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1. Unit Selection with Nonbinary Treatment and Effect

   Li, Ang; Pearl, Judea (February 2024, {AAAI} Press)

   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”, 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 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. 

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2. Unit Selection Based on Counterfactual Logic

   https://doi.org/10.24963/ijcai.2019/248  

   Li, Ang; Pearl, Judea (August 2019, Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence)

   The unit selection problem aims to identify a set of individuals who are most likely to exhibit a desired mode of behavior, which is defined in counterfactual terms. A typical example is that of selecting individuals who would respond one way if encouraged and a different way if not encouraged. Unlike previous works on this problem, which rely on ad-hoc heuristics, we approach this problem formally, using counterfactual logic, to properly capture the nature of the desired behavior. This formalism enables us to derive an informative selection criterion which integrates experimental and observational data. We demonstrate the superiority of this criterion over A/B-test-based approaches. 

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3. Probabilities of Causation with Nonbinary Treatment and Effect

   Li, Ang; Pearl, Judea (February 2024, {AAAI} Press)

   This paper deals with the problem of estimating the probabilities of causation when treatment and effect are not binary. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN) using experimental and observational data. In this paper, we provide theoretical bounds for all types of probabilities of causation to 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 combinations of data. 

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4. Assessing Disparate Impact of Personalized Interventions: Identifiability and Bounds

   Kallus, Nathan; Zhou, Angela (January 2019, Advances in neural information processing systems)

   Personalized interventions in social services, education, and healthcare leverage individual-level causal effect predictions in order to give the best treatment to each individual or to prioritize program interventions for the individuals most likely to benefit. While the sensitivity of these domains compels us to evaluate the fairness of such policies, we show that actually auditing their disparate impacts per standard observational metrics, such as true positive rates, is impossible since ground truths are unknown. Whether our data is experimental or observational, an individual's actual outcome under an intervention different than that received can never be known, only predicted based on features. We prove how we can nonetheless point-identify these quantities under the additional assumption of monotone treatment response, which may be reasonable in many applications. We further provide a sensitivity analysis for this assumption via sharp partial-identification bounds under violations of monotonicity of varying strengths. We show how to use our results to audit personalized interventions using partially-identified ROC and xROC curves and demonstrate this in a case study of a French job training dataset. 

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5. Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding

   Kallus, Nathan; Mao, Xiaojie; Zhou, Angela (January 2019, Proceedings of Machine Learning Research)

   We study the problem of learning conditional average treatment effects (CATE) from observational data with unobserved confounders. The CATE function maps baseline covariates to individual causal effect predictions and is key for personalized assessments. Recent work has focused on how to learn CATE under unconfoundedness, i.e., when there are no unobserved confounders. Since CATE may not be identified when unconfoundedness is violated, we develop a functional interval estimator that predicts bounds on the individual causal effects under realistic violations of unconfoundedness. Our estimator takes the form of a weighted kernel estimator with weights that vary adversarially. We prove that our estimator is sharp in that it converges exactly to the tightest bounds possible on CATE when there may be unobserved confounders. Further, we study personalized decision rules derived from our estimator and prove that they achieve optimal minimax regret asymptotically. We assess our approach in a simulation study as well as demonstrate its application in the case of hormone replacement therapy by comparing conclusions from a real observational study and clinical trial. 

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