Learning Korobov Functions by Correntropy and Convolutional Neural Networks.

Area of Science:

• Machine Learning
• Deep Learning Theory
• Information Theory

Background:

• Combining information-theoretic learning with deep learning is crucial for big data challenges.
• Theoretical understanding of convolutional structures in deep learning models remains incomplete.
• Robust regression is essential for handling noisy data in machine learning.

Purpose of the Study:

• To develop generalization analysis for deep convolutional neural network (CNN) algorithms using learning theory.
• To investigate robust regression using correntropy-induced loss functions.
• To bridge the theoretical gap in understanding CNNs.

Main Methods:

• Applied information-theoretic learning principles to deep learning.
• Utilized learning theory for generalization analysis of CNNs.
• Focused on robust regression with correntropy-induced loss functions.

Main Results:

• Developed explicit convergence rates for deep CNN-based robust regression algorithms.
• Demonstrated theoretical underpinnings for CNN performance in robust regression.
• Showcased convergence when the target function is within the Korobov space.

Conclusions:

• The study provides a theoretical framework for deep CNNs in robust regression.
• The findings enhance the understanding of CNNs' generalization capabilities.
• This research offers insights into the performance and limitations of CNN algorithms.