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From "Sebb (JIRA)" <j...@apache.org>
Subject [jira] Commented: (MATH-278) Robust locally weighted regression (Loess / Lowess)
Date Fri, 19 Jun 2009 20:54:07 GMT

    [ https://issues.apache.org/jira/browse/MATH-278?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12722001#action_12722001
] 

Sebb commented on MATH-278:
---------------------------

serialVersionUID should be private
The patch includes an unrelated change to AbstractIntegrator.java.

It would be useful to add a constructor which had parameters for bandwidth and roubustnessIterators,
and drop the corresponding setxxx() methods
The fields could then be made final, and the class would then be immutable and thus thread-safe.

The SVN keyword $Date$ causes problems when checking releases, so I'd recommend that it is
removed.

> Robust locally weighted regression (Loess / Lowess)
> ---------------------------------------------------
>
>                 Key: MATH-278
>                 URL: https://issues.apache.org/jira/browse/MATH-278
>             Project: Commons Math
>          Issue Type: New Feature
>            Reporter: Eugene Kirpichov
>         Attachments: loess.patch
>
>
> Attached is a patch that implements the robust Loess procedure for smoothing univariate
scatterplots with local linear regression ( http://en.wikipedia.org/wiki/Local_regression)
described by William Cleveland in http://www.math.tau.ac.il/~yekutiel/MA%20seminar/Cleveland%201979.pdf
, with tests.
> (Also, the patch fixes one missing-javadoc checkstyle warning in the AbstractIntegrator
class: I wanted to make it so that the code with my patch does not generate any checkstyle
warnings at all)
> I propose to include the procedure into commons-math because commons-math, as of now,
does not possess a method for robust smoothing of noisy data: there is  interpolation (which
virtually can't be used for noisy data at all) and there's regression, which has quite different
goals. 
> Loess allows one to build a smooth curve with a controllable degree of smoothness that
approximates the overall shape of the data.
> I tried to follow the code requirements as strictly as possible: the tests cover the
code completely, there are no checkstyle warnings, etc. The code is completely written by
myself from scratch, with no borrowings of third-party licensed code.
> The method is pretty computationally intensive (10000 points with a bandwidth of 0.3
and 4 robustness iterations take about 3.7sec on my machine; generally the complexity is O(robustnessIters
* n^2 * bandwidth)), but I don't know how to optimize it further; all implementations that
I have found use exactly the same algorithm as mine for the unidimensional case.
> Some TODOs, in vastly increasing order of complexity:
>  - Make the weight function customizable: according to Cleveland, this is needed in some
exotic cases only, like, where the desired approximation is non-continuous, for example.
>  - Make the degree of the locally fitted polynomial customizable: currently the algorithm
does only a linear local regression; it might be useful to make it also use quadratic regression.
Higher degrees are not worth it, according to Cleveland.
>  - Generalize the algorithm to the multidimensional case: this will require A LOT of
hard work.

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