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Last Update: 10/08/2023 02:57 PM
Current Deck: EEN100: Theory and exercises
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Commit #21167
Representative training set and ERM correctness
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Commit #21167
Assume that the training set \(\mathcal S\) is \(\epsilon/2\) representative.
Then (every) ERM prediction rule \(h_{\mathcal S} \in \arg\min_{h \in \mathcal H} L_{\mathcal S}(h)\) satisfies
\[L_{P_{\mathcal Z}}(h_{\mathcal S}) \le \min_{h' \in \mathcal H} L_{P_{\mathcal Z}}(h') + \epsilon\]i.e. is approximately correct.
Then (every) ERM prediction rule \(h_{\mathcal S} \in \arg\min_{h \in \mathcal H} L_{\mathcal S}(h)\) satisfies
\[L_{P_{\mathcal Z}}(h_{\mathcal S}) \le \min_{h' \in \mathcal H} L_{P_{\mathcal Z}}(h') + \epsilon\]i.e. is approximately correct.