相关论文: On Mean Divergence Measures
Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…
Comparative convexity is a generalization of convexity relying on abstract notions of means. We define the Jensen divergence and the Jensen diversity from the viewpoint of comparative convexity, and show how to obtain the generalized…
When the individual studies assembled for a meta-analysis report means ($\mu_C$, $\mu_T$) for their treatment (T) and control (C) arms, but those data are on different scales or come from different instruments, the customary measure of…
Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here we resolve the conflict by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics.…
In the paper, the authors find the best possible constants appeared in two inequalities for bounding the Seiffert mean by the linear combinations of the arithmetic, centroidal, and contra-harmonic means.
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
We present a novel class of divergences induced by a smooth convex function called total Jensen divergences. Those total Jensen divergences are invariant by construction to rotations, a feature yielding regularization of ordinary Jensen…
A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true…
We present a refinement, by selfimprovement, of the arithmetic geometric inequality.
We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all its…
This paper considers metrics whose curvature tensor makes sense as a distribution. A class of such metrics, the regular metrics, was defined and studied by Geroch and Traschen. Here, we generalize their definition to form a wider class:…
This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent calculations in six dimensions (partly done…
Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities,…
While recent work has established divergence as a key framework for understanding evenness, there is currently no research exploring how the families of measures within the divergence-based framework relate to each other. This paper uses…
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…
Algorithmic fairness is receiving significant attention in the academic and broader literature due to the increasing use of predictive algorithms, including those based on artificial intelligence. One benefit of this trend is that algorithm…
The Harmonic Mean between the number of papers and the citation number per paper is proposed as a simple single-value index to quantify an individual's research output. Two simple comparisons with the Hirsch h-index are performed.
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…
In this paper, we present the greatest values $\alpha$, $\lambda$ and $p$, and the least values $\beta$, $\mu$ and $q$ such that the double inequalities $\alpha D(a,b)+(1-\alpha)H(a,b)<T(a,b)<\beta D(a,b)+(1-\beta) H(a,b)$, $\lambda…