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Philipp Arras
whatisalikelihood
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3e40b830
Commit
3e40b830
authored
Aug 24, 2018
by
Philipp Arras
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3e40b830
...
...
@@ 192,18 +192,18 @@ function:
\begin{align*}
R:
\mathbb
R
^{
s.shape
}
\to
\mathbb
R
^{
d.shape
}
,
\end{align*}
its gradient at the position
\texttt
{
s=position
}
is a linear map of the
following shape:
\footnote
{
There are various ways to think about derivatives and
gradients of
multidimensional functions. A different view on gradients would
be that at a
given point
$
s
=
s
_
0
$
the gradient is a matrix with
\texttt
{
s.size
}
columns and
\texttt
{
d.size
}
rows. Obviously, it is not
feasible to store such a matrix on a
computer due to its size. There we think
of this matrix in terms of a linear
map which maps an array of shape
\texttt
{
s.shape
}
to
an array of shape
\texttt
{
d
.shape
}
. This linear map shall be implemented on the computer in terms
of a function. Think of this map as a linear approximation to
\texttt
{
R
}
based
at
\texttt
{
s
\_
0
}
.
}
its gradient at the position
\texttt
{
s=position
}
is a linear map of the
following shape:
\footnote
{
There are various ways to think about derivatives and
gradients of
multidimensional functions. A different view on gradients would
be that at a
given point
$
s
=
\text
{
position
}
$
the gradient is a matrix with
\texttt
{
s.size
}
columns and
\texttt
{
d.size
}
rows. Obviously, it is not
feasible to store such a matrix on a
computer due to its size. There we think
of this matrix in terms of a linear map which maps
an array of shape
\texttt
{
s
.shape
}
to an array of shape
\texttt
{
d.shape
}
. This linear map shall
be implemented on the computer in terms of a function. Think of this map as a
linear approximation to
\texttt
{
R
}
based at
\texttt
{
position
}
.
}
\begin{align*}
\left
.
\frac
{
dR
}{
ds
}
\right

_{
s=position
}
= R':
\mathbb
R
^{
s.shape
}
\to
\mathbb
R
^{
d.shape
}
\left
.
\frac
{
dR
}{
ds
}
\right

_{
s=
\text
{
position
}
}
= R':
\mathbb
R
^{
s.shape
}
\to
\mathbb
R
^{
d.shape
}
\end{align*}
What needs to be implemented is a function
\texttt
{
R
\_
prime(position, s0)
}
which
takes the arguments
\texttt
{
position
}
(which is an array of shape
\texttt
{
s.shape
}
...
...
@@ 315,8 +315,4 @@ Why is this already sufficient?
R
^
\dagger
$
. All in all, we need an implementation for
$
R
$
and
$
R
^
\dagger
$
.
\end{itemize}
% \section*{Bibliography test}
% RESOLVE was first presented in \cite{Resolve2016}.
% \printbibliography
\end{document}
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