Artif Intell Med - White box radial basis function classifiers with component selection for clinical prediction models.


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JECTIVE: To propose a new flexible and sparse classifier that results in interpretable decision support systems.METHODS: Support vector machines (SVMs) for classification are very powerful methods to obtain classifiers for complex problems. Although the performance of these methods is consistently high and non-linearities and interactions between variables can be handled efficiently when using non-linear kernels such as the radial basis function (RBF) kernel, their use in domains where interpretability is an issue is hampered by their lack of transparency. Many feature selection algorithms have been developed to allow for some interpretation but the impact of the different input variables on the prediction still remains unclear. Alternative models using additive kernels are restricted to main effects, reducing their usefulness in many applications. This paper proposes a new approach to expand the RBF kernel into interpretable and visualizable components, including main and two-way interaction effects. In order to obtain a sparse model representation, an iterative l1-regularized parametric model using the interpretable components as inputs is proposed.RESULTS: Results on toy problems illustrate the ability of the method to select the correct contributions and an improved performance over standard RBF classifiers in the presence of irrelevant input variables. For a 10-dimensional x-or problem, an SVM using the standard RBF kernel obtains an area under the receiver operating characteristic curve (AUC) of 0.947, whereas the proposed method achieves an AUC of 0.997. The latter additionally identifies the relevant components. In a second 10-dimensional artificial problem, the underlying class probability follows a logistic regression model. An SVM with the RBF kernel results in an AUC of 0.975, as apposed to 0.994 for the presented method. The proposed method is applied to two benchmark datasets: the Pima Indian diabetes and the Wisconsin Breast Cancer dataset. The AUC is in both cases comparable to those of the standard method (0.826 versus 0.826 and 0.990 versus 0.996) and those reported in the literature. The selected components are consistent with different approaches reported in other work. However, this method is able to visualize the effect of each of the components, allowing for interpretation of the learned logic by experts in the application domain.CONCLUSIONS: This work proposes a new method to obtain flexible and sparse risk prediction models. The proposed method performs as well as a support vector machine using the standard RBF kernel, but has the additional advantage that the resulting model can be interpreted by experts in the application domain.

Resumo Limpo

jectiv propos new flexibl spars classifi result interpret decis support systemsmethod support vector machin svms classif power method obtain classifi complex problem although perform method consist high nonlinear interact variabl can handl effici use nonlinear kernel radial basi function rbf kernel use domain interpret issu hamper lack transpar mani featur select algorithm develop allow interpret impact differ input variabl predict still remain unclear altern model use addit kernel restrict main effect reduc use mani applic paper propos new approach expand rbf kernel interpret visualiz compon includ main twoway interact effect order obtain spars model represent iter lregular parametr model use interpret compon input proposedresult result toy problem illustr abil method select correct contribut improv perform standard rbf classifi presenc irrelev input variabl dimension xor problem svm use standard rbf kernel obtain area receiv oper characterist curv auc wherea propos method achiev auc latter addit identifi relev compon second dimension artifici problem under class probabl follow logist regress model svm rbf kernel result auc appos present method propos method appli two benchmark dataset pima indian diabet wisconsin breast cancer dataset auc case compar standard method versus versus report literatur select compon consist differ approach report work howev method abl visual effect compon allow interpret learn logic expert applic domainconclus work propos new method obtain flexibl spars risk predict model propos method perform well support vector machin use standard rbf kernel addit advantag result model can interpret expert applic domain

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