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Jung Alex
MLandAITeaching
Commits
e0dfb48e
Commit
e0dfb48e
authored
Nov 20, 2017
by
Alexander Jung
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new HA2 refsol
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b794aa9f
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Regression/Ex2_Regression_final_RefSol.pdf
Regression/Ex2_Regression_final_RefSol.pdf
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Regression/Ex2_Regression_final_RefSol.tex
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...
...
@@ -294,7 +294,7 @@ The dimension is $d=100^2 = 10000$. The gradient is obtained as
\nabla
f (
\vw
) = 2
\lambda
\vw
+
\frac
{
-2
}{
\samplesize
}
\sum
^{
\samplesize
}_{
\sampleidx
=1
}
\vx
^{
(
\sampleidx
)
}
(y
^{
(
\sampleidx
)
}
-
\vw
^{
T
}
\vx
^{
(
\sampleidx
)
}
).
\end{equation}
For the stopping criterion we might use a fixed number of iterations, which requires to have some understanding (``convergence analysis'') of how
fast gradient descent converges to the optimum. Another option is to monitor the relative decrease of the objective value
$
f
(
\vw
$
, i.e.,
fast gradient descent converges to the optimum. Another option is to monitor the relative decrease of the objective value
$
f
(
\vw
)
$
, i.e.,
to stop iterating when
$
\big
|
\frac
{
f
(
\vw
^{
(
k
+
1
)
}
)
-
f
(
\vw
^{
(
k
)
}
)
}{
f
(
\vw
^{
(
k
)
}
)
}
\big
|
$
is below a suitably chosen (small) threshold.
\begin{figure}
[h]
\begin{center}
...
...
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