LeaveQueryOutRankRLS - QueryRankRLS with leave-query-out regularization parameter selection

class rlscore.learner.query_rankrls.LeaveQueryOutRankRLS(X, Y, qids, kernel='LinearKernel', basis_vectors=None, regparams=None, measure=None, **kwargs)

Bases: rlscore.predictor.predictor.PredictorInterface

RankRLS algorithm for learning to rank with query-structured data. Selects automatically regularization parameter using leave-query-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

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

Uses fast solve and holdout algorithms, complexity depends on the sizes of the queries. Complexity is:

m = n_samples, d = n_features, l = n_labels, b = n_bvectors, r=grid_size, k = n_queries

O(m^3 + dm^2 + r*(m^3/k^2 + lm^2)): basic case

O(md^2 + r*(min(m^3/k^2 + lm^2/k, kd^3 + kld^2) + ldm)): Linear Kernel, d < m

O(mb^2 + r*(min(m^3/k^2 + lm^2/k, kb^3 + klb^2) + lbm)): 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

cv_performances : array, shape = [grid_size]

leave-query-out performances for each grid point

cv_predictions : list of 1D or 2D arrays, shape = [grid_size, n_queries]

predictions for each query, shapes [query_size] or [query_size, n_labels]

regparam : float

regparam from grid with best performance

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