Journal of Data Science

Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data science. Recently a class of weighted Support Vector Machines (wSVMs) has been developed to estimate class probabilities through ensemble learning for K-class problems (Wu et al., 2010; Wang et al., 2019), where K is the number of classes. The estimators are robust and achieve high accuracy for probability estimation, but their learning is implemented through pairwise coupling, which demands polynomial time in K. In this paper, we propose two new learning schemes, the baseline learning and the One-vs-All (OVA) learning, to further improve wSVMs in terms of computational efficiency and estimation accuracy. In particular, the baseline learning has optimal computational complexity in the sense that it is linear in K. Though not the most efficient in computation, the OVA is found to have the best estimation accuracy among all the procedures under comparison. The resulting estimators are distribution-free and shown to be consistent. We further conduct extensive numerical experiments to demonstrate their finite sample performance.

Abstract: support vector machines (SVMs) constitute one of the most popular and powerful classification methods. However, SVMs can be limited in their performance on highly imbalanced datasets. A classifier which has been trained on an imbalanced dataset can produce a biased model towards the majority class and result in high misclassification rate for minority class. For many applications, especially for medical diagnosis, it is of high importance to accurately distinguish false negative from false positive results. The purpose of this study is to successfully evaluate the performance of a classifier, keeping the correct balance between sensitivity and specificity, in order to enable the success of trauma outcome prediction. We compare the standard (or classic) SVM (C SVM) with resampling methods and a cost sensitive method, called Two Cost SVM (TC SVM), which constitute widely accepted strategies for imbalanced datasets and the derived results were discussed in terms of the sensitivity analysis and receiver operating characteristic (ROC) curves.

Abstract: Scientific interest often centers on characterizing the effect of one or more variables on an outcome. While data mining approaches such as random forests are flexible alternatives to conventional parametric models, they suffer from a lack of interpretability because variable effects are not quantified in a substantively meaningful way. In this paper we describe a method for quantifying variable effects using partial dependence, which produces an estimate that can be interpreted as the effect on the response for a one unit change in the predictor, while averaging over the effects of all other variables. Most importantly, the approach avoids problems related to model misspecification and challenges to implementation in high dimensional settings encountered with other approaches (e.g., multiple linear regression). We propose and evaluate through simulation a method for constructing a point estimate of this effect size. We also propose and evaluate interval estimates based on a non-parametric bootstrap. The method is illustrated on data used for the prediction of the age of abalone.

Ensemble techniques have been gaining strength among machine learning models, considering supervised tasks, due to their great predictive capacity when compared with some traditional approaches. The random forest is considered to be one of the off-the-shelf algorithms due to its flexibility and robust performance to both regression and classification tasks. In this paper, the random machines method is applied over simulated data sets and benchmarking datasets in order to be compared with the consolidated random forest models. The results from simulated models show that the random machines method has a better predictive performance than random forest in most of the investigated data sets. Three real data situations demonstrate that the random machines may be used to solve real-world problems with competitive payoff.