Related papers: Picturing classical and quantum Bayesian inference

Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…

Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…

Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions --…

We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…

Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing…

We survey some aspects of Frobenius algebras, Frobenius structures and their relation to finite Hopf algebras using graphical calculus. We focus on the `yanking' moves coming from a closed structure in a rigid monoidal category, the…

In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily looks as though it is performing inference…

Bayesian networks (BNs) are a probabilistic graphical model widely used for representing expert knowledge and reasoning under uncertainty. Traditionally, they are based on directed acyclic graphs that capture dependencies between random…

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…

This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It…

We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data, learning an undirected graph we call the unconditional dependence graph. We show that unconditional dependence graphs…

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…

Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…

Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional…

Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…

In this article we present a new modelling framework for structured concepts using a category-theoretic generalisation of conceptual spaces, and show how the conceptual representations can be learned automatically from data, using two very…

Vector space models have become popular in distributional semantics, despite the challenges they face in capturing various semantic phenomena. We propose a novel probabilistic framework which draws on both formal semantics and recent…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…