Piecewise linear regression with automatic knot selection

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Hi everyone,

I am new to Julia, mostly work with R. I am looking for the equivalent of the “segmented” package in R, to fit a piecewise linear (constant in my special case) regression where the knot location is automated. Does this functionality exist in Julia?

Thanks in advance

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Hello and welcome to the community :slight_smile:

Would EllZeroTrendFiltering.jl perhaps fit your bill? I do not think that this package fits the regression models for you, but it solves the most difficult problem, finding the optimal knot points by solving a dynamic-programming problem. With the knot points determined, it should be straightforward to use any of the standard packages for linear regression to fit the models.

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Thank you @baggepinnen for a perfect warm welcome! That is super helpful, it got me thinking. I am concerned that the optimal knot locations that emerge for a piecewise constant function may be not be same as the knots for a piecewise linear function. I am wondering if the recursive problem in the piecewise constant case is identical to fitting a 1-D regression tree.

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The package should find you a piecewise linear function, from the readme

We want to find a piecewise linear, continuous function

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Related: If you first perform an ordinary regression which returns a function for evaluating your regression model, then the problem reduces to finding a piecewise linear approximation to that function. This thread contains several methods for performing adaptive piecewise linear interpolation of an arbitrary function to a user-specified error tolerance.

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Quick question–is there a reason your function has to be piecewise-linear? Smooth approaches like LOESS are almost always better.

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GitHub - iuliancioarca/AdaptiveSampling.jl: Adaptive sampling rate algorithms for waveform compression My simplistic approach.

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For what its worth, I made this package that explicitly does what you want: GitHub - stelmo/LinearSegmentation.jl: Linear segmentation

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Could you explain the method and how to use it in the above context?

There is a simple method based on a proximal gradient method which is described by Adaptive Piecewise Polynomial Estimation via Trend Filtering.

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I have some code for doing linear regressions where the knots are also estimated - all coded up as a NLS/GMM problem. See section 12.2 of these notes (I could probably share the code, if wanted.)

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