# TheilSenRegressor¶

class ibex.sklearn.linear_model.TheilSenRegressor(fit_intercept=True, copy_X=True, max_subpopulation=10000.0, n_subsamples=None, max_iter=300, tol=0.001, random_state=None, n_jobs=1, verbose=False)

Bases: sklearn.linear_model.theil_sen.TheilSenRegressor, ibex._base.FrameMixin

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Note

The documentation following is of the original class wrapped by this class. This class wraps the attribute coef_.

Example:

>>> import pandas as pd
>>> import numpy as np
>>> from ibex.sklearn import datasets
>>> from ibex.sklearn.linear_model import LinearRegression as PdLinearRegression

>>> iris = datasets.load_iris()
>>> features = iris['feature_names']
>>> iris = pd.DataFrame(
...     np.c_[iris['data'], iris['target']],
...     columns=features+['class'])

>>> iris[features]
sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)
0                5.1               3.5                1.4               0.2
1                4.9               3.0                1.4               0.2
2                4.7               3.2                1.3               0.2
3                4.6               3.1                1.5               0.2
4                5.0               3.6                1.4               0.2
...

>>> from ibex.sklearn import linear_model as pd_linear_model
>>>
>>> prd =  pd_linear_model.TheilSenRegressor().fit(iris[features], iris['class'])
>>>
>>> prd.coef_
sepal length (cm)   ...
sepal width (cm)    ...
petal length (cm)   ...
petal width (cm)    ...
dtype: float64


Note

The documentation following is of the original class wrapped by this class. This class wraps the attribute intercept_.

Example:

>>> import pandas as pd
>>> import numpy as np
>>> from ibex.sklearn import datasets
>>> from ibex.sklearn.linear_model import LinearRegression as PdLinearRegression

>>> iris = datasets.load_iris()
>>> features = iris['feature_names']
>>> iris = pd.DataFrame(
...     np.c_[iris['data'], iris['target']],
...     columns=features+['class'])

>>> iris[features]
sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)
0                5.1               3.5                1.4               0.2
1                4.9               3.0                1.4               0.2
2                4.7               3.2                1.3               0.2
3                4.6               3.1                1.5               0.2
4                5.0               3.6                1.4               0.2
...

>>>
>>> from ibex.sklearn import linear_model as pd_linear_model
>>>
>>> prd = pd_linear_model.TheilSenRegressor().fit(iris[features], iris['class'])
>>>
>>> #scalar intercept
>>> type(prd.intercept_)
<class 'numpy.float64'>


Theil-Sen Estimator: robust multivariate regression model.

The algorithm calculates least square solutions on subsets with size n_subsamples of the samples in X. Any value of n_subsamples between the number of features and samples leads to an estimator with a compromise between robustness and efficiency. Since the number of least square solutions is “n_samples choose n_subsamples”, it can be extremely large and can therefore be limited with max_subpopulation. If this limit is reached, the subsets are chosen randomly. In a final step, the spatial median (or L1 median) is calculated of all least square solutions.

Read more in the User Guide.

fit_intercept : boolean, optional, default True
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
max_subpopulation : int, optional, default 1e4
Instead of computing with a set of cardinality ‘n choose k’, where n is the number of samples and k is the number of subsamples (at least number of features), consider only a stochastic subpopulation of a given maximal size if ‘n choose k’ is larger than max_subpopulation. For other than small problem sizes this parameter will determine memory usage and runtime if n_subsamples is not changed.
n_subsamples : int, optional, default None
Number of samples to calculate the parameters. This is at least the number of features (plus 1 if fit_intercept=True) and the number of samples as a maximum. A lower number leads to a higher breakdown point and a low efficiency while a high number leads to a low breakdown point and a high efficiency. If None, take the minimum number of subsamples leading to maximal robustness. If n_subsamples is set to n_samples, Theil-Sen is identical to least squares.
max_iter : int, optional, default 300
Maximum number of iterations for the calculation of spatial median.
tol : float, optional, default 1.e-3
Tolerance when calculating spatial median.
random_state : int, RandomState instance or None, optional, default None
A random number generator instance to define the state of the random permutations generator. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
n_jobs : integer, optional, default 1
Number of CPUs to use during the cross validation. If -1, use all the CPUs.
verbose : boolean, optional, default False
Verbose mode when fitting the model.
coef_ : array, shape = (n_features)
Coefficients of the regression model (median of distribution).
intercept_ : float
Estimated intercept of regression model.
breakdown_ : float
Approximated breakdown point.
n_iter_ : int
Number of iterations needed for the spatial median.
n_subpopulation_ : int
Number of combinations taken into account from ‘n choose k’, where n is the number of samples and k is the number of subsamples.
fit(X, y)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Fit linear model.

X : numpy array of shape [n_samples, n_features]
Training data
y : numpy array of shape [n_samples]
Target values

self : returns an instance of self.

predict(X)

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Predict using the linear model

X : {array-like, sparse matrix}, shape = (n_samples, n_features)
Samples.
C : array, shape = (n_samples,)
Returns predicted values.
score(X, y, sample_weight=None)

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Returns the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - u/v), where u is the residual sum of squares ((y_true - y_pred) ** 2).sum() and v is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.

X : array-like, shape = (n_samples, n_features)
Test samples.
y : array-like, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
sample_weight : array-like, shape = [n_samples], optional
Sample weights.
score : float
R^2 of self.predict(X) wrt. y.