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Kernel Debiased Plug-in Estimation: Simultaneous, Automated Debiasing without Influence Functions for Many Target Parameters
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Proposes kernel debiased plug-in estimation (KDPE), an IF-free TMLE-style procedure that uses regularized RKHS-based likelihood updates to debias a single nuisance distribution estimate for many target parameters at once.
Problem
Plug-in estimators of target parameters in nonparametric models suffer first-order plug-in bias; existing debiasing (DML, TMLE, one-step) requires deriving the influence function separately for each target parameter.
Approach
Iteratively perturb an initial distribution estimate along score directions from a mean-zero universal RKHS (Gaussian kernel) via regularized log-likelihood maximization, with a representer theorem reducing the update to n coefficients; the resulting single debiased distribution solves all score equations, so plug-in bias vanishes for any pathwise differentiable parameter without using the influen
Key results
- On DGP1 KDPE RMSE for ATE was 0.0592 versus 0.0574 for TMLE and 0.0635 for HAL (n=300).
- On DGP2 KDPE RMSE for ATE was 0.0295 versus 0.0731 for LTMLE and 0.0589 for HAL (n=300).
- KDPE uses a single debiased distribution estimate to serve as plug-in for ATE, relative risk and odds ratio simultaneously.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use KDPE instead of the SL plug-in estimate | DGP1 ATE estimation · DGP1 | ATE RMSE: 0.0803 -> 0.0592 | Helped |
| Use KDPE instead of the SL plug-in estimate | DGP1 RR estimation · DGP1 | RR RMSE: 0.2623 -> 0.1752 | Helped |
| Use KDPE instead of the SL plug-in estimate | DGP1 OR estimation · DGP1 | OR RMSE: 0.6796 -> 0.4303 | Helped |
| Use KDPE instead of TMLE | DGP1 ATE estimation · DGP1 | ATE RMSE: 0.0574 -> 0.0592 | Hurt |
| Use KDPE instead of TMLE | DGP1 RR estimation · DGP1 | RR RMSE: 0.1723 -> 0.1752 | Hurt |
| Use KDPE instead of TMLE | DGP1 OR estimation · DGP1 | OR RMSE: 0.4059 -> 0.4303 | Hurt |
| Use KDPE instead of HAL | DGP1 ATE estimation · DGP1 | ATE RMSE: 0.0635 -> 0.0592 | Helped |
| Use KDPE instead of HAL | DGP1 RR estimation · DGP1 | RR RMSE: 0.1987 -> 0.1752 | Helped |
| Use KDPE instead of HAL | DGP1 OR estimation · DGP1 | OR RMSE: 0.4795 -> 0.4303 | Helped |
| Use KDPE instead of the SL plug-in estimate | DGP2 ATE estimation · DGP2 | ATE RMSE: 0.0508 -> 0.0295 | Helped |
| Use KDPE instead of the SL plug-in estimate | DGP2 RR estimation · DGP2 | RR RMSE: 0.0925 -> 0.0778 | Helped |
| Use KDPE instead of the SL plug-in estimate | DGP2 OR estimation · DGP2 | OR RMSE: 0.1555 -> 0.0827 | Helped |
Surprising findings
- On the longitudinal DGP2, KDPE substantially outperforms the IF-based LTMLE at n=300, which the authors attribute to LTMLE needing n around 800 to reach the limiting distribution.
Limitations
- Theory relies on a Donsker-type assumption that the authors note is restrictive; sample-splitting analysis is left to future work.
- Simulations use a specific mean-zero Gaussian kernel with closed-form integrals valid only for binary treatment/outcome settings; hyperparameters (c, gamma, lambda) are set by hand.
- Convergence of the iterative KDPE recursion to an interior point is assumed rather than proven.
Experimental setup
Datasets: simulated observational DGP1 simulated longitudinal DGP2
Benchmarks: simulated DGP1 (observational study) simulated DGP2 (longitudinal study)
Metrics: RMSE distributional closeness to limiting normal
Baselines: TMLE LTMLE HAL-MLE SuperLearner plug-in
Builds on: targeted maximum likelihood estimation double machine learning highly adaptive lasso
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