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Basis Expansions

This module includes some scikit-learn style transformers that perform basis expansions on a feature x for use in regression. A basis expansions for the feature x is a collection of functions

f_0, f_1, f_2, ...

that are meant to be applied to the feature to construct derived features in a regression model. The functions in the expansions are often chosen to allow the model to adapt to non-linear shapes in the predictor/response relationship. When a basis expansion is applied to the feature x, the result is a new matrix or data frame of derived features

f_0(x), f_1(x), f_2(x), ...

Installation

You can install this library directly from github:

pip install git+https://github.com/madrury/basis-expansions.git

If you would prefer to install from source, first clone this repository:

git clone https://github.com/madrury/basis-expansions.git

And then navigate into the cloned directory, and run pip install

cd basis_expansions
pip install .

Supported Expansions

The following classes are included:

  • Binner: Creates indicator variables by segmenting the range of x into disjoint intervals.
  • GaussianKernel: Create Gaussian Kernel features, also known as "radial basis functions" by people cooler than me.
  • Polynomial: Creates polynomial features. Using these features in a regression fits a polynomial function of a given degree x to y.
  • LinearSpline: Creates a piecewise linear spline which joins continuously at the knots. Using this in a regression fits a piecewise linear function of x to y.
  • CubicSpline: Creates a piecewise cubic spline which joins continuously, differentiably, and second differentiably at a set of supplied knots.
  • NaturalCubicSpline: Creates a piecewise natural cubic spline (cubic curves in the interior segments, linear in the exterior segments) which joins continuously, differentiably, and second differentiably at a set of supplied knots.

Basis Expansions

Examples

The most basic use case is to transform a numpy.array:

x = np.random.uniform(0, 1, size=10)
pl = LinearSpline(knots=[0.25, 0.75])
pl.fit_transform(x)

which results in a two dimensional array:

array([[ 0.21776114,  0.        ,  0.        ],
       [ 0.63360478,  0.38360478,  0.        ],
       [ 0.29089787,  0.04089787,  0.        ],
       [ 0.83284663,  0.58284663,  0.08284663],
       [ 0.89158883,  0.64158883,  0.14158883],
       [ 0.97076139,  0.72076139,  0.22076139],
       [ 0.83373019,  0.58373019,  0.08373019],
       [ 0.39301854,  0.14301854,  0.        ],
       [ 0.27773455,  0.02773455,  0.        ],
       [ 0.68772864,  0.43772864,  0.        ]])

If we transform a pandas.Series:

s = pd.Series(x, name="moshi")
pl = LinearSpline(knots=[0.25, 0.75])
pl.fit_transform(s)

the result is a pandas.DataFrame:

   moshi_spline_linear  moshi_spline_0  moshi_spline_1
0             0.217761        0.000000        0.000000
1             0.633605        0.383605        0.000000
2             0.290898        0.040898        0.000000
3             0.832847        0.582847        0.082847
4             0.891589        0.641589        0.141589
5             0.970761        0.720761        0.220761
6             0.833730        0.583730        0.083730
7             0.393019        0.143019        0.000000
8             0.277735        0.027735        0.000000
9             0.687729        0.437729        0.000000

More advanced use can combine these transformers with sklearn.pipeline objects. For helper classes that allow for transformations on pandas.DataFrames, see examples/dftransformers.py.

Examples

See the basis-expansions-regressions.ipynb notebook for examples of use.