The temporal logic of causal structures

Samantha Kleinberg, Bhubaneswar Mishra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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 formulæ, 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 formulæ 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.

Original languageEnglish (US)
Title of host publicationProceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009
Pages303-312
Number of pages10
StatePublished - 2009
Event25th Conference on Uncertainty in Artificial Intelligence, UAI 2009 - Montreal, QC, Canada
Duration: Jun 18 2009Jun 21 2009

Other

Other25th Conference on Uncertainty in Artificial Intelligence, UAI 2009
CountryCanada
CityMontreal, QC
Period6/18/096/21/09

Fingerprint

Temporal logic
Model checking
Temporal Logic
Multiple Hypothesis Testing
Computational complexity
Model Checking
Computational Complexity
Testing
Gene expression
Algorithm Complexity
Computational Analysis
Stock Prices
Causality
Spike
Search Space
Gene Expression
Logic
Relationships

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

Cite this

Kleinberg, S., & Mishra, B. (2009). The temporal logic of causal structures. In Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009 (pp. 303-312)

The temporal logic of causal structures. / Kleinberg, Samantha; Mishra, Bhubaneswar.

Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009. 2009. p. 303-312.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kleinberg, S & Mishra, B 2009, The temporal logic of causal structures. in Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009. pp. 303-312, 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009, Montreal, QC, Canada, 6/18/09.
Kleinberg S, Mishra B. The temporal logic of causal structures. In Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009. 2009. p. 303-312
Kleinberg, Samantha ; Mishra, Bhubaneswar. / The temporal logic of causal structures. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009. 2009. pp. 303-312
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