Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or given means and variances. Assuming this sufficient condition, the former bounds are always tight, and the latter bounds are tight when two probability measures have the same variance. An application of these results for nonequilibrium physics is provided.
翻译:在限制下尽量减少差异措施是一个重要问题。我们提出一个充分的条件,即二进制差异措施为在特定三角歧视或特定手段和差异下采取对称差异措施提供了较低的界限。假设这一足够条件,前者的界限总是紧凑的,而后者的界限是紧凑的,如果两个概率措施存在相同差异,则后者的界限是紧凑的。这些结果适用于不平衡物理学。