IMPLICIT MAXIMUM A POSTERIORI FILTERING VIA ADAPTIVE OPTIMIZATION

Gianluca M. Bencomo, Jake C. Snell, Thomas L. Griffiths

Research output: Contribution to conferencePaperpeer-review

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 either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we frame 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.

Original languageEnglish (US)
StatePublished - 2024
Event12th International Conference on Learning Representations, ICLR 2024 - Hybrid, Vienna, Austria
Duration: May 7 2024May 11 2024

Conference

Conference12th International Conference on Learning Representations, ICLR 2024
Country/TerritoryAustria
CityHybrid, Vienna
Period5/7/245/11/24

All Science Journal Classification (ASJC) codes

  • Language and Linguistics
  • Computer Science Applications
  • Education
  • Linguistics and Language

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