  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 ......
