The Entire Quantile Path of a Risk-Agnostic SVM Classifier

TL;DR

This paper introduces a novel SVM-based method that can recover the entire quantile path of a risk-agnostic classifier, enabling flexible decision thresholds without prior cost knowledge.

Contribution

It extends SVMs to recover all quantile classifiers simultaneously, allowing for distribution estimation and risk-agnostic classification.

Findings

Effective recovery of the entire quantile path demonstrated

Algorithm successfully estimates conditional distribution

Preliminary experiments show promising results

Abstract

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.