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Regularization for Multiple Kernel Learning via Sum-Product Networks

In this paper, we are interested in constructing general graph-based regularizers for multiple kernel learning (MKL) given a structure which is used to describe the way of combining basis kernels. Such structures are represented by sum-product networks (SPNs) in our method. Accordingly we propose a new convex regularization method for MLK based on a path-dependent kernel weighting function which encodes the entire SPN structure in our method. Under certain conditions and from the view of probability, this function can be considered to follow multinomial distributions over the weights associated with product nodes in SPNs. We also analyze the convexity of our regularizer and the complexity of our induced classifiers, and further propose an efficient wrapper algorithm to optimize our formulation. In our experiments, we apply our method to ......