论文标题
用于近似加权模型集成的蒙特卡洛抗分化
Monte Carlo Anti-Differentiation for Approximate Weighted Model Integration
论文作者
论文摘要
混合结构域中的概率推论，即对离散连续域的推断，需要解决离散变量上的两个众所周知的＃p-hard问题1）〜加权模型计数（WMC），而2）〜在连续变量上集成。对于这两种问题，推理技术都是为了管理其＃p-hardness的开发，例如WMC的知识汇编和连续域中（近似）集成的蒙特卡洛（MC）方法。加权模型集成（WMI）是将WMC扩展到杂种结构域的，已被认为是一种形式主义，以研究离散和连续变量的概率推论。最近开发的WMI求解器的重点是利用WMI问题中的结构，为此，他们依赖符号集成来找到积分的原始性，即执行反差异。为了将这些进步与最先进的蒙特卡洛整合技术结合起来，我们介绍了\ textit {Monte Carlo抗差异}（MCAD），该技术计算了MC的抗衍生物近似值。在经验评估中，我们用MCAD后端代替了现有的WMI求解器中的确切符号整合后端。我们的实验表明，将现有的WMI求解器与MCAD配对的情况会产生快速而可靠的推理方案。
Probabilistic inference in the hybrid domain, i.e. inference over discrete-continuous domains, requires tackling two well known #P-hard problems 1)~weighted model counting (WMC) over discrete variables and 2)~integration over continuous variables. For both of these problems inference techniques have been developed separately in order to manage their #P-hardness, such as knowledge compilation for WMC and Monte Carlo (MC) methods for (approximate) integration in the continuous domain. Weighted model integration (WMI), the extension of WMC to the hybrid domain, has been proposed as a formalism to study probabilistic inference over discrete and continuous variables alike. Recently developed WMI solvers have focused on exploiting structure in WMI problems, for which they rely on symbolic integration to find the primitive of an integrand, i.e. to perform anti-differentiation. To combine these advances with state-of-the-art Monte Carlo integration techniques, we introduce \textit{Monte Carlo anti-differentiation} (MCAD), which computes MC approximations of anti-derivatives. In our empirical evaluation we substitute the exact symbolic integration backend in an existing WMI solver with an MCAD backend. Our experiments show that that equipping existing WMI solvers with MCAD yields a fast yet reliable approximate inference scheme.
