Continuous Risk Functionals
As explained in the preceding chapter, the learning algorithm needed to adequately tune a regression-like classifier, based on the information provided by a training set, consists of the minimization of a quantity called risk, whose expression is given by formula (1.7). This formula assigns a number, R L (Y w ), to a function y w , i.e., the formula is an instantiation of an Y W = y w → ℝ mapping. Such mapping type (from a set of functions onto a set of numbers) is called a functional. The risk functional, expressed in terms of a continuous and differentiable loss function L(t(x), y w (x)), is minimized by some algorithm attempting to find a classifier with a probability of error hopefully close to that of z w*: min P e .
KeywordsLoss Function Shannon Entropy Empirical Risk Quadratic Entropy Risk Functional
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