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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 non-convex and non-smooth, and solving for the optimal solution is an [[NP-hard]] combinatorial optimization problem. (cite utah) As a result, we seek continuous, convex '''loss function surrogates''' which are tractable for our learning algorithms. In addition to their computational tractability, the convexity of these functions allows us to provide probabilistic bounds on their estimation error from the true distribution (cite uci).Some of these surrogates are described below.
== Square Loss ==
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