires matrix storage, inversion, and multiplication or Monte Carlo estimation, none of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we consider the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
Supplementary Material: zip
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Submission Number: 6002
Loading