# Regression splines
This module includes two spline implementations splines suitable for regression: linear splines using a hinge function basis, and natural cubic splines.
```python
import numpy as np
import matplotlib.pyplot as plt
from regspline import LinearSpline
plt.close('all')
knots = [0,1,2]
coeffs = [1,2,3]
s = LinearSpline(knots, coeffs)
y=s(np.linspace(0,1))
x=np.linspace(0,np.pi)
y=np.sin(x)
xobs = np.repeat(x,50)
yobs = np.repeat(y,50) + 0.01*np.random.randn(*xobs.shape)
s, res = LinearSpline.from_data(xobs, yobs,
knots=np.linspace(0,np.pi,30),
method='OLS',
return_estim_result=True,
prune=True)
plt.plot(x,y)
plt.plot(x,s(x))
```
Several regression types are supported to extract the splines from data, including OLS, LASSO, and quantile regression. See the example files.
## Installation
You can install this library directly from github:
```bash
pip install regspline.git
```
There are two optional dependencies: `scikit-learn`, and `cvxopt`. They are only required to estimate splines on data with, respectively, support vector regressions, and LASSO.
## Background
The module contains two splines:
- A linear spline represented by Hinge functions: $h_i(x) = \max(x-k_i,0)$, where $k_i$ are the knots.
- A natural cubic spline.
The splines chosen:
- have coefficents that have a one-to-one correspondence with the knots.
- have the ability that knots can be removed, e.g., when the corresponding coefficient is small or insignificant, without changing the basis functions corresponding to other knots.
- have the ability to represent functions with sparse basis.
One way to interpret, e.g., the linear spline in the hings basis is as follows. $h_1(x)$ sets an initial slope from the first knot onwards. Then next basis function $h_2(x)$ can adjust the slope at the knot $k_2$, if no adjustment is required, its coefficient is insignificant and the knot can be removed from the spline without any impact on the other basis functions.
## Related projects
Some projects with related methods:
- [basis-expansions](https://github.com/madrury/basis-expansions)
- [py-earth](https://github.com/scikit-learn-contrib/py-earth)
- Quantile regression using decision trees [scikit-garden](https://scikit-garden.github.io/)
The module differs from these implementations as it implements the splines as functions, and they are not integrated within an estimation framework.
## Development
For development purposes, clone the repo:
```bash
git clone https://github.com/mvds314/regspline.git
```
Then navigate to the folder containing `setup.py` and run
```bash
pip install -e .
```
to install the package in edit mode.
Run unittests with `pytest`.
Install the optional dependencies to test all functionality.
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"description": "# Regression splines\n\nThis module includes two spline implementations splines suitable for regression: linear splines using a hinge function basis, and natural cubic splines.\n\n```python\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom regspline import LinearSpline\nplt.close('all')\n\nknots = [0,1,2]\ncoeffs = [1,2,3]\ns = LinearSpline(knots, coeffs)\ny=s(np.linspace(0,1))\n\nx=np.linspace(0,np.pi)\ny=np.sin(x)\nxobs = np.repeat(x,50)\nyobs = np.repeat(y,50) + 0.01*np.random.randn(*xobs.shape)\n\ns, res = LinearSpline.from_data(xobs, yobs,\n knots=np.linspace(0,np.pi,30),\n method='OLS',\n return_estim_result=True,\n prune=True)\n\nplt.plot(x,y)\nplt.plot(x,s(x))\n```\n\nSeveral regression types are supported to extract the splines from data, including OLS, LASSO, and quantile regression. See the example files.\n\n## Installation\n\nYou can install this library directly from github:\n\n```bash\npip install regspline.git\n```\n\nThere are two optional dependencies: `scikit-learn`, and `cvxopt`. They are only required to estimate splines on data with, respectively, support vector regressions, and LASSO.\n\n## Background\n\nThe module contains two splines:\n\n- A linear spline represented by Hinge functions: $h_i(x) = \\max(x-k_i,0)$, where $k_i$ are the knots.\n- A natural cubic spline.\n\nThe splines chosen:\n\n- have coefficents that have a one-to-one correspondence with the knots.\n- have the ability that knots can be removed, e.g., when the corresponding coefficient is small or insignificant, without changing the basis functions corresponding to other knots.\n- have the ability to represent functions with sparse basis.\n\nOne way to interpret, e.g., the linear spline in the hings basis is as follows. $h_1(x)$ sets an initial slope from the first knot onwards. Then next basis function $h_2(x)$ can adjust the slope at the knot $k_2$, if no adjustment is required, its coefficient is insignificant and the knot can be removed from the spline without any impact on the other basis functions.\n\n## Related projects\n\nSome projects with related methods:\n\n- [basis-expansions](https://github.com/madrury/basis-expansions)\n- [py-earth](https://github.com/scikit-learn-contrib/py-earth)\n- Quantile regression using decision trees [scikit-garden](https://scikit-garden.github.io/)\n\nThe module differs from these implementations as it implements the splines as functions, and they are not integrated within an estimation framework.\n\n## Development\n\nFor development purposes, clone the repo:\n\n```bash\ngit clone https://github.com/mvds314/regspline.git\n```\n\nThen navigate to the folder containing `setup.py` and run\n\n```bash\npip install -e .\n```\n\nto install the package in edit mode.\n\nRun unittests with `pytest`.\n\nInstall the optional dependencies to test all functionality.\n\n",
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