We have got a paper at NIPS this year.
Learning from Distributions via Support Measure Machines (Spotlight)
K. Muandet, K. Fukumizu, F. Dinuzzo, B. Schoelkopf
Abstract This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing these probability distributions as mean embeddings in the reproducing kernel Hilbert space (RKHS), we are able to apply many standard kernel-based learning techniques in straightforward fashion. To accomplish this, we construct a generalization of the support vector machine (SVM) called a support measure machine (SMM). Our analyses of SMMs provides several insights into their relationship to traditional SVMs. Based on such insights, we propose a flexible SVM (Flex-SVM) that places different kernel functions on each training example. Experimental results on both synthetic and real-world data demonstrate the effectiveness of our proposed framework.
This is joint work with Kenji Fukumizu (The Institute for Statistical Mathematics, Japan), Francesco Dinuzzo (MPI-IS), and my supervisor Prof. Bernhard Schoelkopf (MPI-IS). Parts of this work were done while Kenji was visiting us in summer 2011.
The arXiv manuscript can be found here. This is not up-to-date version, but will give a basic idea of this work.