# BayesianRidge¶

class ibex.sklearn.linear_model.BayesianRidge(n_iter=300, tol=0.001, alpha_1=1e-06, alpha_2=1e-06, lambda_1=1e-06, lambda_2=1e-06, compute_score=False, fit_intercept=True, normalize=False, copy_X=True, verbose=False)

Bases: sklearn.linear_model.bayes.BayesianRidge, 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.BayesianRidge().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.BayesianRidge().fit(iris[features], iris['class'])
>>>
>>> #scalar intercept
>>> type(prd.intercept_)
<class 'numpy.float64'>


Bayesian ridge regression

Fit a Bayesian ridge model and optimize the regularization parameters lambda (precision of the weights) and alpha (precision of the noise).

Read more in the User Guide.

n_iter : int, optional
Maximum number of iterations. Default is 300.
tol : float, optional
Stop the algorithm if w has converged. Default is 1.e-3.
alpha_1 : float, optional
Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter. Default is 1.e-6
alpha_2 : float, optional
Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter. Default is 1.e-6.
lambda_1 : float, optional
Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter. Default is 1.e-6.
lambda_2 : float, optional
Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter. Default is 1.e-6
compute_score : boolean, optional
If True, compute the objective function at each step of the model. Default is False
fit_intercept : boolean, optional
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered). Default is True.
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
verbose : boolean, optional, default False
Verbose mode when fitting the model.
coef_ : array, shape = (n_features)
Coefficients of the regression model (mean of distribution)
alpha_ : float
estimated precision of the noise.
lambda_ : float
estimated precision of the weights.
sigma_ : array, shape = (n_features, n_features)
estimated variance-covariance matrix of the weights
scores_ : float
if computed, value of the objective function (to be maximized)
>>> from sklearn import linear_model
>>> clf = linear_model.BayesianRidge()
>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
...
BayesianRidge(alpha_1=1e-06, alpha_2=1e-06, compute_score=False,
copy_X=True, fit_intercept=True, lambda_1=1e-06, lambda_2=1e-06,
n_iter=300, normalize=False, tol=0.001, verbose=False)
>>> clf.predict([[1, 1]])
array([ 1.])


For an example, see examples/linear_model/plot_bayesian_ridge.py.

D. J. C. MacKay, Bayesian Interpolation, Computation and Neural Systems, Vol. 4, No. 3, 1992.

R. Salakhutdinov, Lecture notes on Statistical Machine Learning, http://www.utstat.toronto.edu/~rsalakhu/sta4273/notes/Lecture2.pdf#page=15 Their beta is our self.alpha_ Their alpha is our self.lambda_

fit(X, y)[source]

Note

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

Fit the model

X : numpy array of shape [n_samples,n_features]
Training data
y : numpy array of shape [n_samples]
Target values. Will be cast to X’s dtype if necessary

self : returns an instance of self.

predict(X, return_std=False)[source]

Note

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

Predict using the linear model.

In addition to the mean of the predictive distribution, also its standard deviation can be returned.

X : {array-like, sparse matrix}, shape = (n_samples, n_features)
Samples.
return_std : boolean, optional
Whether to return the standard deviation of posterior prediction.
y_mean : array, shape = (n_samples,)
Mean of predictive distribution of query points.
y_std : array, shape = (n_samples,)
Standard deviation of predictive distribution of query points.
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.