Related papers: Belief propagation in monoidal categories

We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In…

We develop our interpretation of the joint belief distribution and of evidential updating that matches the following basic requirements: * there must exist an efficient method for reasoning within this framework * there must exist a clear…

The aim of this paper is to firmly establish subjective fiducial inference as a rival to the more conventional schools of statistical inference, and to show that Fisher's intuition concerning the importance of the fiducial argument was…

The local computation technique (Shafer et al. 1987, Shafer and Shenoy 1988, Shenoy and Shafer 1986) is used for propagating belief functions in so called a Markov Tree. In this paper, we describe an efficient implementation of belief…

In this paper, we address the problem of finding a correspondence, or matching, between the functions of two programs in binary form, which is one of the most common task in binary diffing. We introduce a new formulation of this problem as…

A variant of the trace in a monoidal category is given in the setting of closed monoidal derivators, which is applicable to endomorphisms of fiberwise dualizable objects. Functoriality of this trace is established. As an application, an…

Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned…

We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.

We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities $a/n$ and $b/n$ for inter- and intra-block edge probabilities, respectively. It was recently shown that one can do better…

We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. The aim of the paper is to justify and contextualize the new notion by…

Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate…

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…

Subset models provide a new semantics for justifcation logic. The main idea of subset models is that evidence terms are interpreted as sets of possible worlds. A term then justifies a formula if that formula is true in each world of the…

Gaussian belief propagation (BP) is a computationally efficient method to approximate the marginal distribution and has been widely used for inference with high dimensional data as well as distributed estimation in large-scale networks.…

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…

The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…

We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation,…

We address the question of convergence in the loopy belief propagation (LBP) algorithm. Specifically, we relate convergence of LBP to the existence of a weak limit for a sequence of Gibbs measures defined on the LBP s associated computation…

In this paper, we prove that given a differential graded category C and B a full differential graded subcategory closed under coproducts, there is a canonical recollement of differential graded categories, for which we use enriched…

Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…