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Abstract: There is rapidly accumulating evidence that the application of machine learning classification to neuroimaging measurements may be valuable for the development of diagnostic and prognostic prediction tools in psychiatry. However, current methods do not produce a measure of the reliability of the predictions. Knowing the risk of the error associated with a given prediction is essential for the development of neuroimaging-based clinical tools. We propose a general probabilistic classification method to produce measures of confidence for magnetic resonance imaging (MRI) data. We describe the application of transductive conformal predictor (TCP) to MRI images. TCP generates the most likely prediction and a valid measure of confidence, as well as the set of all possible predictions for a given confidence level. We present the theoretical motivation for TCP, and we have applied TCP to structural and functional MRI data in patients and healthy controls to investigate diagnostic and prognostic prediction in depression. We verify that TCP predictions are as accurate as those obtained with more standard machine learning methods, such as support vector machine, while providing the additional benefit of a valid measure of confidence for each prediction. [Copyright &y& Elsevier]

Abstract: The paper applies the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice. In the traditional setting of a countable number of experts and a finite number of outcomes, the Defensive Forecasting Algorithm is very close to the well-known Aggregating Algorithm. Not only the performance guarantees but also the predictions are the same for these two methods of fundamentally different nature. The paper also discusses a new setting where the experts can give advice conditional on the learner’s future decision. Both the algorithms can be adapted to the new setting and give the same performance guarantees as in the traditional setting. Finally, an application of defensive forecasting to a setting with several loss functions is outlined. [Copyright &y& Elsevier]