Estimating the support of a high-dimensional distribution.
2001
Article
ei
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. |
Journal: | Neural Computation |
Volume: | 13 |
Number (issue): | 7 |
Pages: | 1443-1471 |
Year: | 2001 |
Month: | March |
Day: | 0 |
Department(s): | Empirical Inference |
Bibtex Type: | Article (article) |
Digital: | 0 |
DOI: | 10.1162/089976601750264965 |
Language: | en |
Organization: | Max-Planck-Gesellschaft |
School: | Biologische Kybernetik |
Links: |
Web
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BibTex @article{970, title = {Estimating the support of a high-dimensional distribution.}, author = {Sch{\"o}lkopf, B. and Platt, JC. and Shawe-Taylor, J. and Smola, AJ. and Williamson, RC.}, journal = {Neural Computation}, volume = {13}, number = {7}, pages = {1443-1471}, organization = {Max-Planck-Gesellschaft}, school = {Biologische Kybernetik}, month = mar, year = {2001}, doi = {10.1162/089976601750264965}, month_numeric = {3} } |