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https://issues.apache.org/jira/browse/MATH-278?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Eugene Kirpichov updated MATH-278:
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Attachment: loess.patch.v2
Attached a patch that does not change the AbstractIntegrator class, the $Date$
argument is replaced with '???', and parameters are made final and initialized
in two constructors. Tests and Javadocs updated accordingly.
Actually, I don't know what the $Revision$ and $Date$ are for and where they
come from. Are they filled in automatically by a pre-commit hook? If so, should
I leave them like '???' in the patch?
If I omit them altogether, I get a checkstyle error about the missing @version
tag.
> 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, loess.patch.v2
>
>
> 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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