Schölkopf, Bernhard; Platt, John C.; Shawe-Taylor, John; Smola, Alex J.; Williamson, Robert C. Estimating the support of a high-dimensional distribution. (English) Zbl 1009.62029 Neural Comput. 13, No. 7, 1443-1471 (2001). Summary: 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. Cited in 103 Documents MSC: 62G07 Density estimation 90C90 Applications of mathematical programming Keywords:quadratic programming Software:SVMlight PDF BibTeX XML Cite \textit{B. Schölkopf} et al., Neural Comput. 13, No. 7, 1443--1471 (2001; Zbl 1009.62029) Full Text: DOI OpenURL References: [1] DOI: 10.1006/jcss.1997.1507 · Zbl 0880.68106 [2] DOI: 10.1214/aos/1030741073 · Zbl 0897.62034 [3] DOI: 10.1137/0138038 · Zbl 0479.62028 [4] DOI: 10.1214/aos/1176348670 · Zbl 0757.60012 [5] Gayraud G., Mathematical Methods of Statistics 6 (1) pp 26– (1997) · Zbl 0873.62038 [6] DOI: 10.1162/089976698300017269 [7] DOI: 10.2307/2289162 · Zbl 0607.62045 [8] DOI: 10.1016/0047-259X(91)90106-C · Zbl 0739.62042 [9] DOI: 10.1006/jmva.1995.1067 · Zbl 0847.62027 [10] DOI: 10.1214/aos/1176324626 · Zbl 0841.62045 [11] DOI: 10.2307/2286331 · Zbl 0428.62040 [12] DOI: 10.1162/089976600300015565 [13] Shawe-Taylor J., IEEE Transactions on Information Theory. Submitted. (2000) [14] DOI: 10.1016/S0893-6080(98)00032-X [15] DOI: 10.1109/6.769272 [16] DOI: 10.1214/aos/1069362732 · Zbl 0881.62039 [17] Williamson R. C., IEEE Transactions on Information Theory (in press). (1998) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.