A1361
Title: Generalization of CNNs under $\mathcal{C}$-mixing dependence
Authors: Fangjia Dong - Hong Kong Baptist University (Hong Kong) [presenting]
Abstract: The generalization performance of convolutional neural networks (CNNs) for nonparametric regression is investigated under two fundamental challenges: heavy-tailed noise and data dependence. Unlike existing works assuming sub-Gaussian noise or finite variance, much weaker moment conditions are considered: the noise only requires a finite $p$-th conditional moment and a $q$-th marginal moment for $p, q > 1$, allowing for infinite variance. The input sequence dependence is formalized via the $\mathcal{C}$-mixing condition. To address these challenges, a robust learning framework is developed using the Huber loss function and complexity-regularized CNN hypothesis spaces. By leveraging a recent Bernstein concentration inequality for $\mathcal{C}$-mixing sequences, high-probability convergence rates for the empirical risk minimizer are established. The results show that, even under these minimal assumptions, CNNs can achieve minimax-optimal generalization rates up to logarithmic factors. Overall, the findings demonstrate the feasibility of robust deep learning in realistic scenarios with complex dependencies and heavy-tailed, potentially infinite-variance noise.
