Generalization and Regularization in Nonlinear Learning Systems

Generalization and Regularization in Nonlinear Learning Systems 1 by Grace Wahba

The Effective Number of Parameters: An Analysis of Generalization and Regularization in Nonlinear Learning Systems

We present an analysis of how the generalization performance (expected test set error) relates to the expected training set error for nonlinear learning systems, such as multilayer perceptrons and radial basis functions. The principal result is the following relationship (computed to second order) between the expected test set and tlaining set errors: (1) Here, n is the size of the training sam...

Existence of solutions of infinite systems of integral equations in the Frechet spaces

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...

Deep learning - Regularization

where, θ̃ is an estimator of θ coming from update equations or solution of optimization procedure. Variability in θ̃ is because of randomness in data and bias is due to model mismatch. Well known bias-variance trade offAs complexity of the model is increased model mismatch(bias) is decreased while variance in the prediction is increased because of randomness in training inputs. 4. Deep Learning s...

Near-Orthogonality Regularization in Kernel Methods

Kernel methods perform nonlinear learning in high-dimensional reproducing kernel Hilbert spaces (RKHSs). Even though their large model-capacity leads to high representational power, it also incurs substantial risk of overfitting. To alleviate this problem, we propose a new regularization approach, nearorthogonality regularization, which encourages the RKHS functions to be close to being orthogo...