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Add the following about 0-1-losses to cost sensitivity chapter
We can express the 0-1-loss by a cost-matrix $\mathbf{C} \in \R^{g \times g}$ $$ \mathbf{C} = \left(\begin{array}{cccc} 0 & 1 & \hdots & 1 \\ 1 & 0 & \hdots & 1 \\ 1 & 1 & \hdots & 1 \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 1 & \hdots & 0 \\ \end{array}\right)\, = \mathbf{1} \mathbf{1}^\top - \left(\begin{array}{cccc} 1 & 0 & \hdots & 0 \\ 0 & 1 & \hdots & 0 \\ 0 & 0 & \hdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \hdots & 1 \\ \end{array}\right)\, $$ The entry $c_{ij}$ expresses how we weight the error if we classify $\hx = j$ but $y = i$. \lz In the case of the 0-1-loss, any type of misclassification is weighted equally.
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Add the following about 0-1-losses to cost sensitivity chapter
The text was updated successfully, but these errors were encountered: