Related papers: Conditional Distributions for Quantum Systems
Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach ("contextuality-by-default") is based on the…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
Neural posterior estimation (NPE), a simulation-based computational approach for Bayesian inference, has shown great success in approximating complex posterior distributions. Existing NPE methods typically rely on normalizing flows, which…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random matrix theory are expressed in terms of solutions of coupled differential equations. Series solutions up to order 50 in the level spacing are obtained, thus…
Conditional density matrix represents a quantum state of subsystem in different schemes of quantum communication. Here we discuss some properties of conditional density matrix and its place in general scheme of quantum mechanics.
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…
Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
We propose a class of transformation hazard models for right-censored failure time data. It includes the proportional hazards model (Cox) and the additive hazards model (Lin and Ying) as special cases. Due to the requirement of a…
We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our…
In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen…
From a given nuclear triplet we construct a nuclear triplet of sequence spaces and introduce a correlated Gaussian measure via the Bochner-Minlos theorem. Considering special types of correlation operators on such sequence spaces, certain…
Parametric conditional copula models allow the copula parameters to vary with a set of covariates according to an unknown calibration function. Flexible Bayesian inference for the calibration function of a bivariate conditional copula is…
We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…
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…
New definitions of $Q$-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of $Q$-conditional symmetry of a system generate…