Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Bregman Distances and Divergences of Probability Measures   The paper introduces scaled Bregman distances of probability distributions
which admit non-uniform contributions of observed events. They are introduced
in a general form covering not only the distances of discrete and continuous
stochastic observations, but also the distances of random processes and
signals. It is shown that the scaled Bregman distances extend not only the
classical ones studied in the previous literature, but also the information
divergence and the related wider class of convex divergences of probability
measures. An information processing theorem is established too, but only in the
sense of invariance w.r.t. statistically sufficient transformations and not in
the sense of universal monotonicity. Pathological situations where coding can
increase the classical Bregman distance are illustrated by a concrete example.
In addition to the classical areas of application of the Bregman distances and
convex divergences such as recognition, classification, learning and evaluation
of proximity of various features and signals, the paper mentions a new
application in 3D-exploratory data analysis. Explicit expressions for the
scaled Bregman distances are obtained in general exponential families, with
concrete applications in the binomial, Poisson and Rayleigh families, and in
the families of exponential processes such as the Poisson and diffusion
processes including the classical examples of the Wiener process and geometric
Brownian motion.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: physics