Loss functions for classification: Difference between revisions

Revision as of 22:16, 5 December 2014

Revision as of 22:17, 5 December 2014

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The hinge loss function is defined as

:<math>V(f(\vec{x}),y) = \max(0, 1-yf(\vec{x})) = |1 - yf(\vec{x})|_{+}</math>

The hinge loss provides a relatively tight, convex upper bound on the 0-1 [[indicator function]]. Specifically, the hinge loss equals the 0-1 [[indicator function]] when <math>signsgn(f(\vec{x})) = y</math> and <math> |y f(\vec{x})| ≥ 1</math>.

== Logistic Loss ==