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Estimating the support of a high-dimensional distribution.




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


  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},
  month_numeric = {3}