Multiscale Dictionary Learning for Estimating Conditional Distributions
Abstract
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.
Cite
@article{arxiv.1312.1099,
title = {Multiscale Dictionary Learning for Estimating Conditional Distributions},
author = {Francesca Petralia and Joshua Vogelstein and David B. Dunson},
journal= {arXiv preprint arXiv:1312.1099},
year = {2013}
}