PPRankRLS - ranking regularized least-squares, pairwise preferences¶
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class
rlscore.learner.rankrls_with_pairwise_preferences.PPRankRLS(X, pairs_start_inds, pairs_end_inds, regparam=1.0, kernel='LinearKernel', basis_vectors=None, **kwargs)¶ Bases:
rlscore.predictor.predictor.PredictorInterfaceRegularized least-squares ranking (RankRLS) with pairwise preferences
Parameters: - X : {array-like, sparse matrix}, shape = [n_samples, n_features]
Data matrix
- pairs_start_inds : {array-like}, shape = [n_preferences]
pairwise preferences: pairs_start_inds[i] > pairs_end_inds[i]
- pairs_end_inds : {array-like}, shape = [n_preferences]
pairwise preferences: pairs_start_inds[i] > pairs_end_inds[i]
- regparam : float, optional
regularization parameter, regparam > 0 (default=1.0)
- 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)
Other Parameters: - 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: m = n_samples, d = n_features, p = n_preferences, b = n_bvectors
O(m^3 + dm^2 + p): basic case
O(dm^2 + p): Linear Kernel, d < m
O(bm^2 + p): Sparse approximation with basis vectors
RankRLS algorithm was generalized in [1] to learning directly from pairwise preferences.
References
[1] Tapio Pahikkala, Evgeni Tsivtsivadze, Antti Airola, Jouni Jarvinen, and Jorma Boberg. An efficient algorithm for learning to rank from preference graphs. Machine Learning, 75(1):129-165, 2009.
Attributes: - predictor : {LinearPredictor, KernelPredictor}
trained predictor
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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
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solve(regparam)¶ Re-trains RankRLS for the given regparam.
Parameters: - regparam : float, optional
regularization parameter, regparam > 0 (default=1.0)