Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals

• URL: http://arxiv.org/abs/2104.02929v1
• Date: Wed, 7 Apr 2021 05:52:15 GMT
• Title: Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals
• Authors: AmirEmad Ghassami, Andrew Ying, Ilya Shpitser, Eric Tchetgen Tchetgen
• Abstract summary: We consider a class of doubly robust moment functions originally introduced in (Robins et al., 2008) We demonstrate that this moment function can be used to construct estimating equations for the nuisance functions. The convergence rates of the nuisance functions are analyzed using the modern techniques in statistical learning theory.
• Score: 16.768606469968113
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A moment function is called doubly robust if it is comprised of two nuisance functions and the estimator based on it is a consistent estimator of the target parameter even if one of the nuisance functions is misspecified. In this paper, we consider a class of doubly robust moment functions originally introduced in (Robins et al., 2008). We demonstrate that this moment function can be used to construct estimating equations for the nuisance functions. The main idea is to choose each nuisance function such that it minimizes the dependency of the expected value of the moment function to the other nuisance function. We implement this idea as a minimax optimization problem. We then provide conditions required for asymptotic linearity of the estimator of the parameter of interest, which are based on the convergence rate of the product of the errors of the nuisance functions, as well as the local ill-posedness of a conditional expectation operator. The convergence rates of the nuisance functions are analyzed using the modern techniques in statistical learning theory based on the Rademacher complexity of the function spaces. We specifically focus on the case that the function spaces are reproducing kernel Hilbert spaces, which enables us to use its spectral properties to analyze the convergence rates. As an application of the proposed methodology, we consider the parameter of average causal effect both in presence and absence of latent confounders. For the case of presence of latent confounders, we use the recently proposed proximal causal inference framework of (Miao et al., 2018; Tchetgen Tchetgen et al., 2020), and hence our results lead to a robust non-parametric estimator for average causal effect in this framework.

Related papers

• Two-Stage Nuisance Function Estimation for Causal Mediation Analysis [8.288031125057524]
  We propose a two-stage estimation strategy that estimates the nuisance functions based on the role they play in the structure of the bias of the influence function-based estimator of the mediation functional. We provide analysis of the proposed method, as well as sufficient conditions for consistency and normality of the estimator of the parameter of interest.
  arXiv  Detail & Related papers  (2024-03-31T16:38:48Z)
• Doubly Robust Proximal Causal Learning for Continuous Treatments [56.05592840537398]
  We propose a kernel-based doubly robust causal learning estimator for continuous treatments. We show that its oracle form is a consistent approximation of the influence function. We then provide a comprehensive convergence analysis in terms of the mean square error.
  arXiv  Detail & Related papers  (2023-09-22T12:18:53Z)
• Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization [73.80101701431103]
  The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. We study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility.
  arXiv  Detail & Related papers  (2023-04-17T14:23:43Z)
• One-Step Estimation of Differentiable Hilbert-Valued Parameters [2.0305676256390934]
  We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. These estimators correspond to generalizations of cross-fitted one-step estimators based on Hilbert-valued efficient influence functions.
  arXiv  Detail & Related papers  (2023-03-29T14:06:00Z)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• Nuisance Function Tuning and Sample Splitting for Optimal Doubly Robust Estimation [5.018363990542611]
  We consider the problem of how to estimate nuisance functions to obtain optimal rates of convergence for a doubly robust nonparametric functional. We show that plug-in and first-order biased-corrected estimators can achieve minimax rates of convergence across all H"older smoothness classes of the nuisance functions.
  arXiv  Detail & Related papers  (2022-12-30T18:17:06Z)
• Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regression [1.7227952883644062]
  This paper studies the convergence performance of divide-and-conquer estimators in the scenario that the target function does not reside in the underlying kernel space. As a decomposition-based scalable approach, the divide-and-conquer estimators of functional linear regression can substantially reduce the algorithmic complexities in time and memory.
  arXiv  Detail & Related papers  (2022-11-20T12:29:06Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Inference on Strongly Identified Functionals of Weakly Identified Functions [71.42652863687117]
  We study a novel condition for the functional to be strongly identified even when the nuisance function is not. We propose penalized minimax estimators for both the primary and debiasing nuisance functions.
  arXiv  Detail & Related papers  (2022-08-17T13:38:31Z)
• Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach [84.29777236590674]
  We study the estimation of causal parameters when not all confounders are observed and instead negative controls are available. Recent work has shown how these can enable identification and efficient estimation via two so-called bridge functions.
  arXiv  Detail & Related papers  (2021-03-25T17:59:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.