# Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confounding

arXiv: https://arxiv.org/abs/2306.09520 · HTML: https://mlsanity.com/paper/2306.09520/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 64 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 30 of 40)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [BERTopic: Neural topic modeling with a class-based TF-IDF procedure](https://mlsanity.com/paper/2203.05794/) (2022)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning](https://mlsanity.com/paper/2002.06470/) (2020)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [A Theoretically Grounded Application of Dropout in Recurrent Neural Networks](https://mlsanity.com/paper/1512.05287/) (2015)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [Should ChatGPT be Biased? Challenges and Risks of Bias in Large Language Models](https://mlsanity.com/paper/2304.03738/) (2023)
- [Inductive Biases and Variable Creation in Self-Attention Mechanisms](https://mlsanity.com/paper/2110.10090/) (2021)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Distributional conformal prediction](https://mlsanity.com/paper/1909.07889/) (2019)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
- [Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing](https://mlsanity.com/paper/2102.04543/) (2021)
- [A Rigorous Link between Deep Ensembles and (Variational) Bayesian Methods](https://mlsanity.com/paper/2305.15027/) (2023)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)

## Built on by (most cited first, 7 of 7)

- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework](https://mlsanity.com/paper/2311.18460/) (2023)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Estimating Causal Effects of Text Interventions Leveraging LLMs](https://mlsanity.com/paper/2410.21474/) (2024)
- [Conformal Prediction with Corrupted Labels: Uncertain Imputation and Robust Re-weighting](https://mlsanity.com/paper/2505.04733/) (2025)
- [Amortizing Causal Sensitivity Analysis via Prior Data-Fitted Networks](https://mlsanity.com/paper/2605.10590/) (2026)
- [Uncertainty-aware Causal Decision Making via Effect Bound Decomposition](https://mlsanity.com/paper/2601.22736/) (2026)

## Abstract (arXiv)

Causal inference of exact individual treatment outcomes in the presence of hidden confounders is rarely possible. Recent work has extended prediction intervals with finite-sample guarantees to partially identifiable causal outcomes, by means of a sensitivity model for hidden confounding. In deep learning, predictors can exploit their inductive biases for better generalization out of sample. We argue that the structure inherent to a deep ensemble should inform a tighter partial identification of the causal outcomes that they predict. We therefore introduce an approach termed Caus-Modens, for characterizing causal outcome intervals by modulated ensembles. We present a simple approach to partial identification using existing causal sensitivity models and show empirically that Caus-Modens gives tighter outcome intervals, as measured by the necessary interval size to achieve sufficient coverage. The last of our three diverse benchmarks is a novel usage of GPT-4 for observational experiments with unknown but probeable ground truth.