On the optimal estimation of probability measures in weak and strong topologies

Sriperumbudur, Bharath K.

doi:10.3150/15-bej713

Cited by 28 publications

(36 citation statements)

References 30 publications

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“…The desired result follows from [40], as quoted by [31,Theorem 1.1]. The arguments for other counterfactual distributions are identical.…”

Section: Denote the Samples Constructed Bymentioning

confidence: 53%

Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Singh¹

2022

Preprint

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I propose kernel ridge regression estimators for long term causal inference, where a short term experimental data set containing randomized treatment and short term surrogates is fused with a long term observational data set containing short term surrogates and long term outcomes. I propose estimators of treatment effects, dose responses, and counterfactual distributions with closed form solutions in terms of kernel matrix operations. I allow covariates, treatment, and surrogates to be discrete or continuous, and low, high, or infinite dimensional. For long term treatment effects, I prove √ n consistency, Gaussian approximation, and semiparametric efficiency. For long term dose responses, I prove uniform consistency with finite sample rates. For long term counterfactual distributions, I prove convergence in distribution.Preprint. Under review.

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“…The desired result follows from [40], as quoted by [31,Theorem 1.1]. The arguments for other counterfactual distributions are identical.…”

Section: Denote the Samples Constructed Bymentioning

confidence: 53%

Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Singh¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The desired result follows from [68], as quoted by [62,Theorem 1.1]. The arguments for other counterfactual distributions are identical.…”

Section: Proof Of Theoremmentioning

confidence: 53%

Kernel Methods for Multistage Causal Inference: Mediation Analysis and Dynamic Treatment Effects

Singh¹,

Xu²,

Gretton³

2021

Preprint

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We propose kernel ridge regression estimators for mediation analysis and dynamic treatment effects over short horizons. We allow treatments, covariates, and mediators to be discrete or continuous, and low, high, or infinite dimensional. We propose estimators of means, increments, and distributions of counterfactual outcomes with closed form solutions in terms of kernel matrix operations. For the continuous treatment case, we prove uniform consistency with finite sample rates. For the discrete treatment case, we prove √ n consistency, Gaussian approximation, and semiparametric efficiency. We conduct simulations then estimate mediated and dynamic treatment effects of the US Job Corps program for disadvantaged youth.

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“…Here we impose two conditions on the RKHS: universality and that the unit ball is P-Donsker. These conditions hold for most commonly used kernels, such as the Gaussian kernel and Matérn kernel (Sriperumbudur et al, 2016).…”

Section: Asymptotic Propertiesmentioning

confidence: 95%

Robust Sample Weighting to Facilitate Individualized Treatment Rule Learning for a Target Population

Chen¹,

Huling²,

Chen³

et al. 2021

Preprint

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Learning individualized treatment rules (ITRs) is an important topic in precision medicine. Current literature mainly focuses on deriving ITRs from a single source population. We consider the observational data setting when the source population differs from a target population of interest. We assume subject covariates are available from both populations, but treatment and outcome data are only available from the source population. Although adjusting for differences between source and target populations can potentially lead to an improved ITR for the target population, it can substantially increase the variability in ITR estimation. To address this dilemma, we develop a weighting framework that aims to tailor an ITR for a given target population and protect against high variability due to superfluous covariate shift adjustments. Our method seeks covariate balance over a nonparametric function class characterized by a reproducing kernel Hilbert space and can improve many ITR learning methods that rely on weights. We show that the proposed method encompasses importance weights and the so-called overlap weights as two extreme cases, allowing for a better bias-variance trade-off in between. Numerical examples demonstrate that the use of our weighting method can greatly improve ITR estimation for the target population compared with other weighting methods.

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On the optimal estimation of probability measures in weak and strong topologies

Cited by 28 publications

References 30 publications

Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Kernel Methods for Multistage Causal Inference: Mediation Analysis and Dynamic Treatment Effects

Robust Sample Weighting to Facilitate Individualized Treatment Rule Learning for a Target Population

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