Results 101 to 110 of about 7,890 (182)
Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2135-2160, 15 March 2026.ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
wiley +1 more source
Statistical Analysis of Distance Estimators with Density Differences and Density Ratios
Entropy, 2014 Estimating a discrepancy between two probability distributions from samples is an important task in statistics and machine learning. There are mainly two classes of discrepancy measures: distance measures based on the density difference, such as the Lp ...
Takafumi Kanamori, Masashi Sugiyama
doaj +1 more source
On the Centroids of Symmetrized Bregman Divergences
CoRR, 2007 In this paper, we generalize the notions of centroids and barycenters to the broad class of information-theoretic distortion measures called Bregman divergences. Bregman divergences are versatile, and unify quadratic geometric distances with various statistical entropic measures.
Frank Nielsen, Richard Nock
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General H-theorem and Entropies that Violate the Second Law
Entropy, 2014 H-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the entropy production is positive for random transformation of signals (the ...
Alexander N. Gorban
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Proper scoring rules and Bregman divergence
Bernoulli, 2018 We revisit the mathematical foundations of proper scoring rules (PSRs) and Bregman divergences and present their characteristic properties in a unified theoretical framework. In many situations it is preferable not to generate a PSR directly from its convex entropy on the unit simplex but instead by the sublinear extension of the entropy to the ...
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Entropy, 2017 An abstract, quantitative theory which connects elements of information —key ingredients in the cognitive proces—is developed. Seemingly unrelated results are thereby unified.
Flemming Topsøe
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Robustness Property of Robust-BD Wald-Type Test for Varying-Dimensional General Linear Models
Entropy, 2018 An important issue for robust inference is to examine the stability of the asymptotic level and power of the test statistic in the presence of contaminated data.
Xiao Guo, Chunming Zhang
doaj +1 more source
Total Jensen divergences: Definition, Properties and k-Means++ Clustering
, 2013 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 divergences by a ...
Nielsen, Frank, Nock, Richard
core
Bregman Divergences and Triangle Inequality [PDF]
Proceedings of the 2013 SIAM International Conference on Data Mining, 2013 Sreangsu Acharyya +2 more
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Income Distributions and Decomposable Divergence Measures [PDF]
Inequality indices (i) evaluate the divergence between the income distribution and the hypothetical situation where all individuals have the mean income and (ii) are unambiguously reduced by a Pigou-Dalton progressive transfer.
Brice Magdalou, Richard Nock
core