Copula-Induced Correntropy for Robust Conjugate Gradient Learning

Abstract

Robust learning in the presence of non-Gaussian and statistically dependent noise remains a fundamental challenge in signal processing and adaptive systems. Although information-theoretic learning criteria such as correntropy offer strong robustness against impulsive and heavy-tailed disturbances, existing formulations are commonly applied componentwise and therefore do not explicitly exploit the dependence structures inherent in multivariate, multi-sensor, and temporal signals. In this paper, we propose a learning framework, termed \textit{copula-induced information-theoretic learning} (CITL), which extends correntropy by embedding a copula space representation of residual dependence into the similarity measure. Unlike conventional correntropy-based approaches that operate pointwise on raw residuals, the proposed criterion is defined in a copula-transformed residual space, thus separating marginal robustness from dependence weighting. We derive a copula-induced correntropy (CIC) objective and a mixed marginal--dependence objective used in the implementation, provide information-theoretic and Bayesian interpretations, and develop a robust conjugate gradient (CG) learning algorithm tailored to this criterion. For fixed smooth marginal estimators, a fixed copula-space metric, and a regularized radial penalty, we establish sufficient descent and global stationarity guarantees for the corresponding fixed-estimator subproblem under standard line-search conditions. Experiments on synthetic multivariate signal processing regression problems demonstrate that the proposed method consistently outperforms mean squared error (MSE), Huber, Student's-$t$, and classical correntropy-based approaches, particularly in the presence of dependent heavy-tailed noise.