Varying-coefficient models with isotropic Gaussian process priors
This work addresses the problem of efficient Bayesian inference for varying-coefficient models, which is significant for researchers and practitioners in machine learning dealing with multitask or spatiotemporal data, though it is incremental as it builds on existing Gaussian process methods.
The paper tackles the intractability of Bayesian inference in varying-coefficient models with Gaussian process priors by showing that inference with isotropic priors reduces to standard Gaussian process inference, enabling efficient solutions. In experiments on geospatial prediction, this approach resolves MAP inference to multitask learning with task and instance kernels.
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this conditional. Varying-coefficient models subsume hierarchical Bayesian multitask models, but also generalizations in which the conditional varies continuously, for instance, in time or space. However, Bayesian inference in varying-coefficient models is generally intractable. We show that inference for varying-coefficient models with isotropic Gaussian process priors resolves to standard inference for a Gaussian process that can be solved efficiently. MAP inference in this model resolves to multitask learning using task and instance kernels, and inference for hierarchical Bayesian multitask models can be carried out efficiently using graph-Laplacian kernels. We report on experiments for geospatial prediction.