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Machine Learning: Difference between revisions
→Rademacher Complexity
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Given a set <math>A \subset \mathbb{R}^m</math> the Rademacher complexity is:<br> | Given a set <math>A \subset \mathbb{R}^m</math> the Rademacher complexity is:<br> | ||
<math>R(A) = \frac{1}{m}E_{\sigma} [\sup_{a \in A} \sum_{i=1}^{m} \sigma_i a_i]</math><br> | <math>R(A) = \frac{1}{m}E_{\sigma} [\sup_{a \in A} \sum_{i=1}^{m} \sigma_i a_i]</math><br> | ||
where each <math>\sigma_i</math> are from a discrete uniform distribution <math>\{-1, 1\}</math> | where each <math>\sigma_i</math> are from a discrete uniform distribution <math>\{-1, 1\}</math><br> | ||
Given a sample <math>S=\{z_1,...,z_n\}</math> and a function class <math>F</math>, the empirical rademacher complexity is:<br> | Given a sample <math>S=\{z_1,...,z_n\}</math> and a function class <math>F</math>, the empirical rademacher complexity is:<br> | ||
<math>R(F \circ S)</math><br> | <math>R(F \circ S)</math><br> | ||
where <math>F \circ S = \{(f(z_1),...,f(z_n)) \mid f \in F\}</math><br> | where <math>F \circ S = \{(f(z_1),...,f(z_n)) \mid f \in F\}</math><br> | ||
;Notes | |||