Related papers: Conditional constrained and unconstrained quantiza…
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…
In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values…
The Borel--Kolmogorov paradox of conditioning with respect to events of prior probability zero has fascinated students and researchers since its discovery more than 100 years ago. Classical conditioning is only valid with respect to events…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
These two accompanying papers treat two mode entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. Entanglement is a key quantum feature of composite systems where…
The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…
Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schr\"odinger equation. In addition, linking data points into clusters…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
Most work in neural networks focuses on estimating the conditional mean of a continuous response variable given a set of covariates.In this article, we consider estimating the conditional distribution function using neural networks for both…
In the Quantum-Bayesian interpretation of quantum theory (or QBism), the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In…
We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing…
The quantum nonlocality is limited by relativistic causality, however, the reason is not fully understood yet. The relativistic causality condition on nonlocal correlations has been usually accepted as a prohibition of faster-than-light…
For a family $(\mathscr{A}_x)_{x \in (0,1)}$ of integral quasiarithmetic means sattisfying certain measurability-type assumptions we search for an integral mean $K$ such that $K\big((\mathscr{A}_x(\mathbb{P}))_{x \in…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
Randomized (dithered) quantization is a method capable of achieving white reconstruction error independent of the source. Dithered quantizers have traditionally been considered within their natural setting of uniform quantization. In this…
Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also…
In this work we reexamine the EPR paradox for composite systems with a finite number of levels. The analysis emphasizes the connection between measurements and conditional probabilities. This connection implies that when a measurement is…
While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is…
We propose a summary measure defined as the expected value of a random variable over disjoint subsets of its support that are specified by a given grid of proportions, and consider its use in a regression modeling framework. The obtained…