additional typos
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@@ -370,24 +370,24 @@ The idea of the gradient descent algorithm is to update parameters in
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direction where the cost function decreases goes to a minimum.
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<p>
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In general, the update of some parameters \( \vec \omega \) given a cost
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function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \),
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In general, the update of some parameters \( \hat{\omega} \) given a cost
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function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \),
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goes as follows:
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$$
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\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega),
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\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}),
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$$
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<p>
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for a number of iterations or until $ \big|\big| \vec
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\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some
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for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \)
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is smaller than some
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given tolerance.
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<p>
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The value of \( \lambda \) decides how large steps the algorithm must take
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in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The
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notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to
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the elements in \( \vec \omega \).
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in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The
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notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to
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the elements in \( \hat{\omega} \).
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<p>
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<p>
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