Related papers: Viewing the Welch bound inequality from the kernel…
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from…
Fair machine learning is receiving an increasing attention in machine learning fields. Researchers in fair learning have developed correlation or association-based measures such as demographic disparity, mistreatment disparity, calibration,…
Infinite--Layer Networks (ILN) have recently been proposed as an architecture that mimics neural networks while enjoying some of the advantages of kernel methods. ILN are networks that integrate over infinitely many nodes within a single…
The paper discusses the concept of separation of quantum mechanical systems in the algebraic approach. We review known theorems, then establish a link between the C*-algebraic and the corresponding W*-algebraic concepts. A characterization…
In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…
Bell inequalities characterize the boundary of the local-realist correlation polytope -- the set of joint probability distributions achievable by classical hidden-variable models. Quantum mechanics exceeds this boundary through…
Despite the high interest for Machine Learning (ML) in academia and industry, many issues related to the application of ML to real-life problems are yet to be addressed. Here we put forward one limitation which arises from a lack of…
The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed,…
Behavioural metrics have been shown to be an effective mechanism for constructing representations in reinforcement learning. We present a novel perspective on behavioural metrics for Markov decision processes via the use of positive…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…
Causal inequalities are bounds on correlations obtained when operations take place in a causal sequence, i.e. in which the background time or definite causal structure pre-exists such that every operation is either in the future, in the…
The Welch Bound is a lower bound on the root mean square cross correlation between $n$ unit-norm vectors $f_1,...,f_n$ in the $m$ dimensional space ($\mathbb{R} ^m$ or $\mathbb{C} ^m$), for $n\geq m$. Letting $F = [f_1|...|f_n]$ denote the…
Algorithmic fairness, the research field of making machine learning (ML) algorithms fair, is an established area in ML. As ML technologies expand their application domains, including ones with high societal impact, it becomes essential to…
The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive…
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
Quantum channel discrimination is a fundamental problem in quantum information science. In this study, we consider general quantum channel discrimination problems, and derive the lower bounds of the error probability. Our lower bounds are…
We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or…
An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system…
This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper \cite{Gower:1986}. The first correction is needed in order to establish the existence of…