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Minimax quantum state estimation under Bregman divergence [PDF]
Quantum, 2019 We investigate minimax estimators for quantum state tomography under general Bregman divergences. First, generalizing the work of Koyama et al. [Entropy 19, 618 (2017)] for relative entropy, we find that given any estimator for a quantum state, there ...
Maria Quadeer +2 more
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The Burbea-Rao and Bhattacharyya centroids [PDF]
, 2011 We study the centroid with respect to the class of information-theoretic Burbea-Rao divergences that generalize the celebrated Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and differentiable ...
Frank Nielsen +2 more
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Entropy, 2014 Information geometry studies the dually flat structure of a manifold, highlighted by the generalized Pythagorean theorem. The present paper studies a class of Bregman divergences called the (ρ,τ)-divergence.
Shun-ichi Amari
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Cost-sensitive learning based on Bregman divergences [PDF]
Machine Learning, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Santos-Rodríguez, Raúl +3 more
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Domain Adaptation via Bregman divergence minimization [PDF]
Scientia Iranica, 2021 In recent years, Fisher linear discriminant analysis (FLDA) based classifi- cation is one of the most successful approaches and has been shown effective performance in different classification tasks. However, when the learning data (source domain) have a different distribution against the testing data (tar- get domain), the FLDA-based models may not be ...
Mozhdeh Zandifar +2 more
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Beta-Divergence as a Subclass of Bregman Divergence [PDF]
IEEE Signal Processing Letters, 2011 In this paper, we present a complete proof that the β-divergence is a particular case of Bregman divergence. This little-known result makes it possible to straightforwardly apply theorems about Bregman divergences to β-divergences. This is of interest for numerous applications since these divergences are widely used, for instance in non-negative matrix
Romain Hennequin +2 more
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Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities
Entropy, 2010 In this paper, we extend and overview wide families of Alpha-, Beta- and Gamma-divergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) divergence is considered.
Andrzej Cichocki, Shun-ichi Amari
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Sum decomposition of divergence into three divergences
, 2018 Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the f-divergences. In
Nishiyama, Tomohiro
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Machine Learning and Knowledge ExtractionThe purpose of this paper is twofold. On a technical side, we propose an extension of the Hausdorff distance from metric spaces to spaces equipped with asymmetric distance measures.
Tuyen Pham +2 more
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Entropy, 2015 A scoring rule is a device for evaluation of forecasts that are given in terms of the probability of an event. In this article we will restrict our attention to binary forecasts.
Gareth Hughes, Cairistiona F.E. Topp
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