Learning from Label Proportions by Optimizing Cluster Model Selection

In a supervised learning scenario, we learn a mapping from input to output values, based on labeled examples. Can we learn such a mapping also from groups of unlabeled observations, only knowing, for each group, the proportion of observations with a particular label? Solutions have real world applications. Here, we consider groups of steel sticks as samples in quality control. Since the steel sticks cannot be marked individually, for each group of sticks it is only known how many sticks of high (low) quality it contains. We want to predict the achieved quality for each stick before it reaches the final production station and quality control, in order to save resources. We define the problem of learning from label proportions and present a solution based on clustering. Our method empirically shows a better prediction performance than recent approaches based on probabilistic SVMs, Kernel k-Means or conditional exponential models.