A Logic for Causal Inference in Time Series with Discrete and Continuous Variables

Kleinberg, Samantha

doi:10.5591/978-1-57735-516-8/IJCAI11-163

A Logic for Causal Inference in Time Series with Discrete and Continuous Variables

Samantha Kleinberg

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Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence. Pages 943-949.

https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-163

Abstract

Many applications of causal inference, such as finding the relationship between stock prices and news reports, involve both discrete and continuous variables observed over time. Inference with these complex sets of temporal data, though, has remained difficult and required a number of simplifications. We show that recent approaches for inferring temporal relationships (represented as logical formulas) can be adapted for inference with continuous valued effects. Building on advances in logic, PCTLc (an extension of PCTL with numerical constraints) is introduced here to allow representation and inference of relationships with a mixture of discrete and continuous components. Then, finding significant relationships in the continuous case can be done using the conditional expectation of an effect, rather than its conditional probability. We evaluate this approach on both synthetically generated and actual financial market data, demonstrating that it can allow us to answer different questions than the discrete approach can.

Samantha Kleinberg. 2011. A Logic for Causal Inference in Time Series with Discrete and Continuous Variables. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11. IJCAI, 943–949. https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-163

@inproceedings{ijcai2011p163,
  title     = {A Logic for Causal Inference in Time Series with Discrete and Continuous Variables},
  author    = {Kleinberg, Samantha},
  booktitle = {Proceedings of the Twenty-Second International Joint Conference on
               Artificial Intelligence, {IJCAI-11}},
  publisher = {AAAI Press/International Joint Conferences on Artificial Intelligence},
  editor    = {Toby Walsh},
  pages     = {943--949},
  year      = {2011},
  month     = {7},
  doi       = {10.5591/978-1-57735-516-8/IJCAI11-163},
  url       = {https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-163},
}

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TI  - A Logic for Causal Inference in Time Series with Discrete and Continuous Variables
AU  - Kleinberg, Samantha
T2  - Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11
PB  - AAAI Press/International Joint Conferences on Artificial Intelligence
PY  - 2011
SP  - 943
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DO  - 10.5591/978-1-57735-516-8/IJCAI11-163
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