Inference for a Large Directed Acyclic Graph with Unspecified Interventions.

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2023-01-01
Chunlin Li, Xiaotong Shen, Wei Pan
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引用次数: 0

Abstract

Statistical inference of directed relations given some unspecified interventions (i.e., the intervention targets are unknown) is challenging. In this article, we test hypothesized directed relations with unspecified interventions. First, we derive conditions to yield an identifiable model. Unlike classical inference, testing directed relations requires to identify the ancestors and relevant interventions of hypothesis-specific primary variables. To this end, we propose a peeling algorithm based on nodewise regressions to establish a topological order of primary variables. Moreover, we prove that the peeling algorithm yields a consistent estimator in low-order polynomial time. Second, we propose a likelihood ratio test integrated with a data perturbation scheme to account for the uncertainty of identifying ancestors and interventions. Also, we show that the distribution of a data perturbation test statistic converges to the target distribution. Numerical examples demonstrate the utility and effectiveness of the proposed methods, including an application to infer gene regulatory networks. The R implementation is available at https://github.com/chunlinli/intdag.

Abstract Image

Abstract Image

Abstract Image

具有未指定干预的大有向非循环图的推理。
在给定一些未指明的干预措施(即干预目标未知)的情况下,对定向关系进行统计推断是具有挑战性的。在这篇文章中,我们测试了假设的直接关系与未指明的干预措施。首先,我们导出了产生可识别模型的条件。与经典推理不同,测试定向关系需要识别特定假设的主要变量的祖先和相关干预。为此,我们提出了一种基于节点回归的剥离算法来建立主变量的拓扑顺序。此外,我们证明了剥离算法在低阶多项式时间内产生了一致的估计量。其次,我们提出了一种与数据扰动方案相结合的似然比检验,以解释识别祖先和干预措施的不确定性。此外,我们还证明了数据扰动测试统计量的分布收敛于目标分布。数值例子证明了所提出的方法的实用性和有效性,包括推断基因调控网络的应用。R的实施可在https://github.com/chunlinli/intdag.
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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