A learning problem that has only recently gained attention in the machine learning community is that of learning a classifier from group probabilities. It is a learning task that lies somewhere between the well-known tasks of supervised and unsupervised learning, in the sense that for a set of observations we do not know the labels, but for some groups of observations, the frequency distribution of the label is known. This learning problem has important practical applications, for example in privacy-preserving data mining. This paper presents an approach to learn a classifier from group probabilities based on support vector regression and the idea of inverting a classifier calibration process. A detailed analysis will show that this new approach outperforms existing approaches.