QueryRankRLS - ranking regularized least-squares, query-structured data¶
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class
rlscore.learner.query_rankrls.QueryRankRLS(X, Y, qids, regparam=1.0, kernel='LinearKernel', basis_vectors=None, **kwargs)¶ Bases:
rlscore.predictor.predictor.PredictorInterfaceRankRLS algorithm for learning to rank
Implements the learning algorithm for learning from query-structured data.
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
- qids : list of query ids, shape = [n_samples]
Training set qids
- 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: - 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: m = n_samples, d = n_features, l = n_labels, b = n_bvectors
O(m^3 + dm^2 + lm^2): basic case
O(md^2 +lmd): Linear Kernel, d < m
O(mb^2 +lmb): Sparse approximation with basis vectors
RankRLS algorithm was first introduced in [1], extended version of the work and the efficient leave-query-out cross-validation method implemented in the method ‘holdout’ are found in [2].
References
[1] Tapio Pahikkala, Evgeni Tsivtsivadze, Antti Airola, Jorma Boberg and Tapio Salakoski Learning to rank with pairwise regularized least-squares. In Thorsten Joachims, Hang Li, Tie-Yan Liu, and ChengXiang Zhai, editors, SIGIR 2007 Workshop on Learning to Rank for Information Retrieval, pages 27–33, 2007.
[2] 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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holdout(indices)¶ Computes hold-out predictions for a trained RLS.
Parameters: - indices : list of indices, shape = [n_hsamples]
list of indices of training examples belonging to the set for which the hold-out predictions are calculated. Should correspond to one query.
Returns: - F : array, shape = [n_hsamples, n_labels]
holdout query predictions
Notes
Computational complexity of holdout: m = n_samples, d = n_features, l = n_labels, b = n_bvectors, h=n_hsamples
O(h^3 + lmh): basic case
O(min(h^3 + lh^2, d^3 + ld^2) +ldh): Linear Kernel, d < m
O(min(h^3 + lh^2, b^3 + lb^2) +lbh): Sparse approximation with basis vectors
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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=1.0)¶ Trains the learning algorithm, using the given regularization parameter.
Parameters: - regparam : float (regparam > 0)
regularization parameter
Notes
Computational complexity of re-training: m = n_samples, d = n_features, l = n_labels, b = n_bvectors
O(lm^2): basic case
O(lmd): Linear Kernel, d < m
O(lmb): Sparse approximation with basis vectors