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arXiv 1205.2634cs.AI
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因果结构的时间逻辑

The Temporal Logic of Causal Structures

Courant Institute of Mathematical Sciences(柯朗数学科学研究所);New York University(纽约大学)

Samantha Kleinberg, Bud Mishra

摘要:

具有潜在因果结构的时程数据的计算分析在各种领域都是需要的,包括神经尖峰序列、股票价格波动和基因表达水平。然而,仅从数值时间过程数据确定什么在协调可见过程、将潜在的初步原因分离成真正的原因和虚假的原因并且以可行的计算复杂性来这样做可能是具有挑战性的。为此,我们一直在开发一种新的算法的基础上的框架相结合的概念,因果关系的哲学与算法的方法建立在模型检验和统计技术的多个假设检验。因果关系的时序逻辑公式,重构推理问题的模型检验。所使用的逻辑PCTL允许描述因果关系之间的时间以及观察到这种关系的概率。我们表明,配备了这些因果公式与其相关的概率,我们可以计算的平均影响的原因,使其效果,然后发现统计上显着的原因,通过多个假设检验的概念(治疗每个因果关系作为一个假设),和错误的发现控制。通过探索一个精心选择的家庭的潜在的所有重要的假设与合理的最小描述长度,它是可能的驯服算法的计算复杂性,同时探索几乎完整的搜索空间的所有表面原因。我们已经在许多领域测试了这些想法,并在这里用两个例子来说明它们。

英文摘要:

Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine from just the numerical time course data alone what is coordinating the visible processes, to separate the underlying prima facie causes into genuine and spurious causes and to do so with a feasible computational complexity. For this purpose, we have been developing a novel algorithm based on a framework that combines notions of causality in philosophy with algorithmic approaches built on model checking and statistical techniques for multiple hypotheses testing. The causal relationships are described in terms of temporal logic formulae, reframing the inference problem in terms of model checking. The logic used, PCTL, allows description of both the time between cause and effect and the probability of this relationship being observed. We show that equipped with these causal formulae with their associated probabilities we may compute the average impact a cause makes to its effect and then discover statistically significant causes through the concepts of multiple hypothesis testing (treating each causal relationship as a hypothesis), and false discovery control. By exploring a well-chosen family of potentially all significant hypotheses with reasonably minimal description length, it is possible to tame the algorithm's computational complexity while exploring the nearly complete search-space of all prima facie causes. We have tested these ideas in a number of domains and illustrate them here with two examples.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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