用神经核密度建模特征依赖关系，提升分类准确率与校准性。
Deep Copula Classifier: Theory, Consistency, and Empirical Evaluation
- 分离边缘分布与依赖结构，用神经核密度建模特征间相关性。
- 在强相关数据中准确率达97.1%，校准后糖尿病数据集精度达87.9%。
- 理论保证贝叶斯一致性，适合需要可解释概率输出的场景。
我们提出深度似然分类器（DCC），一种基于条件类别的生成模型，通过神经核密度分离边缘估计与依赖建模。DCC具备可解释性、贝叶斯一致性，对r-光滑核密度具有$O(n^{-r/(2r+d)})$的超额风险收敛速率。在强依赖条件下（|ρ|=0.995）的两分类实验中，DCC学习到与贝叶斯最优决策区一致的区域；使用真值或合并边缘分布时，性能接近最优（准确率≈0.971；ROC-AUC≈0.998）。而每类独立核密度估计（KDE）表现较差（准确率0.873；ROC-AUC 0.957；PR-AUC 0.966）。在Pima Indians Diabetes数据集上，校准后的DCC（τ=1）达到准确率0.879，ROC-AUC 0.936，PR-AUC 0.870，优于逻辑回归、SVM（RBF）、朴素贝叶斯，且预期校准误差（ECE）最低；随机森林也表现相近（准确率0.892；ROC-AUC 0.933；PR-AUC 0.880）。直接建模特征依赖带来强性能与良好校准性，兼具清晰的概率解释，是独立假设分类器的理论坚实替代方案。
原文摘要 · Abstract (English)
We present the Deep Copula Classifier (DCC), a class-conditional generative model that separates marginal estimation from dependence modeling using neural copula densities. DCC is interpretable, Bayes-consistent, and achieves excess-risk $O(n^{-r/(2r+d)})$ for $r$-smooth copulas. In a controlled two-class study with strong dependence ($|ρ|=0.995$), DCC learns Bayes-aligned decision regions. With oracle or pooled marginals, it nearly reaches the best possible performance (accuracy $\approx 0.971$; ROC-AUC $\approx 0.998$). As expected, per-class KDE marginals perform less well (accuracy $0.873$; ROC-AUC $0.957$; PR-AUC $0.966$). On the Pima Indians Diabetes dataset, calibrated DCC ($τ=1$) achieves accuracy $0.879$, ROC-AUC $0.936$, and PR-AUC $0.870$, outperforming Logistic Regression, SVM (RBF), and Naive Bayes, and matching Logistic Regression on the lowest Expected Calibration Error (ECE). Random Forest is also competitive (accuracy $0.892$; ROC-AUC $0.933$; PR-AUC $0.880$). Directly modeling feature dependence yields strong, well-calibrated performance with a clear probabilistic interpretation, making DCC a practical, theoretically grounded alternative to independence-based classifiers.
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