YODO算法:贝叶斯网络灵敏度分析的有效计算框架

R. Ballester-Ripoll, Manuele Leonelli
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引用次数: 1

摘要

灵敏度分析测量贝叶斯网络参数对网络定义的感兴趣的数量的影响,例如变量取特定值的概率。已经定义了各种灵敏度度量来量化这种影响,最常见的是有关网络条件概率的兴趣偏导数数量的一些函数。然而,在具有数千个参数的大型网络中计算这些度量可能会变得非常昂贵。我们提出了一种结合自动微分和精确推理的算法,可以一次有效地计算灵敏度测度。它首先使用变量消去等方法将整个网络边缘化一次,然后反向传播该操作以获得关于所有输入参数的梯度。该方法可用于单向和多向灵敏度分析和可容许区域的推导。仿真研究通过将该算法扩展到具有多达100,000个参数的大规模网络来突出该算法的效率,并研究了通用多路分析的可行性。我们的日常工作还通过两个中等规模的贝叶斯网络进行了展示:第一个网络模拟了人道主义危机的国家风险,第二个网络研究了COVID-19大流行期间技术使用与被迫社会隔离的心理影响之间的关系。使用流行的机器学习库PyTorch的方法实现是免费的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networks
Sensitivity analysis measures the influence of a Bayesian network's parameters on a quantity of interest defined by the network, such as the probability of a variable taking a specific value. Various sensitivity measures have been defined to quantify such influence, most commonly some function of the quantity of interest's partial derivative with respect to the network's conditional probabilities. However, computing these measures in large networks with thousands of parameters can become computationally very expensive. We propose an algorithm combining automatic differentiation and exact inference to efficiently calculate the sensitivity measures in a single pass. It first marginalizes the whole network once, using e.g. variable elimination, and then backpropagates this operation to obtain the gradient with respect to all input parameters. Our method can be used for one-way and multi-way sensitivity analysis and the derivation of admissible regions. Simulation studies highlight the efficiency of our algorithm by scaling it to massive networks with up to 100'000 parameters and investigate the feasibility of generic multi-way analyses. Our routines are also showcased over two medium-sized Bayesian networks: the first modeling the country-risks of a humanitarian crisis, the second studying the relationship between the use of technology and the psychological effects of forced social isolation during the COVID-19 pandemic. An implementation of the methods using the popular machine learning library PyTorch is freely available.
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