Regularizing double machine learning in partially linear endogenous models

Emmenegger, Corinne; Bühlmann, Peter

doi:10.1214/21-ejs1931

Cited by 3 publications

(2 citation statements)

References 92 publications

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“…In this paper we focus on linear structural equation models and the two-stage least squares estimator for the sake for simplicity. However, there are many popular alternative instrumental variable estimators, such as the LIML and the JIVE estimator (Anderson et al, 1949;Phillips and Hale, 1977;Angrist et al, 1999) among many others (Okui et al, 2012;Vansteelandt and Didelez, 2018;Emmenegger and Bühlmann, 2021). It remains an interesting research question to what extent our results generalise to these alternative estimators as well as more general settings.…”

Section: Discussionmentioning

confidence: 86%

Graphical tools for selecting conditional instrumental sets

Henckel¹,

Buttenschön²,

Maathuis³

2022

Preprint

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We consider the accurate estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we fully characterise the class of conditional instrumental sets that result in a consistent two-stage least squares estimator for our target total effect. We refer to members of this class as valid conditional instrumental sets. Equipped with this definition, we provide three graphical tools for selecting accurate and valid conditional instrumental sets: First, a graphical criterion that for certain pairs of valid conditional instrumental sets identifies which of the two corresponding estimators has the smaller asymptotic variance. Second, a forward algorithm that greedily adds covariates that reduce the asymptotic variance to a valid conditional instrumental set. Third, a valid conditional instrumental set for which the corresponding estimator has the smallest asymptotic variance we can ensure with a graphical criterion.

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Section: Discussionmentioning

confidence: 86%

Graphical tools for selecting conditional instrumental sets

Henckel¹,

Buttenschön²,

Maathuis³

2022

Preprint

View full text Add to dashboard Cite

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“…All of these works require prior knowledge of valid IVs, while our current paper focuses on the different robust IV frameworks with all IVs being possibly invalid. Double machine learning [15] and regularizing double machine learning [16] were proposed to apply machine learning algorithms to construct estimators of nuisance models. The framework is still built on assuming valid IVs, and the effect identification only uses a linear association between the treatment and the IVs.…”

Section: Comparison To Existing Literaturementioning

confidence: 99%

Two Stage Curvature Identification with Machine Learning: Causal Inference with Possibly Invalid Instrumental Variables

Guo¹,

Bühlmann²

2022

Preprint

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Instrumental variables regression is a popular causal inference method for endogenous treatment. A significant concern in practical applications is the validity and strength of instrumental variables. This paper aims to perform causal inference when all instruments are possibly invalid. To do this, we propose a novel methodology called two stage curvature identification (TSCI) together with a generalized concept to measure the strengths of possibly invalid instruments: such invalid instruments can still be used for inference in our framework. We fit the treatment model with a general machine learning method and propose a novel bias correction method to remove the overfitting bias from machine learning methods. Among a collection of spaces of violation functions, we choose the best one by evaluating invalid instrumental variables' strength. We demonstrate our proposed TSCI methodology in a large-scale simulation study and revisit the important economics question on the effect of education on earnings.

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Sandwich boosting for accurate estimation in partially linear models for grouped data

Young,

Shah

2024

Journal of the Royal Statistical Society Series B: Statistical Methodology

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We study partially linear models in settings where observations are arranged in independent groups but may exhibit within-group dependence. Existing approaches estimate linear model parameters through weighted least squares, with optimal weights (given by the inverse covariance of the response, conditional on the covariates) typically estimated by maximizing a (restricted) likelihood from random effects modelling or by using generalized estimating equations. We introduce a new ‘sandwich loss’ whose population minimizer coincides with the weights of these approaches when the parametric forms for the conditional covariance are well-specified, but can yield arbitrarily large improvements in linear parameter estimation accuracy when they are not. Under relatively mild conditions, our estimated coefficients are asymptotically Gaussian and enjoy minimal variance among estimators with weights restricted to a given class of functions, when user-chosen regression methods are used to estimate nuisance functions. We further expand the class of functional forms for the weights that may be fitted beyond parametric models by leveraging the flexibility of modern machine learning methods within a new gradient boosting scheme for minimizing the sandwich loss. We demonstrate the effectiveness of both the sandwich loss and what we call ‘sandwich boosting’ in a variety of settings with simulated and real-world data.

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Regularizing double machine learning in partially linear endogenous models

Cited by 3 publications

References 92 publications

Graphical tools for selecting conditional instrumental sets

Graphical tools for selecting conditional instrumental sets

Two Stage Curvature Identification with Machine Learning: Causal Inference with Possibly Invalid Instrumental Variables

Sandwich boosting for accurate estimation in partially linear models for grouped data

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