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The Entire Quantile Path of a Risk-Agnostic SVM Classifier
Jin Yu, Vishwanathan S.V.N. and Jian Zhang
Conference on Uncertainty in Artificial Intelligence
2009.
Abstract A 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. [Edit]
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