Related papers: Representation of Conditional Expectations in Gaus…

We give a formula in terms of a joint Gibbs measure on Brownian paths and the measure of a random-time Poisson process of the ground state expectations of fractional (in fact, any real) powers of the boson number operator in the Nelson…

We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse…

Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variables to the reals. We call such a law-determined map, which…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…

Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…

We study ``selective'' or ``conditional'' classification problems under an agnostic setting. Classification tasks commonly focus on modeling the relationship between features and categories that captures the vast majority of data. In…

We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…

We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…

Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…

We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian…

Probabilities enter quantum mechanics via Born's rule, the uniqueness of which was proven by Gleason. Busch subsequently relaxed the assumptions of this proof, expanding its domain of applicability in the process. Extending this work to…

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…

Based on a recent proof of free choices in linking equations to the experiments they describe, I clarify relations among some purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and…

Gaussian correlation conjecture states that the Gaussian measure of the intersection of two symmetric convex sets is greater or equal to the product of the measures.

Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…

We consider the problem of estimating the conditional probability distribution of missing values given the observed ones. We propose an approach, which combines the flexibility of deep neural networks with the simplicity of Gaussian mixture…

The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…