Nystr\"om Approximation

The Nyström approximation is a widely used technique for efficiently approximating large kernel matrices, primarily aiming to reduce computational complexity in machine learning tasks. Current research focuses on improving the accuracy and speed of Nyström methods through techniques like multi-level sketched preconditioning, adaptive sampling strategies (e.g., k-means, leverage scores), and boosting algorithms that iteratively refine approximations. These advancements enable the application of kernel methods to significantly larger datasets, impacting fields such as Gaussian process regression, discrete choice modeling, and time series forecasting by providing scalable and accurate solutions to previously intractable problems.