Github user njayaram2 commented on a diff in the pull request:
https://github.com/apache/incubator-madlib/pull/162#discussion_r132339557
--- Diff: doc/design/modules/neural-network.tex ---
@@ -46,41 +47,49 @@ \subsection{Formal Description}
In the remaining part of this section, we will give a formal description
of the derivation of objective function and its gradient.
\paragraph{Objective function.}
-We mostly follow the notations in example 1.5.3 from Bertsekas
\cite{bertsekas1999nonlinear}, for a multilayer perceptron that has $N$ layers
(stages), and the $k$th stage has $n_k$ activation units ($\phi : \mathbb{R}
\to \mathbb{R}$), the objective function is given as
-\[f_{(y, z)}(u) = \frac{1}{2} \|h(u, y) - z\|_2^2,\]
-where $y \in \mathbb{R}^{n_0}$ is the input vector, $z \in
\mathbb{R}^{n_N}$ is the output vector,
+We mostly follow the notations in example 1.5.3 from Bertsekas
\cite{bertsekas1999nonlinear}, for a multilayer perceptron that has $N$ layers
(stages), and the $k$th stage has $n_k$ activation units ($\phi : \mathbb{R}
\to \mathbb{R}$), the objective function for regression is given as
+\[f_{(x, y)}(u) = \frac{1}{2} \|h(u, x) - y\|_2^2,\]
--- End diff --
`$k$th` -> `$k$^{th}`.
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