additional typos

This commit is contained in:
mhjensen
2018-10-19 06:30:26 +02:00
parent 092fdecd9b
commit 97ee7402a8
9 changed files with 54 additions and 60 deletions
@@ -370,24 +370,24 @@ The idea of the gradient descent algorithm is to update parameters in
direction where the cost function decreases goes to a minimum.
<p>
In general, the update of some parameters \( \vec \omega \) given a cost
function defined by some weights \( \vec \omega \), \( c(x, \vec \omega) \),
In general, the update of some parameters \( \hat{\omega} \) given a cost
function defined by some weights \( \hat{\omega} \), \( c(x, \hat{\omega}) \),
goes as follows:
$$
\vec \omega_{\mathrm{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega),
\hat{\omega}_{\mathrm{new} } = \hat{\omega} - \lambda \nabla_{\hat{\omega}} c(x, \hat{\omega}),
$$
<p>
for a number of iterations or until $ \big|\big| \vec
\omega_{\mathrm{new} } - \vec \omega \big|\big|$ is smaller than some
for a number of iterations or until \( \big|\big| \hat{\omega}_{\mathrm{new} } - \hat{\omega} \big|\big| \)
is smaller than some
given tolerance.
<p>
The value of \( \lambda \) decides how large steps the algorithm must take
in the direction of $ \nabla_{\vec \omega} c(x, \vec \omega)$. The
notatation \( \nabla_{\vec \omega} \) denotes the gradient with respect to
the elements in \( \vec \omega \).
in the direction of $ \nabla_{\hat{\omega}} c(x, \hat{\omega})$. The
notatation \( \nabla_{\hat{\omega}} \) denotes the gradient with respect to
the elements in \( \hat{\omega} \).
<p>
<p>