DeepAI AI Chat
Log In Sign Up

Dependent Bayesian Lenses: Categories of Bidirectional Markov Kernels with Canonical Bayesian Inversion

by   Dylan Braithwaite, et al.
University of Strathclyde

We generalise an existing construction of Bayesian Lenses to admit lenses between pairs of objects where the backwards object is dependent on states on the forwards object (interpreted as probability distributions). This gives a natural setting for studying stochastic maps with Bayesian inverses restricted to the points supported by a given prior. In order to state this formally we develop a proposed definition by Fritz of a support object in a Markov category and show that these give rise to a section into the category of dependent Bayesian lenses encoding a more canonical notion of Bayesian inversion.


page 1

page 2

page 3

page 4


Dependent Optics

A wide variety of bidirectional data accessors, ranging from mixed optic...

The Compositional Structure of Bayesian Inference

Bayes' rule tells us how to invert a causal process in order to update o...

Bayesian Updates Compose Optically

Bayes' rule tells us how to invert a causal process in order to update o...

Conditional distributions for quantum systems

Conditional distributions, as defined by the Markov category framework, ...

Cyber Kittens, or Some First Steps Towards Categorical Cybernetics

We define a categorical notion of cybernetic system as a dynamical reali...

Disintegration and Bayesian Inversion, Both Abstractly and Concretely

The notions of disintegration and Bayesian inversion are fundamental in ...

Borel Kernels and their Approximation, Categorically

This paper introduces a categorical framework to study the exact and app...