Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divergence functions in dually flat spaces and their properties   In the field of statistics, many kind of divergence functions have been
studied as an amount which measures the discrepancy between two probability
distributions. In the differential geometrical approach in statistics
(information geometry), dually flat spaces play a key role. In a dually flat
space, there exist dual affine coordinate systems and strictly convex functions
called potential and a canonical divergence is naturally introduced as a
function of the affine coordinates and potentials. The canonical divergence
satisfies a relational expression called triangular relation. This can be
regarded as a generalization of the law of cosines in Euclidean space.
  In this paper, we newly introduce two kinds of divergences. The first
divergence is a function of affine coordinates and it is consistent with the
Jeffreys divergence for exponential or mixture families. For this divergence,
we show that more relational equations and theorems similar to Euclidean space
hold in addition to the law of cosines. The second divergences are functions of
potentials and they are consistent with the Bhattacharyya distance for
exponential families and are consistent with the Jensen-Shannon divergence for
mixture families respectively. We derive an inequality between the the first
and the second divergences and show that the inequality is a generalization of
Lin's inequality.

27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom