Stability Analysis for Regularized Least Squares Regression
| dc.creator | Rudin, Cynthia | |
| dc.date | 2005-02-03 | |
| dc.date.accessioned | 2026-07-07T03:22:28Z | |
| dc.date.available | 2026-07-07T03:22:28Z | |
| dc.description | We discuss stability for a class of learning algorithms with respect to noisy labels. The algorithms we consider are for regression, and they involve the minimization of regularized risk functionals, such as L(f) := 1/N sum_i (f(x_i)-y_i)^2+ lambda ||f||_H^2. We shall call the algorithm `stable' if, when y_i is a noisy version of f*(x_i) for some function f* in H, the output of the algorithm converges to f* as the regularization term and noise simultaneously vanish. We consider two flavors of this problem, one where a data set of N points remains fixed, and the other where N -> infinity. For the case where N -> infinity, we give conditions for convergence to f_E (the function which is the expectation of y(x) for each x), as lambda -> 0. For the fixed N case, we describe the limiting 'non-noisy', 'non-regularized' function f*, and give conditions for convergence. In the process, we develop a set of tools for dealing with functionals such as L(f), which are applicable to many other problems in learning theory. | |
| dc.description | 14 pages, 0 figures, 1 class file | |
| dc.identifier | https://arxiv.org/abs/cs/0502016 | |
| dc.identifier | http://arxiv.org/abs/cs/0502016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/32606 | |
| dc.subject | Machine Learning | |
| dc.title | Stability Analysis for Regularized Least Squares Regression | |
| dc.type | text |