Estimating the support of a high-dimensional distribution
Estimating the support of a high-dimensional distribution
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DOI：
10.1162/089976601750264965
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发表时间：
2001-07-01
影响因子：
2.9
通讯作者：
Williamson, RC
中科院分区：
文献类型：
--
作者：
Schölkopf, B;Platt, JC;Williamson, RC
假设给定一个从概率分布P中抽取的数据集，并希望估计输入空间的一个“简单”子集S，使得从P中抽取的测试点位于S之外的概率等于0到1之间的某个先验指定值. f的函数形式由训练数据的潜在小子集的核扩展给出;它通过控制相关特征空间中的权重向量的长度来正则化。通过求解一个二次规划问题，我们通过对输入模式进行顺序优化来找到扩展系数。我们还对算法的统计性能进行了理论分析，该算法是支持向量机算法在无标记数据情况下的自然扩展。
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.