Understanding Convolutional Neural Networks: Statistical Generative Models for Unstructured Image Data.

Convolutional Neural Networks (CNNs) are foundational in modern image analysis due to their ability to efficiently learn feature representations. However, theoretical understanding of their efficiency remains limited, largely due to inadequate modeling of image structures and their interaction with CNNs. To address this, we introduce novel statistical generative models (SGMs) that decompose images into task-relevant signals and noise, capturing the complexities of natural image data. Based on these SGMs, we propose a feature mapping approach (FMA) to characterize the transformation from raw image data to feature vectors. We analyze CNNs' approximation capabilities, their adaptation to low-dimensional structures, and their efficiency in vision tasks, ultimately developing statistical learning theories for CNN-based image analysis. Our findings reveal the challenges inherent in vision tasks and highlight CNNs' remarkable efficiency in addressing them, providing new insights into their theoretical and practical capabilities. This is based on the joint work with Dr. Guohao Shen.

Convolutional neural networks

Image data

Statistical generative model

Point process

Approximation Theory