Related papers: Representable Markov Categories and Comparison of …

Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…

We introduce partial Markov categories as a synthetic framework for synthetic probabilistic inference, blending the work of Cho and Jacobs, Fritz, and Golubtsov on Markov categories with the work of Cockett and Lack on cartesian restriction…

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…

Increasingly in recent years, probabilistic computation has been investigated through the lenses of categorical algebra, especially via string diagrammatic calculi. Whereas categories of discrete and Gaussian probabilistic processes have…

We introduce quantum Markov categories as a structure that refines and extends a synthetic approach to probability theory and information theory so that it includes quantum probability and quantum information theory. In this broader…

We give qualitative and quantitative improvements to theorems which enable significance testing in Markov Chains, with a particular eye toward the goal of enabling strong, interpretable, and statistically rigorous claims of political…

Markov categories have recently emerged as a powerful high-level framework for probability theory and theoretical statistics. Here we study a quantum version of this concept, called involutive Markov categories. These are equivalent to…

Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian…

Markov combination is an operation that takes two statistical models and produces a third whose marginal distributions include those of the original models. Building upon and extending existing work in the Gaussian case, we develop Markov…

Normalization, $D(X + 1) \to D(X) + 1$, is almost a distributive law; but because one of the distributive law axioms only holds up-to-idempotent, it yields a non-associative composition of normalized kernels. We introduce the Markov magmoid…

Categorical probability has recently seen significant advances through the formalism of Markov categories, within which several classical theorems have been proven in entirely abstract categorical terms. Closely related to Markov categories…

A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish…

We introduce a sound and complete equational theory capturing equivalence of discrete probabilistic programs, that is, programs extended with primitives for Bernoulli distributions and conditioning, to model distributions over finite sets…

The Glivenko--Cantelli theorem is a uniform version of the strong law of large numbers. It states that for every IID sequence of random variables, the empirical measure converges to the underlying distribution (in the sense of uniform…

Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the structure of a commutative comonoid. They arise for example…

This work introduces a novel cause-effect relation in Markov decision processes using the probability-raising principle. Initially, sets of states as causes and effects are considered, which is subsequently extended to regular path…

Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…

Markov decision processes (MDPs) are a popular model for decision-making in the presence of uncertainty. The conventional view of MDPs in verification treats them as state transformers with probabilities defined over sequences of states and…

We introduce a probabilistic framework for two-sample comparison based on a nonparametric process taking the form of a Markov model that transitions between a "divide" and a "merge" state on a multi-resolution partition tree of the sample…

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…