1,472 research outputs found
Marginal and simultaneous predictive classification using stratified graphical models
An inductive probabilistic classification rule must generally obey the
principles of Bayesian predictive inference, such that all observed and
unobserved stochastic quantities are jointly modeled and the parameter
uncertainty is fully acknowledged through the posterior predictive
distribution. Several such rules have been recently considered and their
asymptotic behavior has been characterized under the assumption that the
observed features or variables used for building a classifier are conditionally
independent given a simultaneous labeling of both the training samples and
those from an unknown origin. Here we extend the theoretical results to
predictive classifiers acknowledging feature dependencies either through
graphical models or sparser alternatives defined as stratified graphical
models. We also show through experimentation with both synthetic and real data
that the predictive classifiers based on stratified graphical models have
consistently best accuracy compared with the predictive classifiers based on
either conditionally independent features or on ordinary graphical models.Comment: 18 pages, 5 figure
A closed-form approach to Bayesian inference in tree-structured graphical models
We consider the inference of the structure of an undirected graphical model
in an exact Bayesian framework. More specifically we aim at achieving the
inference with close-form posteriors, avoiding any sampling step. This task
would be intractable without any restriction on the considered graphs, so we
limit our exploration to mixtures of spanning trees. We consider the inference
of the structure of an undirected graphical model in a Bayesian framework. To
avoid convergence issues and highly demanding Monte Carlo sampling, we focus on
exact inference. More specifically we aim at achieving the inference with
close-form posteriors, avoiding any sampling step. To this aim, we restrict the
set of considered graphs to mixtures of spanning trees. We investigate under
which conditions on the priors - on both tree structures and parameters - exact
Bayesian inference can be achieved. Under these conditions, we derive a fast an
exact algorithm to compute the posterior probability for an edge to belong to
{the tree model} using an algebraic result called the Matrix-Tree theorem. We
show that the assumption we have made does not prevent our approach to perform
well on synthetic and flow cytometry data
- …