Github user WeichenXu123 commented on a diff in the pull request:
https://github.com/apache/spark/pull/13381#discussion_r66715565
--- Diff: docs/ml-classification-regression.md ---
@@ -685,6 +685,76 @@ The implementation matches the result from R's
survival function
</div>
+## Isotonic regression
+[Isotonic regression](http://en.wikipedia.org/wiki/Isotonic_regression)
+belongs to the family of regression algorithms. Formally isotonic
regression is a problem where
+given a finite set of real numbers `$Y = {y_1, y_2, ..., y_n}$`
representing observed responses
+and `$X = {x_1, x_2, ..., x_n}$` the unknown response values to be fitted
+finding a function that minimises
+
+`\begin{equation}
+ f(x) = \sum_{i=1}^n w_i (y_i - x_i)^2
+\end{equation}`
+
+with respect to complete order subject to
+`$x_1\le x_2\le ...\le x_n$` where `$w_i$` are positive weights.
+The resulting function is called isotonic regression and it is unique.
+It can be viewed as least squares problem under order restriction.
+Essentially isotonic regression is a
+[monotonic function](http://en.wikipedia.org/wiki/Monotonic_function)
+best fitting the original data points.
+
+In `spark.ml`, we implement a
--- End diff --
@jkbradley Done.
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