Probabilities of causation are proven to be critical in modern decision-making. This paper deals with the problem of estimating the probabilities of causation when treatment and effect are not binary. Pearl defined the binary probabilities of causation, such as the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN). Tian and Pearl then derived sharp bounds for these probabilities of causation using experimental and observational data. In this paper, we define and provide theoretical bounds for all types of probabilities of causation with multivalued treatments and effects. We further discuss examples where our bounds guide practical decisions and use simulation studies to evaluate how informative the bounds are for various data combinations.

Probabilities of Causation with Nonbinary Treatment and Effect

The unit selection problem aims to identify a set of individuals who are most likely to exhibit a desired mode of behavior or to evaluate the percentage of such individuals in a given population, for example, selecting individuals who would respond one way if encouraged and a different way if not encouraged (Li and Pearl 2019). Using a combination of experimental and observational data, Li and Pearl solved the binary unit selection problem (binary treatment and effect) by deriving tight bounds on the "benefit function," which is the payoff/cost associated with selecting an individual with given characteristics. This paper extends the benefit function to the general form such that the treatment and effect are not restricted to binary. We then propose an algorithm to test the identifiability of the nonbinary benefit function and an algorithm to compute the bounds of the nonbinary benefit function using experimental and observational data.

Unit Selection with Nonbinary Treatment and Effect

The unit selection problem aims to identify a set of individuals who are most likely to exhibit a desired mode of behavior, for example, selecting individuals who would respond one way if encouraged and a different way if not encouraged. Using a combination of experimental and observational data, Li and Pearl derived tight bounds on the "benefit function" - the payoff/cost associated with selecting an individual with given characteristics. This paper shows that these bounds can be narrowed significantly (enough to change decisions) when structural information is available in the form of a causal model. We address the problem of estimating the benefit function using observational and experimental data when specific graphical criteria are assumed to hold.

Unit Selection with Causal Diagram

This paper addresses the problem of estimating causal effects when adjustment variables in the back-door or front-door criterion are partially observed. For such scenarios, we derive bounds on the causal effects by solving two non-linear optimization problems, and demonstrate that the bounds are sufficient. Using this optimization method, we propose a framework for dimensionality reduction that allows one to trade bias for estimation power, and demonstrate its performance using simulation studies.

Bounds on Causal Effects and Application to High Dimensional Data

Main Track - RU

technical paper

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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. 

Main_Track

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

Judea Pearl

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SHORT BIO

Presentations

Probabilities of Causation with Nonbinary Treatment and Effect

Unit Selection with Nonbinary Treatment and Effect

Unit Selection with Causal Diagram

Bounds on Causal Effects and Application to High Dimensional Data

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