Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a simple subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.
| Author(s): | Schölkopf, B. and Platt, JC. and Shawe-Taylor, J. and Smola, AJ. and Williamson, RC. |
| Links: | |
| Journal: | Neural Computation |
| Volume: | 13 |
| Number (issue): | 7 |
| Pages: | 1443-1471 |
| Year: | 2001 |
| Month: | March |
| Day: | 0 |
| BibTeX Type: | Article (article) |
| DOI: | 10.1162/089976601750264965 |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
BibTeX
@article{970,
title = {Estimating the support of a high-dimensional distribution.},
journal = {Neural Computation},
abstract = {Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a simple subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1.
We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm.
The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.},
volume = {13},
number = {7},
pages = {1443-1471},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
month = mar,
year = {2001},
author = {Sch{\"o}lkopf, B. and Platt, JC. and Shawe-Taylor, J. and Smola, AJ. and Williamson, RC.},
doi = {10.1162/089976601750264965},
month_numeric = {3}
}