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1. Robust and Agnostic Learning of Conditional Distributional Treatment Effects

   Nathan Kallus, Miruna Oprescu (January 2023, Proceedings of the 26th International Conference on Artificial Intelligence and Statistics)

   The conditional average treatment effect (CATE) is the best measure of individual causal effects given baseline covariates. However, the CATE only captures the (conditional) average, and can overlook risks and tail events, which are important to treatment choice. In aggregate analyses, this is usually addressed by measuring the distributional treatment effect (DTE), such as differences in quantiles or tail expectations between treatment groups. Hypothetically, one can similarly fit conditional quantile regressions in each treatment group and take their difference, but this would not be robust to misspecification or provide agnostic best-in-class predictions. We provide a new robust and model-agnostic methodology for learning the conditional DTE (CDTE) for a class of problems that includes conditional quantile treatment effects, conditional super-quantile treatment effects, and conditional treatment effects on coherent risk measures given by f-divergences. Our method is based on constructing a special pseudo-outcome and regressing it on covariates using any regression learner. Our method is model-agnostic in that it can provide the best projection of CDTE onto the regression model class. Our method is robust in that even if we learn these nuisances nonparametrically at very slow rates, we can still learn CDTEs at rates that depend on the class complexity and even conduct inferences on linear projections of CDTEs. We investigate the behavior of our proposal in simulations, as well as in a case study of 401(k) eligibility effects on wealth. 

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2. 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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3. Boosted CVaR Classification

   Zhai, R.; Dan, C.; Suggala, A.; Kolter, Z.; Ravikumar, P. (December 2021, Advances in Neural Information Processing Systems (NeurIPS), 2021)

   Many modern machine learning tasks require models with high tail performance, i.e. high performance over the worst-off samples in the dataset. This problem has been widely studied in fields such as algorithmic fairness, class imbalance, and risk-sensitive decision making. A popular approach to maximize the model’s tail performance is to minimize the CVaR (Conditional Value at Risk) loss, which computes the average risk over the tails of the loss. However, for classification tasks where models are evaluated by the 0/1 loss, we show that if the classifiers are deterministic, then the minimizer of the average 0/1 loss also minimizes the CVaR 0/1 loss, suggesting that CVaR loss minimization is not helpful without additional assumptions. We circumvent this negative result by minimizing the CVaR loss over randomized classifiers, for which the minimizers of the average 0/1 loss and the CVaR 0/1 loss are no longer the same, so minimizing the latter can lead to better tail performance. To learn such randomized classifiers, we propose the Boosted CVaR Classification framework which is motivated by a direct relationship between CVaR and a classical boosting algorithm called LPBoost. Based on this framework, we design an algorithm called alpha-AdaLPBoost. We empirically evaluate our proposed algorithm on four benchmark datasets and show that it achieves higher tail performance than deterministic model training methods. 

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4. Learning to Rank for Optimal Treatment Allocation Under Resource Constraints

   Kamran, Fahad; Makar, Maggie; Wiens, Jenna (May 2024, Proceedings of The 27th International Conference on Artificial Intelligence and Statistics)

   Current causal inference approaches for estimating conditional average treatment effects (CATEs) often prioritize accuracy. However, in resource constrained settings, decision makers may only need a ranking of individuals based on their estimated CATE. In these scenarios, exact CATE estimation may be an unnecessarily challenging task, particularly when the underlying function is difficult to learn. In this work, we study the relationship between CATE estimation and optimizing for CATE ranking, demonstrating that optimizing for ranking may be more appropriate than optimizing for accuracy in certain settings. Guided by our analysis, we propose an approach to directly optimize for rankings of individuals to inform treatment assignment that aims to maximize benefit. Our tree-based approach maximizes the expected benefit of the treatment assignment using a novel splitting criteria. In an empirical case-study across synthetic datasets, our approach leads to better treatment assignments compared to CATE estimation methods as measured by expected total benefit. By providing a practical and efficient approach to learning a CATE ranking, this work offers an important step towards bridging the gap between CATE estimation techniques and their downstream applications. 

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5. A Stochastic Primal-Dual Method for Optimization with Conditional Value at Risk Constraints

   https://doi.org/10.1007/s10957-021-01888-x  

   Madavan, Avinash N.; Bose, Subhonmesh (June 2021, Journal of optimization theory and applications)

   We study a first-order primal-dual subgradient method to optimize risk-constrained risk-penalized optimization problems, where risk is modeled via the popular conditional value at risk (CVaR) measure. The algorithm processes independent and identically distributed samples from the underlying uncertainty in an online fashion and produces an η/√K-approximately feasible and η/√K-approximately optimal point within K iterations with constant step-size, where η increases with tunable risk-parameters of CVaR. We find optimized step sizes using our bounds and precisely characterize the computational cost of risk aversion as revealed by the growth in η. Our proposed algorithm makes a simple modification to a typical primal-dual stochastic subgradient algorithm. With this mild change, our analysis surprisingly obviates the need to impose a priori bounds or complex adaptive bounding schemes for dual variables to execute the algorithm as assumed in many prior works. We also draw interesting parallels in sample complexity with that for chance-constrained programs derived in the literature with a very different solution architecture. 

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