In this paper we consider the problem of learning an n x n Kernel matrix from m similarity matrices under general convex loss. Past research have extensively studied the m =1 case and have derived several algorithms which require sophisticated techniques like ACCP, SOCP, etc. The existing algorithms do not apply if one uses arbitrary losses and often can not handle m > 1 case. We present several provably convergent iterative algorithms, where each iteration requires either an SVM or a Multiple Kernel Learning (MKL) solver for m > 1 case. One of the major contributions of the paper is to extend the well known Mirror Descent(MD) framework to handle Cartesian product of psd matrices. This novel extension leads to an algorithm, called EMKL, which solves the problem in O(m^2 log n) iterations; in each iteration one solves an MKL involving m kernels and m eigen-decomposition of n x n matrices. By suitably defining a restriction on the objective function, a faster version of EMKL is proposed, called REKL, which avoids the eigen-decomposition. An alternative to both EMKL and REKL is also suggested which requires only an SVM solver. Experimental results on real world protein data set involving several similarity matrices illustrate the efficacy of the proposed algorithms.

This paper presents a new algorithm for sequence prediction over long categorical event streams. The input to the algorithm is a set of target event types whose occurrences we wish to predict. The algorithm examines windows of events that precede occurrences of the target event types in historical data. The set of significant frequent episodes associated with each target event type is obtained based on formal connections between frequent episodes and Hidden Markov Models (HMMs). Each significant episode is associated with a specialized HMM, and a mixture of such HMMs is estimated for every target event type. The likelihoods of the current window of events, under these mixture models, are used to predict future occurrences of target events in the data. The only user-defined model parameter in the algorithm is the length of the windows of events used during model estimation. We first evaluate the algorithm on synthetic data that was generated by embedding (in varying levels of noise) patterns which are preselected to characterize occurrences of target events. We then present an application of the algorithm for predicting targeted user-behaviors from large volumes of anonymous search session interaction logs from a commercially-deployed web browser tool-bar.