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

Singh, Krishna Nand; Xu, Lei; Gretton, Arthur

doi:10.48550/arxiv.2111.03950

Cited by 4 publications

(13 citation statements)

References 38 publications

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“…[24] present an RKHS estimator for distributional ATT and ATE with binary treatment. The present work more closely relates to works that incorporate kernel ridge regression into treatment effect, dose response, and counterfactual distribution estimation in static [36], proximal [32], dynamic [37], and missing-at-random settings [34]. I prove equally strong results despite additional complexity in the chain of causal influence and in the scope for nonlinearity due to data fusion.…”

Section: Related Workmentioning

confidence: 61%

“…Second, multiple robustness is with respect to ν 0 rather than the conditional density f (m|G = 0, x, d). The technique of sequential mean embeddings permits estimation of ν 0 without estimation of f (m|d, x) [37]. Third, the objects are all feasible in the sense that the treatment only appears for the experimental subpopulation (G = 0) and the outcome only appears for the observational subpopulation (G = 1).…”

Section: If In Addition Assumption 32 Holds Thenmentioning

confidence: 99%

“…See [30,Table 1] for additional examples. In Appendix E, I argue that it is sufficient for either the kernels of the propensity scores to have polynomial spectral decay or for the kernels of the partial mean ν 0 and regression γ 0 to have polynomial spectral decaya kind of multiple spectral robustness [36,37].…”

Section: Guarantees: Discrete Treatmentmentioning

confidence: 99%

“…Derivation of Algorithm 5.1. I adapt the techniques of [37,Algorithm 3] to the long term causal problem. Recall that…”

Section: Finallymentioning

confidence: 99%

“…Lemma E.1 (Uniform regression rate; Proposition 5 of [37]). Suppose Assumptions 5.1, 5.2, and 5.3 hold.…”

Section: E11 Uniform Ratementioning

confidence: 99%

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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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Section: Related Workmentioning

confidence: 61%

Section: If In Addition Assumption 32 Holds Thenmentioning

confidence: 99%

Section: Guarantees: Discrete Treatmentmentioning

confidence: 99%

“…Derivation of Algorithm 5.1. I adapt the techniques of [37,Algorithm 3] to the long term causal problem. Recall that…”

Section: Finallymentioning

confidence: 99%

“…Lemma E.1 (Uniform regression rate; Proposition 5 of [37]). Suppose Assumptions 5.1, 5.2, and 5.3 hold.…”

Section: E11 Uniform Ratementioning

confidence: 99%

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

Singh¹

2022

Preprint

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HILAMA: High-dimensional multi-omic mediation analysis with latent confounding

Wang,

Liu,

et al. 2023

Preprint

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Motivation: The increasingly available multi-omic datasets have posed both new opportunities and challenges to the development of quantitative methods for discovering novel mechanisms in biomedical research. One natural approach to analyzing such datasets is mediation analysis originated from the causal inference literature. Mediation analysis can help unravel the mechanisms through which exposure(s) exert the effect on outcome(s). However, existing methods fail to consider the case where (1) both exposures and mediators are potentially high-dimensional and (2) it is very likely that some important confounding variables are unmeasured or latent; both issues are quite common in practice. To the best of our knowledge, however, no methods have been developed to address these challenges with statistical guarantees. Results: In this article, we propose a new method for HIgh-dimensional LAtent-confounding Mediation Analysis, abbreviated as "HILAMA", that considers both high-dimensional exposures and mediators, and more importantly, the possible existence of latent confounding variables. HILAMA achieves false discovery rate (FDR) control under finite sample size for multiple mediation effect testing. The proposed method is evaluated through extensive simulation experiments, demonstrating its improved stability in FDR control and superior power in finite sample size compared to existing competitive methods. Furthermore, our method is applied to the proteomics-radiomics data from ADNI, identifying some key proteins and brain regions relating to Alzheimer's disease. The results show that HILAMA can effectively control FDR and provide valid statistical inference for high dimensional mediation analysis with latent confounding variables. Availability: The R package HILAMA is publicly available at https://github.com/Cinbo Wang/HILAMA. Contact: cinbo_w@sjtu.edu.cn

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Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection

Singh¹

2021

Preprint

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I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select observations, the outcome is observed. I assume selection is as good as random conditional on treatment and a sufficiently rich set of observed covariates, where the covariates are allowed to cause treatment or be caused by treatment-an extension of missingness-at-random (MAR). I propose estimators of means, increments, and distributions of counterfactual outcomes with closed form solutions in terms of kernel matrix operations, allowing treatment and covariates to be discrete or continuous, and low, high, or infinite dimensional. For the continuous treatment case, I prove uniform consistency with finite sample rates. For the discrete treatment case, I prove √ n consistency, Gaussian approximation, and semiparametric efficiency.

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

Cited by 4 publications

References 38 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

HILAMA: High-dimensional multi-omic mediation analysis with latent confounding

Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection

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