马尔可夫边界在表格预测中的应用:理论、实践与挑战
阅读原文· arxiv.org在标准图模型下,马尔可夫边界是使目标变量条件独立于其他特征的最小特征子集。本文在包含3450个任务的合成基准SCM3K上评估发现,直接将模型限制在理论“神谕”边界特征上,通常能显著提升预测性能,且特征空间越大越稀疏时改进越明显。然而,通过因果发现算法自动恢复边界再训练的常规流程效果不佳。原因有三:现有发现算法优化结构而非预测、误报与漏报的预测代价严重不对称,以及优于全特征的特征集远不止精确边界一种。
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.