An Efficient Convolutional Framework for Multitask Learning

Structured prediction of multiple outputs (commonly referred to as multi-task learning) presents a problem for kernel methods: how do we best compute the kernel between the different outputs? Several solutions have been suggested (e.g. [1, 2, 3, 4]), but many of them can be seen as corresponding to an affine transformation of the target data followed by independent modelling of outputs. Such linear transformations are clearly limiting. A potentially more powerful class of approximations involves convolutions [5, 6]. Temporal or spatial convolutions contain affine transformations of outputs as a (trivial) special case, providing a much broader class of models. The major problem with these models is their computational complexity, prohibitive for systems involving thousands of data points or outputs. We approach the problem from a Gaussian process (GP) perspective. A way to model multiple correlated outputs with GPs is to assume that they are generated from a small set of R latent GP functions analogously to the linear latent variable models commonly used in machine learning [3, 4]. A significant generalization of this approach is to combine it with a convolution-based framework as proposed in [5, 6, 7]. Thus, the value yq(x) for the q-th output at input x is generated according to