Deep Copula Classifier: Theory, Consistency, and Empirical Evaluation

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 ≈ 0.971; ROC-AUC ≈ 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.