50,730 research outputs found
Approximate learning of high dimensional Bayesian network structures via pruning of Candidate Parent Sets.
Score-based algorithms that learn Bayesian Network (BN) structures provide
solutions ranging from different levels of approximate learning to exact
learning. Approximate solutions exist because exact learning is generally not
applicable to networks of moderate or higher complexity. In general,
approximate solutions tend to sacrifice accuracy for speed, where the aim is to
minimise the loss in accuracy and maximise the gain in speed. While some
approximate algorithms are optimised to handle thousands of variables, these
algorithms may still be unable to learn such high dimensional structures. Some
of the most efficient score-based algorithms cast the structure learning
problem as a combinatorial optimisation of candidate parent sets. This paper
explores a strategy towards pruning the size of candidate parent sets, aimed at
high dimensionality problems. The results illustrate how different levels of
pruning affect the learning speed relative to the loss in accuracy in terms of
model fitting, and show that aggressive pruning may be required to produce
approximate solutions for high complexity problems
Advances in Learning Bayesian Networks of Bounded Treewidth
This work presents novel algorithms for learning Bayesian network structures
with bounded treewidth. Both exact and approximate methods are developed. The
exact method combines mixed-integer linear programming formulations for
structure learning and treewidth computation. The approximate method consists
in uniformly sampling -trees (maximal graphs of treewidth ), and
subsequently selecting, exactly or approximately, the best structure whose
moral graph is a subgraph of that -tree. Some properties of these methods
are discussed and proven. The approaches are empirically compared to each other
and to a state-of-the-art method for learning bounded treewidth structures on a
collection of public data sets with up to 100 variables. The experiments show
that our exact algorithm outperforms the state of the art, and that the
approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table
Bayesian Discovery of Multiple Bayesian Networks via Transfer Learning
Bayesian network structure learning algorithms with limited data are being
used in domains such as systems biology and neuroscience to gain insight into
the underlying processes that produce observed data. Learning reliable networks
from limited data is difficult, therefore transfer learning can improve the
robustness of learned networks by leveraging data from related tasks. Existing
transfer learning algorithms for Bayesian network structure learning give a
single maximum a posteriori estimate of network models. Yet, many other models
may be equally likely, and so a more informative result is provided by Bayesian
structure discovery. Bayesian structure discovery algorithms estimate posterior
probabilities of structural features, such as edges. We present transfer
learning for Bayesian structure discovery which allows us to explore the shared
and unique structural features among related tasks. Efficient computation
requires that our transfer learning objective factors into local calculations,
which we prove is given by a broad class of transfer biases. Theoretically, we
show the efficiency of our approach. Empirically, we show that compared to
single task learning, transfer learning is better able to positively identify
true edges. We apply the method to whole-brain neuroimaging data.Comment: 10 page
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