Improving importance estimation in covariate shift for providing accurate prediction error

In traditional Machine Learning, the algorithms predictions are based on the assumption that the data follows the same distribution in both the training and the test datasets. However, in real world data this condition does not hold and, for instance, the distribution of the covariates changes whereas the conditional distribution of the targets remains unchanged. This situation is called covariate shift problem where standard error estimation may be no longer accurate. In this context, the importance is a measure commonly used to alleviate the influence of covariate shift on error estimations. The main drawback is that it is not easy to compute. The Kullback-Leibler Importance Estimation Procedure (KLIEP) is capable of estimating importance in a promising way. Despite its good performance, it fails to ignore target information, since it only includes the covariates information for computing the importance. In this direction, this paper explores the potential performance improvement if target information is considered in the computation of the importance. Then, a redefinition of the importance arises in order to be generalized in this way. Besides the potential improvement in performance, including target information make possible the application to a real application about plankton classification that motivates this research and characterized by its great dimensionality, since considering targets rather than covariates reduces the computation and the noise in the covariates. The impact of taking target information is also explored when Logistic Regression (LR), Kernel Mean Matching (KMM), Ensemble Kernel Mean Matching (EKMM) and the naive predecessor of KLIEP called Kernel Density Estimation (KDE) methods estimate the importance. The experimental results lead to a more accurate error estimation using target information, especially in case of the more promising method KLIEP.

Regularized boosting with an increasing coefficient magnitude stop criterion as meta-learner in hyperparameter optimization stacking ensemble

In Hyperparameter Optimization (HPO), only the hyperparameter configuration with the best performance is chosen after performing several trials, then, discarding the effort of training all the models with every hyperparameter configuration trial and performing an ensemble of all them. This ensemble consists of simply averaging the model predictions or weighting the models by a certain probability. Recently, other more sophisticated ensemble strategies, such as the Caruana method or the stacking strategy has been proposed. On the one hand, the Caruana method performs well in HPO ensemble, since it is not affected by the effects of multicollinearity, which is prevalent in HPO. It just computes the average over a subset of predictions with replacement. But it does not benefit from the generalization power of a learning process. On the other hand, stacking methods include a learning procedure since a meta-learner is required to perform the ensemble. Yet, one hardly finds advice about which meta-learner is adequate. Besides, some meta-learners may suffer from the effects of multicollinearity or need to be tuned to reduce them. This paper explores meta-learners for stacking ensemble in HPO, free of hyperparameter tuning, able to reduce the effects of multicollinearity and considering the ensemble learning process generalization power. At this respect, the boosting strategy seems promising as a stacking meta-learner. In fact, it completely removes the effects of multicollinearity. This paper also proposes an implicit regularization in the classical boosting method and a novel non-parametric stop criterion suitable only for boosting and specifically designed for HPO. The synergy between these two improvements over boosting exhibits competitive and promising predictive power performance compared to other existing meta-learners and ensemble approaches for HPO other than the stacking ensemble.