Quantifying Confidence for Computer-Intensive Classifiers

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Classification is about prediction a class label Y with finitely many potential values from a vector X of covariables. Traditionally this amounts to choosing a classifier or estimating the conditional distributions of Y given X = x based on a set of training observations. To quantify the confidence for each instance (i.e. future observation X with unknown class membership Y ), one can also use certain p-values to provide a set of plausible class labels. One advantage of the latter approach is that prior information about the different classes’ probability isn’t needed, and there are nonparametric procedures based on permutation tests which are valid under minimal assumptions. In the present project, the latter methods are extended in various directions, in particular: (i) The underlying classifiers should be moderately robust which necessitates computationally feasible procedures. Recent progress in multivariate M-estimation will be helpful in this respect. (ii) Given the success of support vector machines and other large margin classifiers in combination with complexity penalties, it is desirable to develop corresponding p-values. A major conceptual problem will be the data-driven choice of tuning parameters. (iii) We want to develop general theory for the asymptotic properties of these methods when both the sample size and the dimension of X are growing.