LeaveOneOutRLS - RLS with leave-one-out regularization parameter selection¶
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class
rlscore.learner.rls.
LeaveOneOutRLS
(X, Y, kernel='LinearKernel', basis_vectors=None, regparams=None, measure=None, **kwargs)¶ Bases:
rlscore.predictor.predictor.PredictorInterface
Regularized least-squares regression/classification. Wrapper code that selects regularization parameter automatically based on leave-one-out cross-validation.
Parameters: - X : {array-like, sparse matrix}, shape = [n_samples, n_features]
Data matrix
- Y : {array-like}, shape = [n_samples] or [n_samples, n_labels]
Training set labels
- kernel : {‘LinearKernel’, ‘GaussianKernel’, ‘PolynomialKernel’, ‘PrecomputedKernel’, …}
kernel function name, imported dynamically from rlscore.kernel
- basis_vectors : {array-like, sparse matrix}, shape = [n_bvectors, n_features], optional
basis vectors (typically a randomly chosen subset of the training data)
- regparams : {array-like}, shape = [grid_size] (optional)
regularization parameter values to be tested, default = [2^-15,…,2^15]
- measure : function(Y, P) (optional)
a performance measure from rlscore.measure used for model selection, default sqerror (mean squared error)
Other Parameters: - Typical kernel parameters include:
- bias : float, optional
LinearKernel: the model is w*x + bias*w0, (default=1.0)
- gamma : float, optional
GaussianKernel: k(xi,xj) = e^(-gamma*<xi-xj,xi-xj>) (default=1.0) PolynomialKernel: k(xi,xj) = (gamma * <xi, xj> + coef0)**degree (default=1.0)
- coef0 : float, optional
PolynomialKernel: k(xi,xj) = (gamma * <xi, xj> + coef0)**degree (default=0.)
- degree : int, optional
PolynomialKernel: k(xi,xj) = (gamma * <xi, xj> + coef0)**degree (default=2)
Notes
Computational complexity of training (model selection is basically free due to fast regularization and leave-one-out): m = n_samples, d = n_features, l = n_labels, b = n_bvectors, r=grid_size
O(m^3 + dm^2 + rlm^2): basic case
O(md^2 + rlmd): Linear Kernel, d < m
O(mb^2 + rlmb): Sparse approximation with basis vectors
Basic information about RLS, and a description of the fast leave-one-out method can be found in [1].
References
[1] Ryan Rifkin, Ross Lippert. Notes on Regularized Least Squares. Technical Report, MIT, 2007.
Attributes: - predictor : {LinearPredictor, KernelPredictor}
trained predictor
- cv_performances : array, shape = [grid_size]
leave-one-out performances for each grid point
- cv_predictions : array, shape = [grid_size, n_samples] or [grid_size, n_samples, n_labels]
leave-one-out predictions
- regparam : float
regparam from grid with best performance
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predict
(X)¶ Predicts outputs for new inputs
Parameters: - X : {array-like, sparse matrix}, shape = [n_samples, n_features]
input data matrix
Returns: - P : array, shape = [n_samples, n_tasks]
predictions