1Supervised Learning by Training on Aggregate Outputs

Abstract—Supervised learning is a classic data mining problem where one wishes to be able to predict an output value associated with a particular input vector. We present a new twist on this classic problem where, instead of having the training set contain an individual output value for each input vector, the output values in the training set are only given in aggregate over a number of input vectors. This new problem arose from a particular need in learning on mass spectrometry data, but could easily apply to situations when data has been aggregated in order to maintain privacy. We provide a formal description of this new problem for both classification and regression. We then examine how k-nearest neighbor, neural networks, support vector machines, and decision trees can be adapted for this problem. Index Terms—Data mining, classifier design and evaluation. F