In mathematics, statistics, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts the answer of a problem to a simpler one. It is often used in … See more

Empirical learning of classifiers (from a finite data set) is always an underdetermined problem, because it attempts to infer a function of any $${\displaystyle x}$$ given only examples $${\displaystyle x_{1},x_{2},\dots ,x_{n}}$$. See more

Early stopping can be viewed as regularization in time. Intuitively, a training procedure such as gradient descent tends to learn more and more complex functions with increasing iterations. By regularizing for time, model complexity can be controlled, … See more

When labels are more expensive to gather than input examples, semi-supervised learning can be useful. Regularizers have been designed to guide learning algorithms to learn models that respect the structure of unsupervised training samples. If a … See more

In machine learning, a key challenge is enabling models to accurately predict outcomes on unseen data, not just on familiar training data. Regularization is crucial for addressing See more

These techniques are named for Andrey Nikolayevich Tikhonov, who applied regularization to integral equations and made important … See more

Assume that a dictionary $${\displaystyle \phi _{j}}$$ with dimension $${\displaystyle p}$$ is given such that a function in the function space can be expressed as:
Enforcing a sparsity … See more