Bias-Variance Dilemma
To achieve good overall performance, bias B(w) and variance V(w) of approximating function [Tex]F(x,w) = F(x,\mathcal{T})[/Tex] would both have to be small. In neural networks, achieving a small bias leads to a large variance. However, if we have an infinitely large training sample for a single neural network, we can reduce both bias and variance. This leads to bias/variance dilemma, resulting in very slow convergence.
To address this dilemma, we can intentionally introduce bias into the network, which allows us to reduce or eliminate variance. It’s important to ensure that this bias is harmless and only contributes to mean-square error if we try to infer regressions outside the expected class. Bias needs to be designed for each specific application. To achieve this, we use a constrained network architecture, which performs better than a general-purpose architecture.
Statistical Nature of the Learning Process in Neural Networks
Understanding the statistical nature of the learning process in neural networks (NNs) is pivotal for optimizing their performance. This article aims to provide a comprehensive understanding of the statistical nature of the learning process in NNs. It will delve into the concepts of bias and variance, the bias-variance trade-off, and how these factors influence the performance of NNs. By the end, readers will have a deeper understanding of how to optimize NNs for better performance.