Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/1908#discussion_r16143689
--- Diff: docs/mllib-linear-methods.md ---
@@ -33,24 +33,23 @@ the task of finding a minimizer of a convex function
`$f$` that depends on a var
Formally, we can write this as the optimization problem `$\min_{\wv
\in\R^d} \; f(\wv)$`, where
the objective function is of the form
`\begin{equation}
- f(\wv) :=
- \frac1n \sum_{i=1}^n L(\wv;\x_i,y_i) +
- \lambda\, R(\wv_i)
+ f(\wv) := \lambda\, R(\wv) +
+ \frac1n \sum_{i=1}^n L(\wv;\x_i,y_i)
\label{eq:regPrimal}
\ .
\end{equation}`
Here the vectors `$\x_i\in\R^d$` are the training data examples, for
`$1\le i\le n$`, and
`$y_i\in\R$` are their corresponding labels, which we want to predict.
We call the method *linear* if $L(\wv; \x, y)$ can be expressed as a
function of $\wv^T x$ and $y$.
-Several MLlib's classification and regression algorithms fall into this
category,
+Several of MLlib's classification and regression algorithms fall into this
category,
and are discussed here.
The objective function `$f$` has two parts:
-the loss that measures the error of the model on the training data,
-and the regularizer that measures the complexity of the model.
-The loss function `$L(\wv;.)$` must be a convex function in `$\wv$`.
+the regularizer that controls the complexity of the model,
+and the loss that measures the error of the model on the training data.
+The loss function `$L(\wv;.)$` is typically a convex function in `$\wv$`.
The fixed regularization parameter `$\lambda \ge 0$` (`regParam` in the
code) defines the trade-off
-between the two goals of small loss and small model complexity.
+between the two goals of minimizing the loss (i.e., training error) and
minimizing model complexity (i.e., to avoid overfitting).
--- End diff --
minor: This line is too long. We don't have a style guide for markdown
files. Usually I would try to make each line contain at most 100 chars, and do
not put more than one sentences in the same line.
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