Related papers: A Sequence of Relaxations Constraining Hidden Vari…
The algebraic derivation of the numerical limits of Bell inequalities in either three or four random variables is independent of the assumption of randomness.The limits of the inequalities follow as mathematical consequences of their…
Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables…
This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…
A technique, which we call homogenization, is applied to transform CH-type Bell inequalities, which contain lower order correlations, into CHSH-type Bell inequalities, which are defined for highest order correlation functions. A…
Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing…
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…
Bell nonlocality, the fact that local hidden variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental…
When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
John Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirical adequate hidden-variable models might exist, which presuppose a…
We construct a hidden variable model for the EPR correlations using a Restricted Boltzmann Machine. The model reproduces the expected correlations and thus violates the Bell inequality, as required by Bell's theorem. Unlike most…
In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the…
Latent variable models provide a powerful framework for incorporating and inferring unobserved factors in observational data. In causal inference, they help account for hidden factors influencing treatment or outcome, thereby addressing…
We propose a method to impose homogeneous linear inequality constraints of the form $Ax\leq 0$ on neural network activations. The proposed method allows a data-driven training approach to be combined with modeling prior knowledge about the…
We generalize Bell's hidden variable model describing the singlet state of a two-qubits system by extending it to arbitrary states and observables. As in the original work, we assume a uniform, state-independent probability distribution for…
According to the Bell theorem, local hidden variable theories cannot reproduce all the predictions of quantum mechanics. An important consequence is that under physically reasonable assumptions quantum mechanics predicts correlations that…
The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…
Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments…
Model-free knockoffs is a recently proposed technique for identifying covariates that is likely to have an effect on a response variable. The method is an efficient method to control the false discovery rate in hypothesis tests for separate…
High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…
Bell inequalities play a central role in the study of quantum non-locality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer…