The Good, the Bad, and the Ugly of Markov Boundary for Tabular Prediction

2026-05-28

AI Summary

This study systematically evaluates the practical utility of Markov boundaries in tabular prediction tasks, with a focus on high-dimensional sparse feature settings. Leveraging the SCM3K synthetic benchmark—which encompasses six classes of structural causal models, six regression algorithms, and multiple causal discovery methods—the authors compare predictive performance using the true Markov boundary against boundaries estimated by causal discovery across 3,450 tasks. Results show that the true Markov boundary substantially improves prediction accuracy, especially under high-dimensional sparsity. However, current causal discovery methods often fail to replicate this advantage due to misalignment between causal discovery objectives and predictive goals, asymmetric costs of false negatives and positives, and the existence of multiple near-optimal feature subsets, typically performing no better than using all features. This work highlights a critical disconnect between causal discovery and prediction-oriented feature selection.

Abstract

Under standard graphical assumptions, the Markov boundary of a target variable is the smallest set of features that renders every other feature redundant. Once the boundary is observed, the target is conditionally independent of the rest of the table. This is a tempting object for tabular prediction, since it names exactly the columns a model should need. Yet modern regressors are still trained on the full feature set. We ask whether the Markov boundary is genuinely useful for prediction on SCM3K, a 3,450-task synthetic SCM benchmark with feature counts from 40 to 1000 and six SCM families, evaluated with six regressors. The answer is more nuanced than the theory suggests. Restricting a regressor to the oracle boundary often improves prediction substantially, and the improvement grows as the feature space becomes larger and sparser. But the natural pipeline of recovering the boundary with causal discovery and training on the recovered mask does not deliver. Existing estimators exhaust the compute budget before reaching the regime where the boundary helps most, and even where they run they rarely beat the full feature set. We trace this to three causes. Discovery optimizes structural recovery rather than prediction. False negatives and false positives carry sharply asymmetric predictive cost. The exact boundary is only one of many feature sets that beat all features. We then develop what these facts imply for prediction-aligned feature selection and for tabular models that learn to use causal structure.

Problem

• Markov Boundary
• tabular prediction
• causal discovery
• feature selection
• SCM benchmark

Innovation

• Markov Boundary
• tabular prediction
• causal discovery
• feature selection
• SCM benchmark