30,870 research outputs found
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
Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders
We address the problem of causal discovery from data, making use of the
recently proposed causal modeling framework of modular structural causal models
(mSCM) to handle cycles, latent confounders and non-linearities. We introduce
{\sigma}-connection graphs ({\sigma}-CG), a new class of mixed graphs
(containing undirected, bidirected and directed edges) with additional
structure, and extend the concept of {\sigma}-separation, the appropriate
generalization of the well-known notion of d-separation in this setting, to
apply to {\sigma}-CGs. We prove the closedness of {\sigma}-separation under
marginalisation and conditioning and exploit this to implement a test of
{\sigma}-separation on a {\sigma}-CG. This then leads us to the first causal
discovery algorithm that can handle non-linear functional relations, latent
confounders, cyclic causal relationships, and data from different (stochastic)
perfect interventions. As a proof of concept, we show on synthetic data how
well the algorithm recovers features of the causal graph of modular structural
causal models.Comment: Accepted for publication in Conference on Uncertainty in Artificial
Intelligence 201
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
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