# Piecewise linear regression with automatic knot selection
**URL:** https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984
**Category:** Statistics
**Tags:** question, linear-regression, piecewise
**Created:** [February 3, 2023, 11:20am UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984 "2023-02-03T11:20:36Z")
**Posts on this page:** 10
**Page:** 1
### Author:  [@meghapatnaik](https://discourse.julialang.org/u/meghapatnaik)
#### Post date: [February 3, 2023, 11:20am UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/1 "2023-02-03T11:20:36Z")
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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### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [February 3, 2023, 11:22am UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/2 "2023-02-03T11:22:50Z")
Hello and welcome to the community 🙂
Would [EllZeroTrendFiltering.jl](https://github.com/mfalt/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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### Author:  [@meghapatnaik](https://discourse.julialang.org/u/meghapatnaik)
#### Post date: [February 3, 2023, 3:05pm UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/3 "2023-02-03T15:05:29Z")
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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### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [February 3, 2023, 3:32pm UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/4 "2023-02-03T15:32:41Z")
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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### Author:  [@PeterSimon](https://discourse.julialang.org/u/PeterSimon)
#### Post date: [February 3, 2023, 5:29pm UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/5 "2023-02-03T17:29:29Z")
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](https://discourse.julialang.org/t/hi-i-have-a-function-lets-say-f-sin-0-10-now-i-want-to-break/54826) thread contains several methods for performing adaptive piecewise linear interpolation of an arbitrary function to a user-specified error tolerance.
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### Author:  [@ParadaCarleton](https://discourse.julialang.org/u/ParadaCarleton)
#### Post date: [February 8, 2023, 11:16pm UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/6 "2023-02-08T23:16:49Z")
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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### Author:  [@Iulian.Cioarca](https://discourse.julialang.org/u/Iulian.Cioarca)
#### Post date: [February 9, 2023, 10:40am UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/10 "2023-02-09T10:40:49Z")
[GitHub - iuliancioarca/AdaptiveSampling.jl: Adaptive sampling rate algorithms for waveform compression](https://github.com/iuliancioarca/AdaptiveSampling.jl) My simplistic approach.
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### Author:  [@Elmo](https://discourse.julialang.org/u/Elmo)
#### Post date: [July 6, 2023, 5:11pm UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/11 "2023-07-06T17:11:21Z")
For what its worth, I made this package that explicitly does what you want: [GitHub - stelmo/LinearSegmentation.jl: Linear segmentation](https://github.com/stelmo/LinearSegmentation.jl)
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### Author:  [@RoyiAvital](https://discourse.julialang.org/u/RoyiAvital)
#### Post date: [January 2, 2024, 7:56pm UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/12 "2024-01-02T19:56:04Z")
> [@Iulian.Cioarca](#):
>
> [GitHub - iuliancioarca/AdaptiveSampling.jl: Adaptive sampling rate algorithms for waveform compression](https://github.com/iuliancioarca/AdaptiveSampling.jl) My simplistic approach.
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](https://arxiv.org/abs/1304.2986).
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### Author:  [@Paul\_Soderlind](https://discourse.julialang.org/u/Paul_Soderlind)
#### Post date: [January 2, 2024, 8:42pm UTC](https://discourse.julialang.org/t/piecewise-linear-regression-with-automatic-knot-selection/93984/13 "2024-01-02T20:42:04Z")
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.)
> **[EmpFinPhDAll.pdf](https://drive.google.com/file/d/1k8PmkdVXAA_NR3YD5sdpL4pbXH1-DhAh/view)**
>
> Google Drive file.