Robust locally weighted regression (Loess / Lowess)

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Details

• New Feature
• Status: Closed
• Major
• Resolution: Fixed
• None
• None
• None
• None

Description

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.

Attachments

1. loess.patch
25 kB
Eugene Kirpichov
2. loess.patch.v2
24 kB
Eugene Kirpichov

People

Luc Maisonobe
Eugene Kirpichov