# Model-based causal feature selection for general response types

arXiv: https://arxiv.org/abs/2309.12833 · HTML: https://mlsanity.com/paper/2309.12833/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 90 references that are in the map.
- First posted on arXiv 22 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs](https://mlsanity.com/paper/1303.3216/) (2013)
- [Estimating the effect of joint interventions from observational data in sparse high-dimensional settings](https://mlsanity.com/paper/1407.2451/) (2014)
- [Most Likely Transformations](https://mlsanity.com/paper/1508.06749/) (2015)
- [Conditional Independence Testing in Hilbert Spaces with Applications to Functional Data Analysis](https://mlsanity.com/paper/2101.07108/) (2021)
- [Distributional Anchor Regression](https://mlsanity.com/paper/2101.08224/) (2021)
- [Invariant Ancestry Search](https://mlsanity.com/paper/2202.00913/) (2022)
- [Switching Regression Models and Causal Inference in the Presence of Discrete Latent Variables](https://mlsanity.com/paper/1808.05541/) (2018)
- [Identifying the Causes of Pyrocumulonimbus (PyroCb)](https://mlsanity.com/paper/2211.08883/) (2022)
- [Survival Forests under Test: Impact of the Proportional Hazards Assumption on Prognostic and Predictive Forests for ALS Survival](https://mlsanity.com/paper/1902.01587/) (2019)
- [A Transformation Perspective on Marginal and Conditional Models](https://mlsanity.com/paper/1910.09219/) (2019)

## Built on by (most cited first, 3 of 3)

- [Bayesian Hierarchical Invariant Prediction](https://mlsanity.com/paper/2505.11211/) (2025)
- [A Conditional Distribution Equality Testing Framework using Deep Generative Learning](https://mlsanity.com/paper/2509.17729/) (2025)
- [Prediction-Intervention Games and Invariant Sets](https://mlsanity.com/paper/2605.16828/) (2026)

## Abstract (arXiv)

Discovering causal relationships from observational data is a fundamental yet challenging task. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings and exploits that causal models are invariant. ICP has been extended to general additive noise models and to nonparametric settings using conditional independence tests. However, the latter often suffer from low power (or poor type I error control) and additive noise models are not suitable for applications in which the response is not measured on a continuous scale, but reflects categories or counts. Here, we develop transformation-model (TRAM) based ICP, allowing for continuous, categorical, count-type, and uninformatively censored responses (these model classes, generally, do not allow for identifiability when there is no exogenous heterogeneity). As an invariance test, we propose TRAM-GCM based on the expected conditional covariance between environments and score residuals with uniform asymptotic level guarantees. For the special case of linear shift TRAMs, we also consider TRAM-Wald, which tests invariance based on the Wald statistic. We provide an open-source R package 'tramicp' and evaluate our approach on simulated data and in a case study investigating causal features of survival in critically ill patients.