The Jensen-Shannon divergence is widely reported as a scalar measure of fidelity for synthetic tabular data. Yet, in practice, it is estimated from finite samples using protocols that are often underspecified. This creates a measurement problem. Although the population divergence is well defined, the empirical value depends on the estimator family, sampling protocol, calibration, dimensionality, and class balance. We show that different protocols can yield non-comparable values: marginal-based estimators ignore dependencies in the joint distribution and can severely underestimate divergence, while classifier-based estimators capture joint structure but exhibit strong estimator dependence. We systematically study this behavior across controlled settings with reference divergences and real-world synthetic tabular benchmarks. Our analysis reveals dependence blindness in marginal estimators, prior-shift bias under class imbalance, and estimator sensitivity in high dimensions. To address prior shift, we derive a closed-form posterior correction for classifier-based Jensen-Shannon estimation. Our results show that empirical Jensen-Shannon divergence values are inherently protocol-dependent, making explicit specification of the estimation procedure necessary for meaningful comparison. We provide practical guidelines and an open-source tool for estimator-aware Jensen-Shannon evaluation.

翻译：詹森-香农散度被广泛报道为合成表格数据保真度的标量度量。然而在实际应用中，它往往是通过规定不明确的有限样本协议进行估计的。这导致了测量问题：虽然总体散度定义明确，但经验值取决于估计量族、采样协议、校准方式、数据维度和类别平衡。我们证明不同协议可能产生不可比较的值：基于边际的估计量忽略联合分布中的依赖关系，会严重低估散度；而基于分类器的估计量虽能捕捉联合结构，但表现出强烈的估计量依赖性。我们在受控设置（含参考散度）和真实合成表格基准上系统研究了这一行为。分析揭示了边际估计量的依赖盲区、类别不平衡下的先验偏移偏差，以及高维空间中的估计量敏感性。为应对先验偏移，我们推导了基于分类器的詹森-香农估计的闭式后验修正。结果表明，经验詹森-香农散度值本质上依赖于协议，因此必须明确指定估计流程才能进行有意义的比较。我们提供了实用指南和用于识别估计量感知的詹森-香农评估开源工具。