135 research outputs found
Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models
W-graph refers to a general class of random graph models that can be seen as
a random graph limit. It is characterized by both its graphon function and its
motif frequencies. In this paper, relying on an existing variational Bayes
algorithm for the stochastic block models along with the corresponding weights
for model averaging, we derive an estimate of the graphon function as an
average of stochastic block models with increasing number of blocks. In the
same framework, we derive the variational posterior frequency of any motif. A
simulation study and an illustration on a social network complete our work
Meta learning of bounds on the Bayes classifier error
Meta learning uses information from base learners (e.g. classifiers or
estimators) as well as information about the learning problem to improve upon
the performance of a single base learner. For example, the Bayes error rate of
a given feature space, if known, can be used to aid in choosing a classifier,
as well as in feature selection and model selection for the base classifiers
and the meta classifier. Recent work in the field of f-divergence functional
estimation has led to the development of simple and rapidly converging
estimators that can be used to estimate various bounds on the Bayes error. We
estimate multiple bounds on the Bayes error using an estimator that applies
meta learning to slowly converging plug-in estimators to obtain the parametric
convergence rate. We compare the estimated bounds empirically on simulated data
and then estimate the tighter bounds on features extracted from an image patch
analysis of sunspot continuum and magnetogram images.Comment: 6 pages, 3 figures, to appear in proceedings of 2015 IEEE Signal
Processing and SP Education Worksho
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
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