I have just arxiv’ed a new manuscript on speeding up computation for functional additive models such as functional ANOVA. A functional additive model is essentially a model says that a = b + c, where a, b and c are functions. It is a useful model when we want to express things like: I have three curves and I expect them to be related.
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The trick is to take advantage of the special form of the covariance matrices, which are quasi-Kronecker. For more: http://arxiv.org/abs/1402.4984