# From Training to Deployment: Post-Hoc Causal Feature Identification via Sensitivity Ratios

arXiv: https://arxiv.org/abs/2607.25546 · HTML: https://mlsanity.com/paper/2607.25546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 10 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Contrastive representations of high-dimensional, structured treatments](https://mlsanity.com/paper/2411.19245/) (2024)

## Abstract (arXiv)

Given a model that is already trained, which features does it rely on causally versus spuriously? Existing methods require access to the training procedure and cannot answer this post-hoc. We introduce the Normalised Sensitivity Ratio~(NSR), a post-hoc, model-agnostic diagnostic for this question under a structured-shift regime: environments differ primarily in the mean of spurious features while the causal mechanism and causal marginals remain stable, as in multi-site clinical data or multi-batch genomics. Within this regime, causal features induce constant model sensitivity across environments while spurious features track shift. NSR formalises this as the squared coefficient of variation of per-environment sensitivity. Under a linear structural causal model (SCM) with K≥3 non-degenerate environments, NSR achieves exact identification (Theorem~1). We fully characterise failure: weak shifts (O(varepsilon4) collapse), degenerate geometry, and proxy attenuation (O((1-α)4)), giving practitioners quantitative criteria for assessing whether the regime holds. Finite-sample rates are Op(n-1) under the null and Op(n-1/2) under the alternative. Experiments confirm all theoretical predictions on synthetic data (area under the ROC curve [AUROC] = 1.000 under conditions satisfying the regime), show consistent rankings across five model families (Kendall τ≥0.529), and recover six of eight causal features on bike-sharing data (Precision@7 = 0.75) without modifying any trained model.