Loss functions for classification: Difference between revisions

Revision as of 21:36, 4 December 2014

Revision as of 22:12, 4 December 2014

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:<math>V(f(\vec{x}),y)=\mathbf{\theta}(-yf(\vec{x}))</math>

where <math>\mathbf{\theta}</math> indicates the [[Heaviside step function]].

However, this loss function is not convex, making it intractable for most optimization problems. (cite) As a result, we seek continuous, convex '''loss function surrogates''' which are tractable for our learning algorithms. Some of these surrogates are described below.

== Square Loss ==

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== Hinge Loss ==

{{main|Hinge loss}}

Hinge loss

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

== Logistic Loss ==