Related papers: Picturing classical and quantum Bayesian inference

We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This…

We present an information-theoretic interpretation of quantum formalism based on a Bayesian framework and devoid of any extra axiom or principle. Quantum information is construed as a technique for analyzing a logical system subject to…

We present a new probabilistic model of compact commutative Lie groups that produces invariant-equivariant and disentangled representations of data. To define the notion of disentangling, we borrow a fundamental principle from physics that…

Bayesian networks (BNs) are a foundational model in machine learning and causal inference. Their graphical structure can handle high-dimensional problems, divide them into a sparse collection of smaller ones, underlies Judea Pearl's…

This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate…

One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…

Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…

We show that any quantum density matrix can be represented by a Bayesian network (a directed acyclic graph), and also by a Markov network (an undirected graph). We show that any Bayesian or Markov net that represents a density matrix, is…

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed…

We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial…

Recently quantum prediction problem was proposed in the Bayesian framework. It is shown that Bayesian predictive density operators are the best predictive density operators when we evaluate them by using the average relative entropy based…

Optical fields provide an accessible platform to explore connections between classical and quantum mechanics. We introduce a group-theoretic framework based on the $\mathrm{su}(1,1)$ Lie algebra to construct classical analogs of…

One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…

We present a general framework for Bayesian inference of causal effects that delivers provably robust inferences founded on design-based randomization of treatments. The framework involves fixing the observed potential outcomes and forming…

We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of [1, 2] is used to evaluate the resulting series expansion for the partition function. We show that, for…

This paper presents a quantum version of the Monty Hall problem based upon the quantum inferring acausal structures, which can be identified with generalization of Bayesian networks. Considered structures are expressed in formalism of…