# Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data

arXiv: https://arxiv.org/abs/1710.08074 · HTML: https://mlsanity.com/paper/1710.08074/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2017.

## Built on by (most cited first, 15 of 15)

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- [Outcome Assumptions and Duality Theory for Balancing Weights](https://mlsanity.com/paper/2203.09557/) (2022)
- [A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond](https://mlsanity.com/paper/2205.10198/) (2022)
- [Optimal Treatment Regimes for Proximal Causal Learning](https://mlsanity.com/paper/2212.09494/) (2022)
- [Improving the Finite Sample Estimation of Average Treatment Effects using Double/Debiased Machine Learning with Propensity Score Calibration](https://mlsanity.com/paper/2409.04874/) (2024)
- [Estimating Average Treatment Effects with Support Vector Machines](https://mlsanity.com/paper/2102.11926/) (2021)
- [Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing data](https://mlsanity.com/paper/2107.07371/) (2021)
- [Calibrated and Conformal Propensity Scores for Causal Effect Estimation](https://mlsanity.com/paper/2306.00382/) (2023)
- [Riesz Regression As Direct Density Ratio Estimation](https://mlsanity.com/paper/2511.04568/) (2025)
- [Tractable and Near-Optimal Adversarial Algorithms for Robust Estimation in Contaminated Gaussian Models](https://mlsanity.com/paper/2112.12919/) (2021)
- [De-paradox Tree: Breaking Down Simpson's Paradox via A Kernel-Based Partition Algorithm](https://mlsanity.com/paper/2603.02174/) (2026)
- [Incorporating External Controls for Estimating the Average Treatment Effect on the Treated with High-Dimensional Data: Retaining Double Robustness and Ensuring Double Safety](https://mlsanity.com/paper/2509.20586/) (2025)
- [genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regression](https://mlsanity.com/paper/2602.17543/) (2026)
- [Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes](https://mlsanity.com/paper/2604.27394/) (2026)
- [Target-Aware Linear Regression Under Distribution Shift](https://mlsanity.com/paper/2606.22775/) (2026)

## Abstract (arXiv)

Propensity score methods are widely used for estimating treatment effects from observational studies. A popular approach is to estimate propensity scores by maximum likelihood based on logistic regression, and then apply inverse probability weighted estimators or extensions to estimate treatment effects. However, a challenging issue is that such inverse probability weighting methods including doubly robust methods can perform poorly even when the logistic model appears adequate as examined by conventional techniques. In addition, there is increasing difficulty to appropriately estimate propensity scores when dealing with a large number of covariates. To address these issues, we study calibrated estimation as an alternative to maximum likelihood estimation for fitting logistic propensity score models. We show that, with possible model misspecification, minimizing the expected calibration loss underlying the calibrated estimators involves reducing both the expected likelihood loss and a measure of relative errors which controls the mean squared errors of inverse probability weighted estimators. Furthermore, we propose a regularized calibrated estimator by minimizing the calibration loss with a Lasso penalty. We develop a novel Fisher scoring descent algorithm for computing the proposed estimator, and provide a high-dimensional analysis of the resulting inverse probability weighted estimators of population means, leveraging the control of relative errors for calibrated estimation. We present a simulation study and an empirical application to demonstrate the advantages of the proposed methods compared with maximum likelihood and regularization.