Related papers: Partial Markov Categories
We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning…
We introduce partial Markov categories. In the same way that Markov categories encode stochastic processes, partial Markov categories encode stochastic processes with constraints, observations and updates. In particular, we prove a…
Partial Markov categories are a recent framework for categorical probability theory that provide an abstract account of partial probabilistic computation with updating semantics. In this article, we discuss two order relations on the…
The present work develops a construction of a CD category of partial kernels from a particular type of Markov category called a partializable Markov category. These are a generalization of earlier models of categories of partial morphisms…
We use Markov categories to generalize the basic theory of Markov chains and hidden Markov models to an abstract setting. This comprises characterizations of hidden Markov models in terms of conditional independences and algorithms for…
Triplet Markov chains are general generative models for sequential data which take into account three kinds of random variables: (noisy) observations, their associated discrete labels and latent variables which aim at strengthening the…
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…
Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
In this paper, we develop category theory of Markov kernels to study categorical aspects of Bayesian inversions. As a result, we present a unified model for Bayesian supervised learning, encompassing Bayesian density estimation. We…
Markov categories are the central framework for categorical probability theory. Many important concepts from probability theory can be formalized in terms of Markov categories. In particular, conditional probability distributions and Bayes'…
From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization…
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…
In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the…
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…
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…
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…
In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this paper, we connect some ideas from…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled…