On the design of Bayesian principled algorithms for imbalanced classification

Abstract

Singular Problems are those whose characteristics compromise the correct operation of conventional discriminative machines, obtaining unsatisfactory results. Among them, imbalanced classification problems stand out, those in which there are large differences in the class populations or/and the cost policy penalizes to a greater extent the choice of certain classes, biasing the machine output in favor of the predominant classes. Therefore, the application of specific methods that compensate the imbalance is required, allowing the detection of the minority classes.Particularly for the binary case, a state-of-the-art survey of the existing rebalancing methods is carried out. Most of the proposed techniques are purely empirical, without a complete analysis of the statistical implications of their application.Although their use may provide good results under certain conditions, any change in these conditions may lead to a degradation of their performance. Therefore, a principled methodology based on Bayesian statistical theory is presented with the aim of constructing robust solutions. This methodology is based on the likelihood ratio invariance principle, for which two sufficient and necessary conditions are established: the use of Bregman divergences as a surrogate cost and statistically neutral rebalancing methods. In addition, principled two-step classification procedures are proposed and a rebalanced design process based on the combination of methods is described in detail. Several experiments support the methodology, studying its effects and limitations in real problems under different circumstances: larger or smaller number of available samples and presence of noise.Finally, the SMOTE algorithm, one of the most common rebalancing methods, is studied in more depth. Due to the filiform generation of samples −by means of the nearest neighbors−, SMOTE presents difficulties with high dimensionality problems.Therefore, an alternative, VoluSMOTE, is proposed to correct or mitigate such effects by volumetric generation."La perfeccción es una pulida corrección de errores"

Design of cultural and creative experience products in scenic spots based on CORE model

“…This expression can be rewritten using Bayesian formulas as: Plain Bayesian classification is performed under the simple assumption that the attribute values are also independent of each other when explicitly given target values [20][21]. In other words, the assumption also suggests that in a given instance target value situation, this situation is observable given the joint 12 , , , n a a a K probability is in fact equal to the product of the probabilities of the individual independent attributes:…”