相关论文: A note on Talagrand's concentration inequality for…

We derive transport-entropy inequalities for mixed binomial point processes, and for Poisson point processes. We show that when the finite intensity measure satisfies a Talagrand transport inequality, the law of the point process also…

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large…

A conjecture of Talagrand (2010) states that the so-called expectation and fractional expectation thresholds are always within at most some constant factor from each other. In this note we generalize a method of DeMarco and Kahn and settle…

We prove a new concentration inequality for U-statistics of order two for uniformly ergodic Markov chains. Working with bounded and $\pi$-canonical kernels, we show that we can recover the convergence rate of Arcones and Gin{\'e} who proved…

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…

The goal of the article is to improve constants in the infimum convolution inequalities (IC for short) which were introduced by R. Lata{\l}a and J.O. Wojtaszczyk. We show that the exponential distribution satisfies IC with constant $2$ but…

Kernel-based feature selection is an important tool in nonparametric statistics. Despite many practical applications of kernel-based feature selection, there is little statistical theory available to support the method. A core challenge is…

In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…

For a uniform process $\{ X_t: t\in E\}$ (by which $X_t $ is uniformly distributed on $(0,1)$ for $t\in E$) and a function $w(x)>0$ on $(0,1)$, we give a sufficient condition for the weak convergence of the empirical process based on $\{…

Using the smallest eigenvalues of Hankel forms associated with a multidimensional moment problem, we establish a condition equivalent to the existence of a reproducing kernel. This result is a multivariate analogue of Berg, Chen,and…

Correlations for the Bell gedankenexperiment are constructed using probabilities given by quantum mechanics, and nonlocal information. They satisfy Bell's inequality and exhibit spatial non stationarity in angle. Correlations for three…

We give a direct proof of fractional Hardy inequality by means of Littlewood-Paley decomposition and properties of singular homogeneous kernels of degree -$d$. A refinement when $q>2$ is proved.

We show a Talagrand-type concentration inequality for Multi-Task Learning (MTL), using which we establish sharp excess risk bounds for MTL in terms of distribution- and data-dependent versions of the Local Rademacher Complexity (LRC). We…

In a previous paper, we presented several extensions of ACP with conditional expressions, including one with a retrospection operator on conditions to allow for looking back on conditions under which preceding actions have been performed.…

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain $\Omega$ of a rectangular domain $I\times I$ to a covariance kernel on the entire domain $I\times I$. For a…

We develop a new framework for deriving time-uniform concentration bounds for the output of stochastic sequential algorithms satisfying certain recursive inequalities akin to those defining the almost-supermartingale processes introduced by…

In order to certify performance and safety, feedback control requires precise characterization of sensor errors. In this paper, we provide guarantees on such feedback systems when sensors are characterized by solving a supervised learning…

I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in…

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…

Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…