Spike and Slab Variational Inference for Multi-Task and Multiple Kernel Learning
Michalis Titsias and Miguel Lazaro-Gredilla
In: NIPS 2011, 12-17 Dec 2011, Granada, Spain.
We introduce a variational Bayesian inference algorithm which can be widely applied to sparse linear models. The algorithm is based on the spike and slab prior which, from a Bayesian perspective, is the golden standard for sparse inference. We apply the method to a general multi- task and multiple kernel learning model in which a common set of Gaussian process functions is linearly combined with task-specific sparse weights, thus inducing relation between tasks. This model unifies several sparse linear models, such as generalized linear models, sparse factor analysis and matrix factorization with missing values, so that the variational algorithm can be applied to all these cases. We demonstrate our approach in multioutput Gaussian process regression, multi-class classification, image processing applications and collaborative filtering.