Supervised Learning by Training on Aggregate Outputs

Supervised learning is a classic data mining problem where one wishes to be 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, and support vector machines can be adapted for this problem.