  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.
