21,243 research outputs found
A survey on independence-based Markov networks learning
This work reports the most relevant technical aspects in the problem of
learning the \emph{Markov network structure} from data. Such problem has become
increasingly important in machine learning, and many other application fields
of machine learning. Markov networks, together with Bayesian networks, are
probabilistic graphical models, a widely used formalism for handling
probability distributions in intelligent systems. Learning graphical models
from data have been extensively applied for the case of Bayesian networks, but
for Markov networks learning it is not tractable in practice. However, this
situation is changing with time, given the exponential growth of computers
capacity, the plethora of available digital data, and the researching on new
learning technologies. This work stresses on a technology called
independence-based learning, which allows the learning of the independence
structure of those networks from data in an efficient and sound manner,
whenever the dataset is sufficiently large, and data is a representative
sampling of the target distribution. In the analysis of such technology, this
work surveys the current state-of-the-art algorithms for learning Markov
networks structure, discussing its current limitations, and proposing a series
of open problems where future works may produce some advances in the area in
terms of quality and efficiency. The paper concludes by opening a discussion
about how to develop a general formalism for improving the quality of the
structures learned, when data is scarce.Comment: 35 pages, 1 figur
The IBMAP approach for Markov networks structure learning
In this work we consider the problem of learning the structure of Markov
networks from data. We present an approach for tackling this problem called
IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC
algorithm, designed for avoiding important limitations of existing
independence-based algorithms. These algorithms proceed by performing
statistical independence tests on data, trusting completely the outcome of each
test. In practice tests may be incorrect, resulting in potential cascading
errors and the consequent reduction in the quality of the structures learned.
IBMAP contemplates this uncertainty in the outcome of the tests through a
probabilistic maximum-a-posteriori approach. The approach is instantiated in
the IBMAP-HC algorithm, a structure selection strategy that performs a
polynomial heuristic local search in the space of possible structures. We
present an extensive empirical evaluation on synthetic and real data, showing
that our algorithm outperforms significantly the current independence-based
algorithms, in terms of data efficiency and quality of learned structures, with
equivalent computational complexities. We also show the performance of IBMAP-HC
in a real-world application of knowledge discovery: EDAs, which are
evolutionary algorithms that use structure learning on each generation for
modeling the distribution of populations. The experiments show that when
IBMAP-HC is used to learn the structure, EDAs improve the convergence to the
optimum
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
Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems
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