基于广义热力学积分的靶向感知贝叶斯推断
Target-aware Bayesian inference via generalized thermodynamic integration
AI总结：
本文提出广义热力学积分（GTI）方案，将靶向感知的后验期望估计转化为多个独立边际似然估计任务，并通过数值模拟验证其在不同场景下的有效性。
摘要：
在贝叶斯推断中，我们通常关注对后验期望或边际似然（又称贝叶斯证据）等积分的数值近似。本文聚焦于函数 $f(\x)$ 的后验期望计算。我们考虑一种靶向感知场景，其中 $f(\x)$ 事先已知，并可被利用以改进后验期望的估计。在该场景下，这一任务可归结为执行若干独立的边际似然估计任务。使用一系列温度化后验分布路径的思想已在文献中被广泛用于边际似然的计算。热力学积分、路径采样和退火重要性采样都是属于这一类方法的著名算法示例。在本工作中，我们引入了一种广义热力学积分（GTI）方案，该方案能够执行靶向感知的贝叶斯推断，即 GTI 可以近似给定函数的后验期望。文中讨论了 GTI 的若干应用场景，并提供了不同的数值模拟。
英文摘要：
In Bayesian inference, we are usually interested in the numerical approximation of integrals that are posterior expectations or marginal likelihoods (a.k.a., Bayesian evidence). In this paper, we focus on the computation of the posterior expectation of a function $f(\x)$. We consider a \emph{target-aware} scenario where $f(\x)$ is known in advance and can be exploited in order to improve the estimation of the posterior expectation. In this scenario, this task can be reduced to perform several independent marginal likelihood estimation tasks. The idea of using a path of tempered posterior distributions has been widely applied in the literature for the computation of marginal likelihoods. Thermodynamic integration, path sampling and annealing importance sampling are well-known examples of algorithms belonging to this family of methods. In this work, we introduce a generalized thermodynamic integration (GTI) scheme which is able to perform a target-aware Bayesian inference, i.e., GTI can approximate the posterior expectation of a given function. Several scenarios of application of GTI are discussed and different numerical simulations are provided.
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