# Valid Inference After Causal Discovery

arXiv: https://arxiv.org/abs/2208.05949 · HTML: https://mlsanity.com/paper/2208.05949/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 77 references that are in the map.
- First posted on arXiv 11 Aug 2022.

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

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Preserving Statistical Validity in Adaptive Data Analysis](https://mlsanity.com/paper/1411.2664/) (2014)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Algorithmic Stability for Adaptive Data Analysis](https://mlsanity.com/paper/1511.02513/) (2015)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [Generalization in Adaptive Data Analysis and Holdout Reuse](https://mlsanity.com/paper/1506.02629/) (2015)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [A New Analysis of Differential Privacy's Generalization Guarantees](https://mlsanity.com/paper/1909.03577/) (2019)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [Max-Information, Differential Privacy, and Post-Selection Hypothesis Testing](https://mlsanity.com/paper/1604.03924/) (2016)
- [Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs](https://mlsanity.com/paper/1303.3216/) (2013)
- [Stable discovery of interpretable subgroups via calibration in causal studies](https://mlsanity.com/paper/2008.10109/) (2020)
- [Splitting strategies for post-selection inference](https://mlsanity.com/paper/2102.02159/) (2021)
- [Data fission: splitting a single data point](https://mlsanity.com/paper/2112.11079/) (2021)
- [Exact Post Model Selection Inference for Marginal Screening](https://mlsanity.com/paper/1402.5596/) (2014)
- [Selective inference for effect modification via the lasso](https://mlsanity.com/paper/1705.08020/) (2017)
- [Towards practical differentially private causal graph discovery](https://mlsanity.com/paper/2006.08598/) (2020)
- [Post-Selection Inference via Algorithmic Stability](https://mlsanity.com/paper/2011.09462/) (2020)
- [A causal fused lasso for interpretable heterogeneous treatment effects estimation](https://mlsanity.com/paper/2110.00901/) (2021)
- [Selective Inference in Propensity Score Analysis](https://mlsanity.com/paper/2105.00416/) (2021)

## Built on by (most cited first, 10 of 10)

- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Improving Finite Sample Performance of Causal Discovery by Exploiting Temporal Structure](https://mlsanity.com/paper/2406.19503/) (2024)
- [SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect Estimation With an Unknown Graph](https://mlsanity.com/paper/2502.07857/) (2025)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [Local Causal Discovery for Statistically Efficient Causal Inference](https://mlsanity.com/paper/2510.14582/) (2025)
- [Your Assumed DAG is Wrong and Here's How To Deal With It](https://mlsanity.com/paper/2502.17030/) (2025)
- [Robust Weighted Triangulation of Causal Effects Under Model Uncertainty](https://mlsanity.com/paper/2603.01119/) (2026)
- [Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects](https://mlsanity.com/paper/2505.02781/) (2025)
- [Integrating Background Knowledge for Scalable Causal Discovery](https://mlsanity.com/paper/2607.10456/) (2026)
- [To do(x) or not to do(x): Medical Image Counterfactuals for Dataset Augmentation](https://mlsanity.com/paper/2609.14124/) (2026)

## Abstract (arXiv)

Causal discovery and causal effect estimation are two fundamental tasks in causal inference. While many methods have been developed for each task individually, statistical challenges arise when applying these methods jointly: estimating causal effects after running causal discovery algorithms on the same data leads to "double dipping," invalidating the coverage guarantees of classical confidence intervals. To this end, we develop tools for valid post-causal-discovery inference. Across empirical studies, we show that a naive combination of causal discovery and subsequent inference algorithms leads to highly inflated miscoverage rates; on the other hand, applying our method provides reliable coverage while achieving more accurate causal discovery than data splitting.