# Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithms

arXiv: https://arxiv.org/abs/1712.08914 · HTML: https://mlsanity.com/paper/1712.08914/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2017.

## Built on by (most cited first, 16 of 16)

- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [Normalizing Flows for Interventional Density Estimation](https://mlsanity.com/paper/2209.06203/) (2022)
- [Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation](https://mlsanity.com/paper/2311.11321/) (2023)
- [DiffPO: A causal diffusion model for learning distributions of potential outcomes](https://mlsanity.com/paper/2410.08924/) (2024)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Estimating the treatment effect over time under general interference through deep learner integrated TMLE](https://mlsanity.com/paper/2412.04799/) (2024)
- [Differentiable Pareto-Smoothed Weighting for High-Dimensional Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2404.17483/) (2024)
- [Towards AI-Based Precision Oncology: A Machine Learning Framework for Personalized Counterfactual Treatment Suggestions based on Multi-Omics Data](https://mlsanity.com/paper/2402.12190/) (2024)
- [New User Event Prediction Through the Lens of Causal Inference](https://mlsanity.com/paper/2407.05625/) (2024)
- [Overlap-Adaptive Regularization for Conditional Average Treatment Effect Estimation](https://mlsanity.com/paper/2509.24962/) (2025)
- [Multiple Treatments Causal Effects Estimation with Task Embeddings and Balanced Representation Learning](https://mlsanity.com/paper/2511.09814/) (2025)
- [Matched-Pair Experimental Design with Active Learning](https://mlsanity.com/paper/2509.10742/) (2025)
- [Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes](https://mlsanity.com/paper/2604.27394/) (2026)

## Abstract (arXiv)

We investigate the problem of estimating the causal effect of a treatment on individual subjects from observational data, this is a central problem in various application domains, including healthcare, social sciences, and online advertising. Within the Neyman Rubin potential outcomes model, we use the Kullback Leibler (KL) divergence between the estimated and true distributions as a measure of accuracy of the estimate, and we define the information rate of the Bayesian causal inference procedure as the (asymptotic equivalence class of the) expected value of the KL divergence between the estimated and true distributions as a function of the number of samples. Using Fano method, we establish a fundamental limit on the information rate that can be achieved by any Bayesian estimator, and show that this fundamental limit is independent of the selection bias in the observational data. We characterize the Bayesian priors on the potential (factual and counterfactual) outcomes that achieve the optimal information rate. As a consequence, we show that a particular class of priors that have been widely used in the causal inference literature cannot achieve the optimal information rate. On the other hand, a broader class of priors can achieve the optimal information rate. We go on to propose a prior adaptation procedure (which we call the information based empirical Bayes procedure) that optimizes the Bayesian prior by maximizing an information theoretic criterion on the recovered causal effects rather than maximizing the marginal likelihood of the observed (factual) data. Building on our analysis, we construct an information optimal Bayesian causal inference algorithm.