Indian Buffet process for model selection in convolved multiple-output Gaussian processes
This addresses model selection in multi-output Gaussian processes, particularly for latent force models in domains like motion capture and gene expression, but it is incremental as it builds on existing methods like process convolutions.
The paper tackles the problem of selecting the number of latent Gaussian processes in multi-output Gaussian processes, proposing an Indian Buffet process for model selection and demonstrating performance on artificial and real datasets.
Multi-output Gaussian processes have received increasing attention during the last few years as a natural mechanism to extend the powerful flexibility of Gaussian processes to the setup of multiple output variables. The key point here is the ability to design kernel functions that allow exploiting the correlations between the outputs while fulfilling the positive definiteness requisite for the covariance function. Alternatives to construct these covariance functions are the linear model of coregionalization and process convolutions. Each of these methods demand the specification of the number of latent Gaussian process used to build the covariance function for the outputs. We propose in this paper, the use of an Indian Buffet process as a way to perform model selection over the number of latent Gaussian processes. This type of model is particularly important in the context of latent force models, where the latent forces are associated to physical quantities like protein profiles or latent forces in mechanical systems. We use variational inference to estimate posterior distributions over the variables involved, and show examples of the model performance over artificial data, a motion capture dataset, and a gene expression dataset.