论文标题
退火路径的变分表示：单调嵌入下的布雷格曼信息
Variational Representations of Annealing Paths: Bregman Information under Monotonic Embedding
论文作者
论文摘要
马尔可夫链蒙特卡洛方法用于从复杂分布和估计归一化常数采样的方法通常会模拟沿着退火路径的一系列中间分布的样品，该路径桥梁在可缝隙的初始分布和目标密度之间桥接。先前的工作已经使用准算术手段构建了退火路径，并将所得的中间密度解释为最大程度地减少了对终点的预期差异。为了分析退火路径的这些变异表示，我们扩展了已知的结果，表明算术平均值在参数上最小化了预期的布雷格曼差异到单个代表点。特别是，当对布雷格曼散发的输入在单调嵌入函数下转换时，我们获得了准算术手段的类似结果。我们的分析强调了使用Rho-Tau代表性Bregman Divergence框架，准算术均值，参数族和发散功能之间的相互作用，并将沿着退火路径的中间密度相关联。
Markov Chain Monte Carlo methods for sampling from complex distributions and estimating normalization constants often simulate samples from a sequence of intermediate distributions along an annealing path, which bridges between a tractable initial distribution and a target density of interest. Prior works have constructed annealing paths using quasi-arithmetic means, and interpreted the resulting intermediate densities as minimizing an expected divergence to the endpoints. To analyze these variational representations of annealing paths, we extend known results showing that the arithmetic mean over arguments minimizes the expected Bregman divergence to a single representative point. In particular, we obtain an analogous result for quasi-arithmetic means, when the inputs to the Bregman divergence are transformed under a monotonic embedding function. Our analysis highlights the interplay between quasi-arithmetic means, parametric families, and divergence functionals using the rho-tau representational Bregman divergence framework, and associates common divergence functionals with intermediate densities along an annealing path.
