Statistically guided deep learning

• URL: http://arxiv.org/abs/2504.08489v1
• Date: Fri, 11 Apr 2025 12:36:06 GMT
• Title: Statistically guided deep learning
• Authors: Michael Kohler, Adam Krzyzak,
• Abstract summary: We present a theoretically well-founded deep learning algorithm for nonparametric regression.<n>We show that a theoretical analysis of deep learning which takes into account simultaneously optimization, generalization and approximation can result in a new deep learning estimate.
• Score: 10.619901778151336
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a theoretically well-founded deep learning algorithm for nonparametric regression. It uses over-parametrized deep neural networks with logistic activation function, which are fitted to the given data via gradient descent. We propose a special topology of these networks, a special random initialization of the weights, and a data-dependent choice of the learning rate and the number of gradient descent steps. We prove a theoretical bound on the expected $L_2$ error of this estimate, and illustrate its finite sample size performance by applying it to simulated data. Our results show that a theoretical analysis of deep learning which takes into account simultaneously optimization, generalization and approximation can result in a new deep learning estimate which has an improved finite sample performance.

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