scikit-rvm is a Python module implementing the Relevance Vector Machine (RVM) machine learning technique using the scikit-learn API.

With NumPy, SciPy and scikit-learn available in your environment, install with:

pip install https://github.com/JamesRitchie/scikit-rvm/archive/master.zip

Regression is done with the RVR class:

>>> from skrvm import RVR
>>> X = [[0, 0], [2, 2]]
>>> y = [0.5, 2.5 ]
>>> clf = RVR(kernel='linear')
>>> clf.fit(X, y)
RVR(alpha=1e-06, beta=1e-06, beta_fixed=False, bias_used=True, coef0=0.0,
coef1=None, degree=3, kernel='linear', n_iter=3000,
threshold_alpha=1000000000.0, tol=0.001, verbose=False)
>>> clf.predict([[1, 1]])
array([ 1.49995187])

Classification is done with the RVC class:

>>> from skrvm import RVC
>>> from sklearn.datasets import load_iris
>>> clf = RVC()
>>> clf.fit(iris.data, iris.target)
RVC(alpha=1e-06, beta=1e-06, beta_fixed=False, bias_used=True, coef0=0.0,
coef1=None, degree=3, kernel='rbf', n_iter=3000, n_iter_posterior=50,
threshold_alpha=1000000000.0, tol=0.001, verbose=False)
>>> clf.score(iris.data, iris.target)
0.97999999999999998

The RVM is a sparse Bayesian analogue to the Support Vector Machine, with a number of advantages:

• It provides probabilistic estimates, as opposed to the SVM's point estimates.
• Typically provides a sparser solution than the SVM, which tends to have the number of support vectors grow linearly with the size of the training set.
• Does not need a complexity parameter to be selected in order to avoid overfitting.

However it is more expensive to train than the SVM, although prediction is faster and no cross-validation runs are required.

The RVM's original creator Mike Tipping provides a selection of papers offering detailed insight into the formulation of the RVM (and sparse Bayesian learning in general) on a dedicated page, along with a Matlab implementation.

Most of this implementation was written working from Section 7.2 of Christopher M. Bishops's Pattern Recognition and Machine Learning.

• James Ritchie
• Jonathan Feinberg

• Implement the fast Sequential Sparse Bayesian Learning Algorithm outlined in Section 7.2.3 of Pattern Recognition and Machine Learning
• Handle ill-conditioning errors more gracefully.
• Implement more kernel choices.
• Create more detailed examples with IPython notebooks.