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jj~iZnSxiX&_fFDTZXttA06>YsDa0d$&cGn6Du@0bdRs?= diff --git a/semester6/iml/parts/05_classification.tex b/semester6/iml/parts/05_classification.tex index fc49ae3..d389e3b 100644 --- a/semester6/iml/parts/05_classification.tex +++ b/semester6/iml/parts/05_classification.tex @@ -34,6 +34,10 @@ $$ Unfortunately, $l_{0-1}$ is non-continuous and non-convex.\\ We introduce \textit{surrogate loss} to still apply GD. +{\footnotesize + \remark Note how $\nabla l_{0-1}(\hat{y},y) = 0$ everywhere. +} + Note how $\mathbb{I}_{\hat{y}\neq y} = \mathbb{I}_{\hat{y}\cdot y < 0}$, so $l_{0-1}$ only depends on $z := \hat{y}\cdot y$.\\ We thus define losses over $z$, that are cont. and convex. @@ -179,6 +183,10 @@ Train each model seperately by relabeling for each $\hat{f}_k$: \end{enumerate} \subtext{This leads to $K$ classification problems, which might be slow} +{\footnotesize + \remark Visually, this leads to \textit{convex} regions for each label. +} + Another way to reuse the existing methodology is to use a new loss: \definition \textbf{Cross-Entropy Loss}