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Huber loss : ウィキペディア英語版
Huber loss
In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used.
==Definition==

The Huber loss function describes the penalty incurred by an estimation procedure . Huber (1964) defines the loss function piecewise by
:
L_\delta (a) = \begin
\frac & \text |a| \le \delta, \\
\delta (|a| - \frac\delta), & \text
\end

This function is quadratic for small values of , and linear for large values, with equal values and slopes of the different sections at the two points where |a| = \delta. The variable often refers to the residuals, that is to the difference between the observed and predicted values a = y - f(x), so the former can be expanded to〔 Compared to Hastie ''et al.'', the loss is scaled by a factor of ½, to be consistent with Huber's original definition given earlier.〕
:
L_\delta(y, f(x)) = \begin
\frac(y - f(x))^2 & \textrm |y - f(x)| \le \delta, \\
\delta\, |y - f(x)| - \frac\delta^2 & \textrm
\end


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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