Propensity Score (MIPS) estimator, proving that MR achieves lower variance among a generalized family of MIPS estimators.

Distribution shift between the training domain and the test domain poses a key challenge for modern machine learning. An extensively studied instance is the \emph{covariate shift}, where the marginal distribution of covariates differs across domains, while the conditional distribution of outcome remains the same. The doubly-robust (DR) estimator, recently introduced by \cite{kato2023double}, combines the density ratio estimation with a pilot regression model and demonstrates asymptotic normality and $\sqrt{n}$-consistency, even when the pilot estimates converge slowly. However, the prior arts has focused exclusively on deriving asymptotic results and has left open the question of non-asymptotic guarantees for the DR estimator. This paper establishes the first non-asymptotic learning bounds for the DR covariate shift adaptation. Our main contributions are two-fold: (\romannumeral 1) We establish \emph{structure-agnostic} high-probability upper bounds on the excess target risk of the DR estimator that depend only on the $L^2$-errors of the pilot estimates and the Rademacher complexity of the model class, without assuming specific procedures to obtain the pilot estimate, and (\romannumeral 2) under \emph{well-specified parameterized models}, we analyze the DR covariate shift adaptation based on modern techniques for non-asymptotic analysis of MLE, whose key terms governed by the Fisher information mismatch term between the source and target distributions. Together, these findings bridge asymptotic efficiency properties and a finite-sample out-of-distribution generalization bounds, providing a comprehensive theoretical underpinnings for the DR covariate shift adaptation.

Propensity Score (MIPS) estimator, proving that MR achieves lower variance among a generalized family of MIPS estimators.

Double robustness is a major selling point of semiparametric and missing data methodology. Its virtues lie in protection against partial nuisance misspecification and asymptotic semiparametric efficiency under correct nuisance specification. However, in many applications, complete nuisance misspecification should be regarded as the norm (or at the very least the expected default), and thus doubly robust estimators may behave fragilely. In fact, it has been amply verified empirically that these estimators can perform poorly when all nuisance functions are misspecified. Here, we first characterize this phenomenon of double fragility, and then propose a solution based on adaptive correction clipping (ACC). We argue that our ACC proposal is safe, in that it inherits the favorable properties of doubly robust estimators under correct nuisance specification, but its error is guaranteed to be bounded by a convex combination of the individual nuisance model errors, which prevents the instability caused by the compounding product of errors of doubly robust estimators. We also show that our proposal provides valid inference through the parametric bootstrap when nuisances are well-specified. We showcase the efficacy of our ACC estimator both through extensive simulations and by applying it to the analysis of Alzheimer's disease proteomics data.

This is a key study in the OPE literature, as methods to provide better stability for off-policy methods are required for practical applications of RL. _x000B_ - Table 1 is useful - provides a good summary and comparison of existing OPE estimators. Section 2.1 further provides a good summary of existing OPE estimators based on consistency, stability and boundedness. This is well written and easy to follow - and useful for the community as it provides a direct comparison between existing OPE estimators in terms of several properties.

Statistical methods for causal inference with continuous treatments mainly focus on estimating the mean potential outcome function, commonly known as the dose-response curve. However, it is often not the dose-response curve but its derivative function that signals the treatment effect. In this paper, we investigate nonparametric inference on the derivative of the dose-response curve with and without the positivity condition. Under the positivity and other regularity conditions, we propose a doubly robust (DR) inference method for estimating the derivative of the dose-response curve using kernel smoothing. When the positivity condition is violated, we demonstrate the inconsistency of conventional inverse probability weighting (IPW) and DR estimators, and introduce novel bias-corrected IPW and DR estimators. In all settings, our DR estimator achieves asymptotic normality at the standard nonparametric rate of convergence. Additionally, our approach reveals an interesting connection to nonparametric support and level set estimation problems. Finally, we demonstrate the applicability of our proposed estimators through simulations and a case study of evaluating a job training program.

The problem of evaluating the effectiveness of a treatment or policy commonly appears in causal inference applications under network interference. In this paper, we suggest the new method of high-dimensional network causal inference (HNCI) that provides both valid confidence interval on the average direct treatment effect on the treated (ADET) and valid confidence set for the neighborhood size for interference effect. We exploit the model setting in Belloni et al. (2022) and allow certain type of heterogeneity in node interference neighborhood sizes. We propose a linear regression formulation of potential outcomes, where the regression coefficients correspond to the underlying true interference function values of nodes and exhibit a latent homogeneous structure. Such a formulation allows us to leverage existing literature from linear regression and homogeneity pursuit to conduct valid statistical inferences with theoretical guarantees. The resulting confidence intervals for the ADET are formally justified through asymptotic normalities with estimable variances. We further provide the confidence set for the neighborhood size with theoretical guarantees exploiting the repro samples approach. The practical utilities of the newly suggested methods are demonstrated through simulation and real data examples.