Learning α-integration with partially-labeled data

Sensory data integration is an important task in human brain for multimodal processing as well as in machine learning for multisensor processing. α-integration was proposed by Amari as a principled way of blending multiple positive measures (e.g., stochastic models in the form of probability distributions), providing an optimal integration in the sense of minimizing the α-divergence. It also encompasses existing integration methods as its special case, e.g., weighted average and exponential mixture. In α-integration, the value of α determines the characteristics of the integration and the weight vector w assigns the degree of importance to each measure. In most of the existing work, however, α and w are given in advance rather than learned. In this paper we present two algorithms, for learning α and w from data when only a few integrated target values are available. Numerical experiments on synthetic as well as real-world data confirm the proposed method's effectiveness.