The integration of diverse forms of informative data by learning an optimal combination of base kernels in classification or regression problems can provide enhanced performance when compared to that obtained from any single data source. We present a Bayesian hierarchical model which enables kernel learning and present effective variational Bayes estimators for regression and classification. Illustrative experiments demonstrate the utility of the proposed method. Matlab code replicating results reported is available at http://www.dcs.gla. ac.uk/srogers/kernel comb.html.