2,815 research outputs found
Information Theoretic Structure Learning with Confidence
Information theoretic measures (e.g. the Kullback Liebler divergence and
Shannon mutual information) have been used for exploring possibly nonlinear
multivariate dependencies in high dimension. If these dependencies are assumed
to follow a Markov factor graph model, this exploration process is called
structure discovery. For discrete-valued samples, estimates of the information
divergence over the parametric class of multinomial models lead to structure
discovery methods whose mean squared error achieves parametric convergence
rates as the sample size grows. However, a naive application of this method to
continuous nonparametric multivariate models converges much more slowly. In
this paper we introduce a new method for nonparametric structure discovery that
uses weighted ensemble divergence estimators that achieve parametric
convergence rates and obey an asymptotic central limit theorem that facilitates
hypothesis testing and other types of statistical validation.Comment: 10 pages, 3 figure
Statistical estimation of a growth-fragmentation model observed on a genealogical tree
We model the growth of a cell population by a piecewise deterministic Markov
branching tree. Each cell splits into two offsprings at a division rate
that depends on its size . The size of each cell grows exponentially in
time, at a rate that varies for each individual. We show that the mean
empirical measure of the model satisfies a growth-fragmentation type equation
if structured in both size and growth rate as state variables. We construct a
nonparametric estimator of the division rate based on the observation of
the population over different sampling schemes of size on the genealogical
tree. Our estimator nearly achieves the rate in squared-loss
error asymptotically. When the growth rate is assumed to be identical for every
cell, we retrieve the classical growth-fragmentation model and our estimator
improves on the rate obtained in \cite{DHRR, DPZ} through
indirect observation schemes. Our method is consistently tested numerically and
implemented on {\it Escherichia coli} data.Comment: 46 pages, 4 figure
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