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From mengxr <...@git.apache.org>
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:

https://github.com/apache/spark/pull/4536#discussion_r24532966

--- Diff: docs/mllib-regression.md ---
@@ -0,0 +1,161 @@
+---
+layout: global
+title: Naive Bayes - MLlib
+displayTitle: <a href="mllib-guide.html">MLlib</a> - Regression
+---
+
+## Regression
+[Regression](http://en.wikipedia.org/wiki/Regression_analysis) 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](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
+
+$$+ f(x) = \sum_{i=1}^n w_i (y_i - x_i)^2 +$$
+
+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](http://en.wikipedia.org/wiki/Monotonic_function)
+best fitting the original data points.
+
+MLlib supports a
+which uses an approach to
+[parallelizing isotonic regression](http://softlib.rice.edu/pub/CRPC-TRs/reports/CRPC-TR96640.pdf).
--- End diff --

Same here: http://doi.org/10.1007/978-3-642-99789-1_10

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