Related papers: Belief propagation in monoidal categories
Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise…
We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…
Due to the intractable nature of exact lifted inference, research has recently focused on the discovery of accurate and efficient approximate inference algorithms in Statistical Relational Models (SRMs), such as Lifted First-Order Belief…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
Message passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message passing. In order to achieve this we…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
Near optimal decoding of good error control codes is generally a difficult task. However, for a certain type of (sufficiently) good codes an efficient decoding algorithm with near optimal performance exists. These codes are defined via a…
We argue that category theory should become a part of the daily practice of the physicist, and more specific, the quantum physicist and/or informatician. The reason for this is not that category theory is a better way of doing mathematics,…
Belief propagation (BP) is a classical algorithm that approximates the marginal distribution associated with a factor graph by passing messages between adjacent nodes in the graph. It gained popularity in the 1990's as a powerful decoding…
Usually a name of the category is inherited from the name of objects. However more relevant for a category of objects and morphisms is an algebra of morphisms. Therefore we prefer to say a category of graphs if every morphism is a graph. In…
These expanded lecture notes are based on a tutorial on categorical proof theory presented at the summer school associated with the conference "Topology, Algebra, and Categories in Logic 2021-2022." The chapter delves into various…
Dempster/Shafer (D/S) theory has been advocated as a way of representing incompleteness of evidence in a system's knowledge base. Methods now exist for propagating beliefs through chains of inference. This paper discusses how rules with…
The category of Hilbert modules may be interpreted as a naive quantum field theory over a base space. Open subsets of the base space are recovered as idempotent subunits, which form a meet-semilattice in any firm braided monoidal category.…
This paper considers the noisy group testing problem where among a large population of items some are defective. The goal is to identify all defective items by testing groups of items, with the minimum possible number of tests. The focus of…
It is shown that the fiducial distribution in a group model, or more generally a quasigroup model, determines the optimal equivariant frequentist inference procedures. The proof does not rely on existence of invariant measures, and…
We give two examples of categorical axioms asserting that a canonically defined natural transformation is invertible where the invertibility of any natural transformation implies that the canonical one is invertible. The first example is…
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM…
Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being…