11,520 research outputs found
Application of new probabilistic graphical models in the genetic regulatory networks studies
This paper introduces two new probabilistic graphical models for
reconstruction of genetic regulatory networks using DNA microarray data. One is
an Independence Graph (IG) model with either a forward or a backward search
algorithm and the other one is a Gaussian Network (GN) model with a novel
greedy search method. The performances of both models were evaluated on four
MAPK pathways in yeast and three simulated data sets. Generally, an IG model
provides a sparse graph but a GN model produces a dense graph where more
information about gene-gene interactions is preserved. Additionally, we found
two key limitations in the prediction of genetic regulatory networks using DNA
microarray data, the first is the sufficiency of sample size and the second is
the complexity of network structures may not be captured without additional
data at the protein level. Those limitations are present in all prediction
methods which used only DNA microarray data.Comment: 38 pages, 3 figure
Learning Bounded Treewidth Bayesian Networks with Thousands of Variables
We present a method for learning treewidth-bounded Bayesian networks from
data sets containing thousands of variables. Bounding the treewidth of a
Bayesian greatly reduces the complexity of inferences. Yet, being a global
property of the graph, it considerably increases the difficulty of the learning
process. We propose a novel algorithm for this task, able to scale to large
domains and large treewidths. Our novel approach consistently outperforms the
state of the art on data sets with up to ten thousand variables
Partition MCMC for inference on acyclic digraphs
Acyclic digraphs are the underlying representation of Bayesian networks, a
widely used class of probabilistic graphical models. Learning the underlying
graph from data is a way of gaining insights about the structural properties of
a domain. Structure learning forms one of the inference challenges of
statistical graphical models.
MCMC methods, notably structure MCMC, to sample graphs from the posterior
distribution given the data are probably the only viable option for Bayesian
model averaging. Score modularity and restrictions on the number of parents of
each node allow the graphs to be grouped into larger collections, which can be
scored as a whole to improve the chain's convergence. Current examples of
algorithms taking advantage of grouping are the biased order MCMC, which acts
on the alternative space of permuted triangular matrices, and non ergodic edge
reversal moves.
Here we propose a novel algorithm, which employs the underlying combinatorial
structure of DAGs to define a new grouping. As a result convergence is improved
compared to structure MCMC, while still retaining the property of producing an
unbiased sample. Finally the method can be combined with edge reversal moves to
improve the sampler further.Comment: Revised version. 34 pages, 16 figures. R code available at
https://github.com/annlia/partitionMCM
A hybrid algorithm for Bayesian network structure learning with application to multi-label learning
We present a novel hybrid algorithm for Bayesian network structure learning,
called H2PC. It first reconstructs the skeleton of a Bayesian network and then
performs a Bayesian-scoring greedy hill-climbing search to orient the edges.
The algorithm is based on divide-and-conquer constraint-based subroutines to
learn the local structure around a target variable. We conduct two series of
experimental comparisons of H2PC against Max-Min Hill-Climbing (MMHC), which is
currently the most powerful state-of-the-art algorithm for Bayesian network
structure learning. First, we use eight well-known Bayesian network benchmarks
with various data sizes to assess the quality of the learned structure returned
by the algorithms. Our extensive experiments show that H2PC outperforms MMHC in
terms of goodness of fit to new data and quality of the network structure with
respect to the true dependence structure of the data. Second, we investigate
H2PC's ability to solve the multi-label learning problem. We provide
theoretical results to characterize and identify graphically the so-called
minimal label powersets that appear as irreducible factors in the joint
distribution under the faithfulness condition. The multi-label learning problem
is then decomposed into a series of multi-class classification problems, where
each multi-class variable encodes a label powerset. H2PC is shown to compare
favorably to MMHC in terms of global classification accuracy over ten
multi-label data sets covering different application domains. Overall, our
experiments support the conclusions that local structural learning with H2PC in
the form of local neighborhood induction is a theoretically well-motivated and
empirically effective learning framework that is well suited to multi-label
learning. The source code (in R) of H2PC as well as all data sets used for the
empirical tests are publicly available.Comment: arXiv admin note: text overlap with arXiv:1101.5184 by other author
Information Directed Sampling for Stochastic Bandits with Graph Feedback
We consider stochastic multi-armed bandit problems with graph feedback, where
the decision maker is allowed to observe the neighboring actions of the chosen
action. We allow the graph structure to vary with time and consider both
deterministic and Erd\H{o}s-R\'enyi random graph models. For such a graph
feedback model, we first present a novel analysis of Thompson sampling that
leads to tighter performance bound than existing work. Next, we propose new
Information Directed Sampling based policies that are graph-aware in their
decision making. Under the deterministic graph case, we establish a Bayesian
regret bound for the proposed policies that scales with the clique cover number
of the graph instead of the number of actions. Under the random graph case, we
provide a Bayesian regret bound for the proposed policies that scales with the
ratio of the number of actions over the expected number of observations per
iteration. To the best of our knowledge, this is the first analytical result
for stochastic bandits with random graph feedback. Finally, using numerical
evaluations, we demonstrate that our proposed IDS policies outperform existing
approaches, including adaptions of upper confidence bound, -greedy
and Exp3 algorithms.Comment: Accepted by AAAI 201
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