How to implement the Bayes' formula in the age of ML?
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916480581369856 |
|---|---|
| author | Taghvaei, Amirhossein Mehta, Prashant G. |
| author_facet | Taghvaei, Amirhossein Mehta, Prashant G. |
| contents | This chapter contains a self-contained introduction to the significance of Bayes' formula in the context of nonlinear filtering problems. Both discrete-time and continuous-time settings of the problem are considered in a unified manner. In control theory, the focus on optimization-based solution approaches is stressed together with a discussion of historical developments in this area (from 1960s onwards). The heart of this chapter contains a presentation of a novel optimal transportation formulation for the Bayes formula (developed recently by the first author) and its relationship to some of the prior joint work (feedback particle filter) from the authors. The presentation highlights how optimal transportation theory is leveraged to overcome some of the numerical challenges of implementing Bayes' law by enabling the use of machine learning (ML) tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09653 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to implement the Bayes' formula in the age of ML? Taghvaei, Amirhossein Mehta, Prashant G. Systems and Control Optimization and Control This chapter contains a self-contained introduction to the significance of Bayes' formula in the context of nonlinear filtering problems. Both discrete-time and continuous-time settings of the problem are considered in a unified manner. In control theory, the focus on optimization-based solution approaches is stressed together with a discussion of historical developments in this area (from 1960s onwards). The heart of this chapter contains a presentation of a novel optimal transportation formulation for the Bayes formula (developed recently by the first author) and its relationship to some of the prior joint work (feedback particle filter) from the authors. The presentation highlights how optimal transportation theory is leveraged to overcome some of the numerical challenges of implementing Bayes' law by enabling the use of machine learning (ML) tools. |
| title | How to implement the Bayes' formula in the age of ML? |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2411.09653 |