Year: 1997
Type: book
Abstract: . The problem of regression under Gaussian assumptions is treated generally. The relationship between Bayesian prediction, regularization and smoothing is elucidated. The ideal regression is the posterior mean and its computation scales as O(n 3 ), where n is the sample size. We show that the optimal m-dimensional linear model under a given prior is spanned by the first m eigenfunctions of a covariance operator, which is a trace-class operator. This is an infinite dimensional analogue of principal component analysis. The importance of Hilbert space methods to practical statistics is also discussed. 1 Introduction Many problems in computation and statistics can be generally described as fitting a "curve" from a discrete set of data. Here we allow a liberal interpretation of curve which could be any mapping from a finite dimensional space to a finite dimensional space. Such problems are usually studied under the name "regression" in statistics or "approximation" in numerical analysi...
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1859781365