A category theory framework for Bayesian learning
Inspired by the foundational works by Spivak and Fong and Cruttwell et al., we introduce a categorical framework to formalize Bayesian inference and learning. The two key ideas at play here are the notions of Bayesian inversions and the functor GL as constructed by Cruttwell et al.. In this context, we find that Bayesian learning is the simplest case of the learning paradigm. We then obtain categorical formulations of batch and sequential Bayes updates while also verifying that the two coincide in a specific example.
Code (0)
등록된 구현이 없습니다.
Tasks
Bayesian InferenceSimilar Papers 제목 키워드 기반
Interpreting Dynamical Systems as Bayesian Reasoners
A central concept in active inference is that the internal states of a physical system parametrise probability measures over states of the external world. These can be seen as an agent's beliefs, expressed as a Bayesian …
Bayesian InferenceExplicitly Bayesian Regularizations in Deep Learning
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explic…
Deep LearningFlattening Multiparameter Hierarchical Clustering Functors
We bring together topological data analysis, applied category theory, and machine learning to study multiparameter hierarchical clustering. We begin by introducing a procedure for flattening multiparameter hierarchical c…
BIG-bench Machine LearningClusteringTopological Data AnalysisCausal models in string diagrams
The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally usi…
Causal InferenceA Category Theory Approach to Interoperability
In this article, we propose a Category Theory approach to (syntactic) interoperability between linguistic tools. The resulting category consists of textual documents, including any linguistic annotations, NLP tools that …