[GitHub] spark pull request #13381: [SPARK-15608][ml][examples][doc] add examples and...

[jkbradley <gi...@git.apache.org>]

Github user jkbradley commented on a diff in the pull request:

    https://github.com/apache/spark/pull/13381#discussion_r66698376
  
    --- 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.
    +
    +MLlib supports a
    +[pool adjacent violators algorithm](http://doi.org/10.1198/TECH.2010.10111)
    +which uses an approach to
    +[parallelizing isotonic regression](http://doi.org/10.1007/978-3-642-99789-1_10).
    +The training input is a RDD of tuples of three double values that represent
    --- End diff --
    
    not an RDD


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