马尔可夫边界在表格数据预测中的善、恶与丑

摘要

在标准图形假设下，目标变量的马尔可夫边界是使其他所有特征冗余的最小特征集。一旦观测到该边界，目标变量便与表中其余特征条件独立。这对于表格预测而言具有吸引力，因为它精确指明了模型所需的列。然而，现代回归模型仍是在全特征集上训练的。我们探究马尔可夫边界在SCM3K上是否对预测真正有用——该基准包含3450个合成结构因果模型任务，特征数量从40到1000，涵盖六个SCM家族，并使用六种回归模型评估。答案比理论所暗示的更为微妙。将回归模型限制于最优边界通常会显著提升预测性能，且随着特征空间变得更大更稀疏，这种提升也增大。但是，通过因果发现恢复边界并在恢复的掩膜上训练的自然流程效果不佳。现有估计器在达到边界最有效的区域之前就已耗尽计算预算，即使在运行的情况下，它们也很少能超越全特征集。我们将此归因于三个原因：发现方法优化的是结构恢复而非预测；假阴性和假阳性带来的预测成本高度不对称；精确边界只是众多优于全特征集的特征集之一。随后，我们阐述这些事实对与预测对齐的特征选择以及学会利用因果结构的表格模型的启示。

English

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.