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1. Policy Evaluation with Latent Confounders via Optimal Balance

   Bennett, Andrew; Kallus, Nathan (January 2019, Advances in neural information processing systems)

   Evaluating novel contextual bandit policies using logged data is crucial in applications where exploration is costly, such as medicine. But it usually relies on the assumption of no unobserved confounders, which is bound to fail in practice. We study the question of policy evaluation when we instead have proxies for the latent confounders and develop an importance weighting method that avoids fitting a latent outcome regression model. Surprisingly, we show that there exist no single set of weights that give unbiased evaluation regardless of outcome model, unlike the case with no unobserved confounders where density ratios are sufficient. Instead, we propose an adversarial objective and weights that minimize it, ensuring sufficient balance in the latent confounders regardless of outcome model. We develop theory characterizing the consistency of our method and tractable algorithms for it. Empirical results validate the power of our method when confounders are latent. 

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2. Spectral Representation for Causal Estimation with Hidden Confounders

   Sun, Haotian; Moulin, Antoine; Ren, Tongzheng; Gretton, Arthur; Dai, Bo (May 2025, PMLR)

   Li, Yingzhen; Mandt, Stephan; Agrawal, Shipra; Khan, Emtiyaz (Ed.)

   We study the problem of causal effect estimation in the presence of unobserved confounders, focusing on two settings: instrumental variable (IV) regression with additional observed confounders, and proxy causal learning. Our approach uses a singular value decomposition of a conditional expectation operator combined with a saddle-point optimization method. In the IV regression setting, this can be viewed as a neural network generalization of the seminal approach due to Darolles et al. (2011). Saddle-point formulations have recently gained attention because they mitigate the double-sampling bias and are compatible with modern function approximation methods. We provide experimental validation across various settings and show that our approach outperforms existing methods on common benchmarks. 

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3. Deconfounded Causal Collaborative Filtering

   https://doi.org/10.1145/3606035  

   Xu, Shuyuan; Tan, Juntao; Heinecke, Shelby; Li, Vena Jia; Zhang, Yongfeng (June 2023, ACM Transactions on Recommender Systems)

   Recommender systems may be confounded by various types of confounding factors (also called confounders) that may lead to inaccurate recommendations and sacrificed recommendation performance. Current approaches to solving the problem usually design each specific model for each specific confounder. However, real-world systems may include a huge number of confounders and thus designing each specific model for each specific confounder could be unrealistic. More importantly, except for those “explicit confounders” that experts can manually identify and process such as item’s position in the ranking list, there are also many “latent confounders” that are beyond the imagination of experts. For example, users’ rating on a song may depend on their current mood or the current weather, and users’ preference on ice creams may depend on the air temperature. Such latent confounders may be unobservable in the recorded training data. To solve the problem, we propose Deconfounded Causal Collaborative Filtering (DCCF). We first frame user behaviors with unobserved confounders into a causal graph, and then we design a front-door adjustment model carefully fused with machine learning to deconfound the influence of unobserved confounders. Experiments on real-world datasets show that our method is able to deconfound unobserved confounders to achieve better recommendation performance. 

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4. Binscatter regressions

   https://doi.org/10.1177/1536867X251322960  

   Cattaneo, Matias D; Crump, Richard K; Farrell, Max H; Feng, Yingjie (March 2025, The Stata Journal: Promoting communications on statistics and Stata)

   In this article, we introduce the packagebinsreg, which implements the binscatter methods developed by Cattaneo et al. (2024a, arXiv:2407.15276 [stat.EM]; 2024b,American Economic Review114: 1488–1514). The package comprises seven commands:binsreg, binslogit, binsprobit, binsqreg, binstest binspwc, andbinsregselect. The first four commands implement binscatter plotting, point estimation, and uncertainty quantification (confidence intervals and confidence bands) for least-squares linear binscatter regression (binsreg) and for nonlinear binscatter regression (binslogitfor logit regression,binsprobitfor. probit regression, andbinsqregfor quantile regression). The next two commands focus on pointwise and uniform inference:binstestimplements hypothesis testing procedures for parametric specifications and for nonparametric shape restrictions of the unknown regression function, whilebinspwcimplements multigroup pairwise statistical comparisons. The last command,binsregselect, implements. data-driven number-of-bins selectors. The commands offer binned scatterplots and allow for covariate adjustment, weighting, clustering, and multisample analysis, which is useful when studying treatment-effect heterogeneity in randomizec and observational studies, among many other features. 

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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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