The Entire Quantile Path of a Risk-Agnostic SVM Classifier ## AbstractA quantile binary classifier uses the rule: Classify x as +1 if P(Y=1|X=x) >= tau, and as -1 otherwise, for a fixed quantile parameter tau in [0, 1]. It has been shown that Support Vector Machines (SVMs) in the limit are quantile classifiers with tau = 0.5. 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 tau. We then present a principled algorithm to solve the extended SVM classifier for all values of tau simultaneously. This has two implications: First, one can recover the entire conditional distribution P(Y=1|X=x) = tau for tau in [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.
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