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Convergence Rates of Gradient Methods for Convex Optimization in the Space of Measures
Open Journal of Mathematical Optimization, 2023 We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in $O(\log (k)k^{-1 ...
Chizat, Lénaïc
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Burkholder inequality by Bregman divergence
Bulletin of the Polish Academy of Sciences Mathematics, 2022 We updated a reference, corrected constants c_p and C_p, and made small editorial changes.
Bogdan, Krzysztof, Więcek, Mateusz
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Algorithms, 2022 The family of α-divergences including the oriented forward and reverse Kullback–Leibler divergences is often used in signal processing, pattern recognition, and machine learning, among others.
Frank Nielsen
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Bregman Voronoi Diagrams: Properties, Algorithms and Applications [PDF]
, 2007 The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others.
A. Banerjee +33 more
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Maps on positive definite matrices preserving Bregman and Jensen divergences [PDF]
, 2015 In this paper we determine those bijective maps of the set of all positive definite $n\times n$ complex matrices which preserve a given Bregman divergence corresponding to a differentiable convex function that satisfies certain conditions.
Molnár, Lajos +2 more
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Worst-case and smoothed analysis of k-means clustering with Bregman divergences
Journal of Computational Geometry, 2013 The k-means method is the method of choice for clustering large-scale data sets and it performs exceedingly well in practice despite its exponential worst-case running-time.
Bodo Manthey, Heiko Roeglin
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Non-flat clustering whith alpha-divergences [PDF]
, 2011 International audienceThe scope of the well-known $k$-means algorithm has been broadly extended with some recent results: first, the k-means++ initialization method gives some approximation guarantees; second, the Bregman k-means algorithm generalizes ...
Nielsen, Frank, Schwander, Olivier
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Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences
Entropy, 2015 This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties.
Andrzej Cichocki +2 more
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Discounted dynamic optimization and Bregman divergence
Journal of Mathematical Economics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Metrics defined by Bregman Divergences [PDF]
Communications in Mathematical Sciences, 2008 Bregman divergences are generalizations of the well known Kullback-Leibler divergence. They are based on convex functions and have recently received great attention. We present a class of “squared root metrics” based on Bregman divergences. They can be regarded as natural generalization of Euclidean distance.
Chen, P., Chen, Y., Rao, M.
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