风险不可知SVM分类器的完整分位数路径
The Entire Quantile Path of a Risk-Agnostic SVM Classifier
摘要：
分位数二元分类器使用以下规则：如果P（Y = 1），则将x分类为+1| X = x）>= t，否则为-1，对于固定分位数参数t {[0，1]。已经证明，支持向量机（SVM）在极限下是t = 1/2的分位数分类器。在本文中，我们表明，通过使用不对称的错误分类成本支持向量机可以适当地扩展到恢复，在限制下，分位数二进制分类器的任何t。然后，我们提出了一个原则性的算法来解决扩展的SVM分类器的所有值的t同时。这有两个含义：第一，可以恢复整个条件分布P（Y = 1| X = X）= t，对于t {[0，1]。其次，我们可以建立一个风险不可知的SVM分类器，其中的错误分类成本不需要先验已知。初步的数值实验表明了该算法的有效性。
英文摘要：
A quantile binary classifier uses the rule: Classify x as +1 if P(Y = 1|X = x) >= t, and as -1 otherwise, for a fixed quantile parameter t {[0, 1]. It has been shown that Support Vector Machines (SVMs) in the limit are quantile classifiers with t = 1/2 . In this paper, we show that by using asymmetric cost of misclassification SVMs can be appropriately extended to recover, in the limit, the quantile binary classifier for any t. We then present a principled algorithm to solve the extended SVM classifier for all values of t simultaneously. This has two implications: First, one can recover the entire conditional distribution P(Y = 1|X = x) = t for t {[0, 1]. Second, we can build a risk-agnostic SVM classifier where the cost of misclassification need not be known apriori. Preliminary numerical experiments show the effectiveness of the proposed algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
