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Last Update: 10/08/2023 02:57 PM
Current Deck: EEN100: Theory and exercises
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Commit #21167
Loss function and population loss
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Commit #21167
Suppose data is generated as \(z \sim P_{\mathcal Z}\) on \(\mathcal Z = \mathcal X \times \mathcal Y\).
Assess a learning rule \(h\) determined by some algorithm on \(\mathcal S\) with a loss function \(\ell: \mathcal H \times \mathcal Z \to \mathbb R_+\).
Ex: 0-1 loss \(\ell(h,z) = \boldsymbol{1}_{h(x) = y}\) or quadratic loss \(\ell(h,z) = (h(x) - y)^2\).
Population loss is the true error over the population \(L_{P_{\mathcal Z}} = \mathbb{E}_{Z \sim P_{\mathcal Z}}[\ell(h,Z)]\)
Assess a learning rule \(h\) determined by some algorithm on \(\mathcal S\) with a loss function \(\ell: \mathcal H \times \mathcal Z \to \mathbb R_+\).
Ex: 0-1 loss \(\ell(h,z) = \boldsymbol{1}_{h(x) = y}\) or quadratic loss \(\ell(h,z) = (h(x) - y)^2\).
Population loss is the true error over the population \(L_{P_{\mathcal Z}} = \mathbb{E}_{Z \sim P_{\mathcal Z}}[\ell(h,Z)]\)