16,756 research outputs found
Measures of Variability for Bayesian Network Graphical Structures
The structure of a Bayesian network includes a great deal of information
about the probability distribution of the data, which is uniquely identified
given some general distributional assumptions. Therefore it's important to
study its variability, which can be used to compare the performance of
different learning algorithms and to measure the strength of any arbitrary
subset of arcs.
In this paper we will introduce some descriptive statistics and the
corresponding parametric and Monte Carlo tests on the undirected graph
underlying the structure of a Bayesian network, modeled as a multivariate
Bernoulli random variable. A simple numeric example and the comparison of the
performance of some structure learning algorithm on small samples will then
illustrate their use.Comment: 19 pages, 4 figures. arXiv admin note: substantial text overlap with
arXiv:0909.168
Knowing what you know in brain segmentation using Bayesian deep neural networks
In this paper, we describe a Bayesian deep neural network (DNN) for
predicting FreeSurfer segmentations of structural MRI volumes, in minutes
rather than hours. The network was trained and evaluated on a large dataset (n
= 11,480), obtained by combining data from more than a hundred different sites,
and also evaluated on another completely held-out dataset (n = 418). The
network was trained using a novel spike-and-slab dropout-based variational
inference approach. We show that, on these datasets, the proposed Bayesian DNN
outperforms previously proposed methods, in terms of the similarity between the
segmentation predictions and the FreeSurfer labels, and the usefulness of the
estimate uncertainty of these predictions. In particular, we demonstrated that
the prediction uncertainty of this network at each voxel is a good indicator of
whether the network has made an error and that the uncertainty across the whole
brain can predict the manual quality control ratings of a scan. The proposed
Bayesian DNN method should be applicable to any new network architecture for
addressing the segmentation problem.Comment: Submitted to Frontiers in Neuroinformatic
Bayesian Verification under Model Uncertainty
Machine learning enables systems to build and update domain models based on
runtime observations. In this paper, we study statistical model checking and
runtime verification for systems with this ability. Two challenges arise: (1)
Models built from limited runtime data yield uncertainty to be dealt with. (2)
There is no definition of satisfaction w.r.t. uncertain hypotheses. We propose
such a definition of subjective satisfaction based on recently introduced
satisfaction functions. We also propose the BV algorithm as a Bayesian solution
to runtime verification of subjective satisfaction under model uncertainty. BV
provides user-definable stochastic bounds for type I and II errors. We discuss
empirical results from an example application to illustrate our ideas.Comment: Accepted at SEsCPS @ ICSE 201
Empirical Bayes and Full Bayes for Signal Estimation
We consider signals that follow a parametric distribution where the parameter
values are unknown. To estimate such signals from noisy measurements in scalar
channels, we study the empirical performance of an empirical Bayes (EB)
approach and a full Bayes (FB) approach. We then apply EB and FB to solve
compressed sensing (CS) signal estimation problems by successively denoising a
scalar Gaussian channel within an approximate message passing (AMP) framework.
Our numerical results show that FB achieves better performance than EB in
scalar channel denoising problems when the signal dimension is small. In the CS
setting, the signal dimension must be large enough for AMP to work well; for
large signal dimensions, AMP has similar performance with FB and EB.Comment: This work was presented at the Information Theory and Application
workshop (ITA), San Diego, CA, Feb. 201
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