An application of bayesian model averaging to histograms
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We present a method for learning class posterior probability for one-dimensional input data. It may be used for instance to convert a non probabilistic classifier (e.g. Support Vector Machines) into a probabilistic one or to calibrate a probabilistic classifier. We use the Bayesian Model Averaging method (BMA), which provides a principled way to learn a probability function from data. It achieves an optimal trade-off between complexity and accuracy by averaging over all possible models. Our method is fully non-parametric and relies on the family of histogram models. This family is rich enough to implement arbitrarily close any continuous real function. We show how to perform exact BMA in our case with a dynamic programming algorithm that allows summing over all possible histograms, i.e. number of bins and their boundaries. We provide experimental results that compares the behaviour of our method with other approximation scheme.
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