The Entire Quantile Path of a Risk-Agnostic SVM Classifier
This provides a method for estimating full conditional distributions and handling unknown misclassification costs in binary classification, though it is incremental as it builds on existing SVM theory.
The paper extends Support Vector Machines (SVMs) to recover quantile binary classifiers for any quantile parameter t by using asymmetric misclassification costs, enabling recovery of the entire conditional distribution P(Y=1|X=x) and building a risk-agnostic classifier without prior cost knowledge.
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.