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1. Semiparametric Efficient Inference in Adaptive Experiments

   Cook, Thomas; Mishler, Alan; Ramdas, Aaditya (April 2024, Proceedings of Machine Learning Research)

   We consider the problem of efficient inference of the Average Treatment Effect in a sequential experiment where the policy governing the assignment of subjects to treatment or control can change over time. We first provide a central limit theorem for the Adaptive Augmented Inverse-Probability Weighted estimator, which is semiparametric efficient, under weaker assumptions than those previously made in the literature. This central limit theorem enables efficient inference at fixed sample sizes. We then consider a sequential inference setting, deriving both asymptotic and nonasymptotic confidence sequences that are considerably tighter than previous methods. These anytime-valid methods enable inference under data-dependent stopping times (sample sizes). Additionally, we use propensity score truncation techniques from the recent off-policy estimation literature to reduce the finite sample variance of our estimator without affecting the asymptotic variance. Empirical results demonstrate that our methods yield narrower confidence sequences than those previously developed in the literature while maintaining time-uniform error control. 

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2. CAB: Continuous Adaptive Blending Estimator for Policy Evaluation and Learning

   Su, Yi; Wang, Lequn; Santacatterina, Michele; Joachims, Thorsten (April 2019, Proceedings of Machine Learning Research)

   The ability to perform offline A/B-testing and off-policy learning using logged contextual bandit feedback is highly desirable in a broad range of applications, including recommender systems, search engines, ad placement, and personalized health care. Both offline A/B-testing and offpolicy learning require a counterfactual estimator that evaluates how some new policy would have performed, if it had been used instead of the logging policy. In this paper, we present and analyze a family of counterfactual estimators which subsumes most estimators proposed to date. Most importantly, this analysis identifies a new estimator – called Continuous Adaptive Blending (CAB) – which enjoys many advantageous theoretical and practical properties. In particular, it can be substantially less biased than clipped Inverse Propensity Score (IPS) weighting and the Direct Method, and it can have less variance than Doubly Robust and IPS estimators. In addition, it is subdifferentiable such that it can be used for learning, unlike the SWITCH estimator. Experimental results show that CAB provides excellent evaluation accuracy and outperforms other counterfactual estimators in terms of learning performance. 

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3. Empirical likelihood test for a large-dimensional mean vector

   https://doi.org/10.1093/biomet/asaa005  

   Cui, Xia; Li, Runze; Yang, Guangren; Zhou, Wang (March 2020, Biometrika)

   null (Ed.)

   Summary This paper is concerned with empirical likelihood inference on the population mean when the dimension $$p$$ and the sample size $$n$$ satisfy $$p/n\rightarrow c\in [1,\infty)$$. As shown in Tsao (2004), the empirical likelihood method fails with high probability when $p/n>1/2$ because the convex hull of the $$n$$ observations in $$\mathbb{R}^p$$ becomes too small to cover the true mean value. Moreover, when $p> n$, the sample covariance matrix becomes singular, and this results in the breakdown of the first sandwich approximation for the log empirical likelihood ratio. To deal with these two challenges, we propose a new strategy of adding two artificial data points to the observed data. We establish the asymptotic normality of the proposed empirical likelihood ratio test. The proposed test statistic does not involve the inverse of the sample covariance matrix. Furthermore, its form is explicit, so the test can easily be carried out with low computational cost. Our numerical comparison shows that the proposed test outperforms some existing tests for high-dimensional mean vectors in terms of power. We also illustrate the proposed procedure with an empirical analysis of stock data. 

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4. Statistical inference for time‐to‐event data in non‐randomized cohorts with selective attrition

   https://doi.org/10.1002/sim.9952  

   Wang, Tuo; Mao, Lu; Cocco, Aldo; Kim, KyungMann (January 2024, Statistics in Medicine)

   In multi‐season clinical trials with a randomize‐once strategy, patients enrolled from previous seasons who stay alive and remain in the study will be treated according to the initial randomization in subsequent seasons. To address the potentially selective attrition from earlier seasons for the non‐randomized cohorts, we develop an inverse probability of treatment weighting method using season‐specific propensity scores to produce unbiased estimates of survival functions or hazard ratios. Bootstrap variance estimators are used to account for the randomness in the estimated weights and the potential correlations in repeated events within each patient from season to season. Simulation studies show that the weighting procedure and bootstrap variance estimator provide unbiased estimates and valid inferences in Kaplan‐Meier estimates and Cox proportional hazard models. Finally, data from the INVESTED trial are analyzed to illustrate the proposed method. 

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5. Mitigating Bias in Adaptive Data Gathering via Differential Privacy

   Neel, Seth; Roth, Aaron (January 2018, International Conference on Machine Learning (ICML))

   Data that is gathered adaptively --- via bandit algorithms, for example --- exhibits bias. This is true both when gathering simple numeric valued data --- the empirical means kept track of by stochastic bandit algorithms are biased downwards --- and when gathering more complicated data --- running hypothesis tests on complex data gathered via contextual bandit algorithms leads to false discovery. In this paper, we show that this problem is mitigated if the data collection procedure is differentially private. This lets us both bound the bias of simple numeric valued quantities (like the empirical means of stochastic bandit algorithms), and correct the p-values of hypothesis tests run on the adaptively gathered data. Moreover, there exist differentially private bandit algorithms with near optimal regret bounds: we apply existing theorems in the simple stochastic case, and give a new analysis for linear contextual bandits. We complement our theoretical results with experiments validating our theory. 

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