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From mengxr <>
Subject [GitHub] spark pull request: [MLLIB][SPARK-5502] User guide for isotonic re...
Date Wed, 11 Feb 2015 21:02:50 GMT
Github user mengxr commented on a diff in the pull request:
    --- Diff: docs/ ---
    @@ -0,0 +1,161 @@
    +layout: global
    +title: Naive Bayes - MLlib
    +displayTitle: <a href="mllib-guide.html">MLlib</a> - Regression
    +## Regression
    +[Regression]( is a statistical process
    +for estimating the relationships among variables. It includes many techniques for modeling
    +and analyzing several variables, when the focus is on the relationship between
    +a dependent variable and one or more independent variables.
    +## Isotonic regression
    +[Isotonic regression](
    +belongs to the family of regression algorithms. Formally isotonic regression is a problem
    +given a finite set of real numbers `$Y = {y_1, y_2, ..., y_n}$` representing observed
    +and `$X = {x_1, x_2, ..., x_n}$` the unknown response values to be fitted
    +finding a function that minimises
    +  f(x) = \sum_{i=1}^n w_i (y_i - x_i)^2
    +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](
    +best fitting the original data points.
    +MLlib supports a
    +[pool adjacent violators algorithm](
    +which uses an approach to
    +[parallelizing isotonic regression](
    --- End diff --
    Same here:

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