# Deep Copula Classifier: Theory, Consistency, and Empirical Evaluation

arXiv: https://arxiv.org/abs/2505.22997 · HTML: https://mlsanity.com/paper/2505.22997/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 10 of 10)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Online Optimization : Competing with Dynamic Comparators](https://mlsanity.com/paper/1501.06225/) (2015)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Nonparametric estimation of simplified vine copula models: comparison of methods](https://mlsanity.com/paper/1701.00845/) (2017)
- [Neural Graphical Models](https://mlsanity.com/paper/2210.00453/) (2022)
- [Gaussian Process Vine Copulas for Multivariate Dependence](https://mlsanity.com/paper/1302.3979/) (2013)
- [Nonparametric estimation of multivariate copula using empirical bayes method](https://mlsanity.com/paper/2112.10351/) (2021)

## Built on by (most cited first, 1 of 1)

- [CopulaSMOTE: A Copula-Based Oversampling Approach for Imbalanced Classification in Diabetes Prediction](https://mlsanity.com/paper/2506.17326/) (2025)

## Abstract (arXiv)

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.