Model Uncertainty and Correctability for Directed Graphical Models
Model Uncertainty and Correctability for Directed Graphical Models
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DOI：
10.1137/21m1434453
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
P. Birmpa;Jinchao Feng;M. Katsoulakis;Luc Rey-Bellet
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文献类型：
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作者：
P. Birmpa;Jinchao Feng;M. Katsoulakis;Luc Rey-Bellet
概率图模型是概率建模、机器学习和人工智能的基本工具。它们使我们能够以自然的方式集成专家知识，物理建模，异构和相关数据以及感兴趣的数量。正是由于这个原因，模型不确定性的多个来源是图形模型的模块化结构中固有的。在本文中，我们开发了信息理论，强大的不确定性量化方法和非参数压力测试有向图模型，以评估多源模型的不确定性的影响和传播通过图感兴趣的数量。这些方法使我们能够对不同的不确定性来源进行排名，并通过针对感兴趣的数量来校正图形模型中最具影响力的组件。因此，从机器学习的角度来看，我们提供了一个数学上严格的方法来纠正，保证系统的选择，以改善组件的图形模型，同时控制潜在的新的错误在模型的其他部分的过程中创建。我们证明了我们的方法在两个物理化学的例子，即量子尺度通知化学动力学和材料筛选，以提高燃料电池的效率。
Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest. For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. In this paper we develop information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through the graph of multi-sourced model uncertainties to quantities of interest. These methods allow us to rank the different sources of uncertainty and correct the graphical model by targeting its most impactful components with respect to the quantities of interest. Thus, from a machine learning perspective, we provide a mathematically rigorous approach to correctability that guarantees a systematic selection for improvement of components of a graphical model while controlling potential new errors created in the process in other parts of the model. We demonstrate our methods in two physico-chemical examples, namely quantum scale-informed chemical kinetics and materials screening to improve the efficiency of fuel cells.