论文标题
基本量度问题及其解决方案
The Base Measure Problem and its Solution
论文作者
论文摘要
概率编程系统通常使用概率密度函数计算，从而使每个此类函数的基本度量隐含。这主要是有效的，但是当意外合并或比较有关不同基础措施的密度时会产生问题。当计算变量的连续变化时，这也会发生错误，这通常取决于支持措施。我们在概率分布和公约转换的可组合库中激励和阐明了问题。我们通过将Hausdorff度量标准化为基础来解决问题，并得出用于比较和组合混合尺寸密度的公式，以及在差异变换下对Hausdorff测量的密度更新。我们还提出了一种软件体系结构，该软件体系结构在常见情况下有效地实现了这些公式。我们希望，通过采用解决方案，概率编程系统可以变得更加健壮和一般，并使从业者可以访问更广泛的模型。
Probabilistic programming systems generally compute with probability density functions, leaving the base measure of each such function implicit. This mostly works, but creates problems when densities with respect to different base measures are accidentally combined or compared. Mistakes also happen when computing volume corrections for continuous changes of variables, which in general depend on the support measure. We motivate and clarify the problem in the context of a composable library of probability distributions and bijective transformations. We solve the problem by standardizing on Hausdorff measure as a base, and deriving formulas for comparing and combining mixed-dimension densities, as well as updating densities with respect to Hausdorff measure under diffeomorphic transformations. We also propose a software architecture that implements these formulas efficiently in the common case. We hope that by adopting our solution, probabilistic programming systems can become more robust and general, and make a broader class of models accessible to practitioners.
