  Nonparametric estimation of the conditional distribution of a response given
high-dimensional features is a challenging problem. It is important to allow
not only the mean but also the variance and shape of the response density to
change flexibly with features, which are massive-dimensional. We propose a
multiscale dictionary learning model, which expresses the conditional response
density as a convex combination of dictionary densities, with the densities
used and their weights dependent on the path through a tree decomposition of
the feature space. A fast graph partitioning algorithm is applied to obtain the
tree decomposition, with Bayesian methods then used to adaptively prune and
average over different sub-trees in a soft probabilistic manner. The algorithm
scales efficiently to approximately one million features. State of the art
predictive performance is demonstrated for toy examples and two neuroscience
applications including up to a million features.
