We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.
Multiple kernel learning approaches to multi-view learning [1, 11, 7] have recently become very popular since they can easily combine information from multiple views, e.g., by adding or multiplying kernels. They are particularly effective when the views are class conditionally independent, since the errors committed by each view can be corrected by the other views. Most methods assume that a single set of kernel weights is sufficient for accurate classification, however, one can expect that the set of features important to discriminate between different examples can vary locally. As a result the performance of such global techniques can degrade in the presence of complex noise processes, e.g., heteroscedastic noise, missing data, or when the discriminative properties vary across the input space.