Multiscale dictionary learning for estimating conditional distributions
Abstract
Nonparametric estimation of the conditional distribution of a response given highdimensional
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.
Type
Journal articlePermalink
https://hdl.handle.net/10161/15600Collections
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David B. Dunson
Arts and Sciences Distinguished Professor of Statistical Science
My research focuses on developing new tools for probabilistic learning from complex
data - methods development is directly motivated by challenging applications in ecology/biodiversity,
neuroscience, environmental health, criminal justice/fairness, and more. We seek
to develop new modeling frameworks, algorithms and corresponding code that can be
used routinely by scientists and decision makers. We are also interested in new inference
framework and in studying theoretical properties

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