🤖 AI Summary
This work addresses probabilistic density estimation for high-dimensional complex data. We propose a neural Copula modeling framework that explicitly decouples marginal distributions from dependency structures—a departure from conventional joint modeling approaches. Integrating Copula theory with deep neural networks, our method employs a normalizing flow architecture to separately parameterize marginals and the high-dimensional copula function, enabling differentiable density evaluation, generative sampling, and tractable inference. Leveraging marginal-joint decoupled training and a differentiable mutual information estimator, the model achieves superior performance over kernel density estimation and state-of-the-art neural density estimators across diverse complex distributions. Empirical evaluation demonstrates its effectiveness in high-accuracy mutual information estimation and photorealistic data generation, validating both theoretical design and practical utility.
📝 Abstract
Probability density estimation from observed data constitutes a central task in statistics. Recent advancements in machine learning offer new tools but also pose new challenges. The big data era demands analysis of long-range spatial and long-term temporal dependencies in large collections of raw data, rendering neural networks an attractive solution for density estimation. In this paper, we exploit the concept of copula to explicitly build an estimate of the probability density function associated to any observed data. In particular, we separate univariate marginal distributions from the joint dependence structure in the data, the copula itself, and we model the latter with a neural network-based method referred to as copula density neural estimation (CODINE). Results show that the novel learning approach is capable of modeling complex distributions and it can be applied for mutual information estimation and data generation.