2018/03/09 by Charles K. Chui, Chui, Charles K., Shao-Bo Lin +4 · 1 citation
Computer Science · Mathematics · #Artificial intelligence #Artificial neural network #Computer science #Deep learning #Dimension (graph theory) #Dimensionality reduction #FOS: Computer and information sciences #Face and Expression Recognition #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Machine learning #Mathematics #Neural Networks and Applications #Nonlinear dimensionality reduction #Realization (probability) #Statistics #Variance reduction #cs.LG
paper · pdf · doi:10.48550/arxiv.1803.03503
published in arXiv (Cornell University) (Cornell University) · 22pages
arxiv created 2018/03/09 · openalex publication_date 2018/03/09 · arxiv updated 2018/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
The subject of deep learning has recently attracted users of machine learning from various disciplines, including: medical diagnosis and bioinformatics, financial market analysis and online advertisement, speech and handwriting recognition, computer vision and natural language processing, time series forecasting, and search engines. However, theoretical development of deep learning is still at its infancy. The objective of this paper is to introduce a deep neural network (also called deep-net) approach to localized manifold learning, with each hidden layer endowed with a specific learning task. For the purpose of illustrations, we only focus on deep-nets with three hidden layers, with the first layer for dimensionality reduction, the second layer for bias reduction, and the third layer for variance reduction. A feedback component also designed to eliminate outliers. The main theoretical result in this paper is the order \mathcal O(m-2s/(2s+d)) of approximation of the regression function with regularity s, in terms of the number m of sample points, where the (unknown) manifold dimension d replaces the dimension D of the sampling (Euclidean) space for shallow nets.