Variational Inducing Kernels for Sparse Convolved Multiple
Output Gaussian Processes
Mauricio Alvarez, David Luengo-Garcia, Michalis Titsias and Neil Lawrence
Mauricio Alvarez, Manchester, UK.
Interest in multioutput kernel methods is increasing, whether under the guise of multitask learning, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance function over correlated output functions. One way of constructing such kernels is based on convolution processes (CP). A key problem for this approach is efficient inference.
Alvarez and Lawrence (2009) recently presented a sparse approximation for CPs that enabled efficient inference. In this paper,
we extend this work in two directions: we introduce the concept of variational inducing functions to handle potential non-smooth functions involved in the kernel CP construction and we consider an alternative approach to approximate inference based on variational
methods, extending the work by Titsias (2009) to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler performance and ﬁnancial time series.