mlsanityData to 7 Oct 2026

Covariate Balancing Propensity Score by Tailored Loss Functions

arXiv 1601.05890 ↗First posted 22 Jan 2016stat.MEcited by 34

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Abstract (arXiv)

In observational studies, propensity scores are commonly estimated by maxi- mum likelihood but may fail to balance high-dimensional pre-treatment covariates even after specification search. We introduce a general framework that unifies and generalizes several recent proposals to improve covariate balance when designing an observational study. In- stead of the likelihood function, we propose to optimize special loss functions---covariate balancing scoring rules (CBSR)---to estimate the propensity score. A CBSR is uniquely determined by the link function in the GLM and the estimand (a weighted average treatment effect). We show CBSR does not lose asymptotic efficiency to the Bernoulli likelihood in estimating the weighted average treatment effect compared, but CBSR is much more robust in finite sample. Borrowing tools developed in statistical learning, we propose practical strategies to balance covariate functions in rich function classes. This is useful to estimate the maximum bias of the inverse probability weighting (IPW) estimators and construct honest confidence interval in finite sample. Lastly, we provide several numerical examples to demonstrate the trade-off of bias and variance in the IPW-type estimators and the trade-off in balancing different function classes of the covariates.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Jan 2016.

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Citing papers per year: 2021: 6; 2022: 4; 2023: 7; 2024: 3; 2025: 8; 2026: 6.

34 papers.

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  1. 2023Diagnosing Model Performance Under Distribution Shiftcited by 37
  2. 2023Augmented balancing weights as linear regressioncited by 21
  3. 2021End-to-End Balancing for Causal Continuous Treatment-Effect Estimationcited by 9
  4. 2024Stabilized Inverse Probability Weighting via Isotonic Calibrationcited by 8
  5. 2025Direct Bias-Correction Term Estimation for Average Treatment Effect Estimationcited by 8
  6. 2023Fair and Robust Estimation of Heterogeneous Treatment Effects for Policy Learningcited by 6
  7. 2021Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimensioncited by 5
  8. 2021Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curvescited by 5
  9. 2022Outcome Assumptions and Duality Theory for Balancing Weightscited by 5
  10. 2024Differentially Private Covariate Balancing Causal Inferencecited by 5
  11. 2025Direct Debiased Machine Learning via Bregman Divergence Minimizationcited by 5
  12. 2021Estimating Average Treatment Effects with Support Vector Machinescited by 3
22 more
  1. 2021Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing datacited by 3
  2. 2023Calibrated and Conformal Propensity Scores for Causal Effect Estimationcited by 3
  3. 2026Optimally taming biases in black-box models for efficient semiparametric estimationcited by 3
  4. 2023CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regressioncited by 2
  5. 2025A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regressioncited by 2
  6. 2025Riesz Regression As Direct Density Ratio Estimationcited by 2
  7. 2022Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regressioncited by 1
  8. 2022Estimating causal effects with optimization-based methods: A review and empirical comparisoncited by 1
  9. 2022Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controlscited by 1
  10. 2023Scalable kernel balancing weights in a nationwide observational study of hospital profit status and heart attack outcomescited by 1
  11. 2026De-paradox Tree: Breaking Down Simpson's Paradox via A Kernel-Based Partition Algorithmcited by 1
  12. 2026Tailoring Strictly Proper Scoring Rules for Downstream Tasks: An Application to Causal Inferencecited by 1
  13. 2026Optimal use of a black-box learner in semiparametric estimationcited by 1
  14. 2021Rejoinder: Learning Optimal Distributionally Robust Individualized Treatment Rulescited by 0
  15. 2023Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlapcited by 0
  16. 2024Triple/Debiased Lasso for Statistical Inference of Conditional Average Treatment Effectscited by 0
  17. 2025Penalized Empirical Likelihood for Doubly Robust Causal Inference under Contamination in High Dimensionscited by 0
  18. 2025Data Fusion for High-Resolution Estimationcited by 0
  19. 2025Learning density ratios in causal inference using Bregman-Riesz regressioncited by 0
  20. 2025Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inferencecited by 0
  21. 2026genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regressioncited by 0
  22. 2026Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learningcited by 0