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Statistical Learning Algorithms Based on Bregman Distances
, 1997
"... We present a class of statistical learning algorithms formulated in terms of minimizing Bregman distances, a family of generalized entropy measures associated with convex functions. The inductive learning scheme is akin to growing a decision tree, with the Bregman distance filling the role of the im ..."
Abstract

Cited by 26 (1 self)
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We present a class of statistical learning algorithms formulated in terms of minimizing Bregman distances, a family of generalized entropy measures associated with convex functions. The inductive learning scheme is akin to growing a decision tree, with the Bregman distance filling the role of the impurity function in treebased classifiers. Our approach is based on two components. In the feature selection step, each linear constraint in a pool of candidate features is evaluated by the reduction in Bregman distance that would result from adding it to the model. In the constraint satisfaction step, all of the parameters are adjusted to minimize the Bregman distance subject to the chosen constraints. We introduce a new iterative estimation algorithm for carrying out both the feature selection and constraint satisfaction steps, and outline a proof of the convergence of these algorithms. 1 Introduction In this paper we present a class of statistical learning algorithms formulated in terms...
Bregman divergence as relative operator entropy
"... In this paper the Bregman operator divergence is introduced for density matrices by differentiation of the matrixvalued function x 7! x log x. This quantity is compared with the relative operator entropy of Fujii and Kamei. It turns out that the trace is the usual Umegaki's relative entropy wh ..."
Abstract

Cited by 4 (0 self)
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In this paper the Bregman operator divergence is introduced for density matrices by differentiation of the matrixvalued function x 7! x log x. This quantity is compared with the relative operator entropy of Fujii and Kamei. It turns out that the trace is the usual Umegaki's relative entropy which is the only intersection of the classes of quasientropies and Bregman divergences.