22,504 research outputs found
Multiscale Dictionary Learning for Estimating Conditional Distributions
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
Modelling beyond Regression Functions: an Application of Multimodal Regression to Speed-Flow Data
An enormous amount of publications deals with smoothing in the sense of nonparametric regression. However, nearly all of the literature treats the case where predictors and response are related in the form of a function y=m(x)+noise. In many situations this simple functional model does not capture adequately the essential relation between predictor and response. We show by means of speed-flow diagrams, that a more general setting may be required, allowing for multifunctions instead of only functions. It turns out that in this case the conditional modes are more appropriate for the estimation of the underlying relation than the commonly used mean or the median. Estimation is achieved using a conditional mean-shift procedure, which is adapted to the present situation
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