Deep Copula Classifier: Theory, Consistency, and Empirical Evaluation

TL;DR

The Deep Copula Classifier (DCC) is a neural copula-based model that separates marginal estimation from dependence modeling, achieving strong theoretical guarantees and superior empirical performance in classification tasks.

Contribution

This paper introduces DCC, a novel neural copula-based classifier that is interpretable, Bayes-consistent, and demonstrates superior empirical results compared to traditional methods.

Findings

DCC nearly reaches optimal performance with oracle marginals.

DCC outperforms traditional classifiers on the Pima Indians Diabetes dataset.

DCC provides well-calibrated probabilistic predictions.

Abstract

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 ($|\rho|=0.995$), 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 ($\tau=1$) 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.