26,755 research outputs found
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
Bayesian Structure Learning for Markov Random Fields with a Spike and Slab Prior
In recent years a number of methods have been developed for automatically
learning the (sparse) connectivity structure of Markov Random Fields. These
methods are mostly based on L1-regularized optimization which has a number of
disadvantages such as the inability to assess model uncertainty and expensive
cross-validation to find the optimal regularization parameter. Moreover, the
model's predictive performance may degrade dramatically with a suboptimal value
of the regularization parameter (which is sometimes desirable to induce
sparseness). We propose a fully Bayesian approach based on a "spike and slab"
prior (similar to L0 regularization) that does not suffer from these
shortcomings. We develop an approximate MCMC method combining Langevin dynamics
and reversible jump MCMC to conduct inference in this model. Experiments show
that the proposed model learns a good combination of the structure and
parameter values without the need for separate hyper-parameter tuning.
Moreover, the model's predictive performance is much more robust than L1-based
methods with hyper-parameter settings that induce highly sparse model
structures.Comment: Accepted in the Conference on Uncertainty in Artificial Intelligence
(UAI), 201
Non-Bayesian Social Learning, Second Version
We develop a dynamic model of opinion formation in social networks. Relevant information is spread throughout the network in such a way that no agent has enough data to learn a payoff-relevant parameter. Individuals engage in communication with their neighbors in order to learn from their experiences. However, instead of incorporating the views of their neighbors in a fully Bayesian manner, agents use a simple updating rule which linearly combines their personal experience and the views of their neighbors (even though the neighbors’ views may be quite inaccurate). This non-Bayesian learning rule is motivated by the formidable complexity required to fully implement Bayesian updating in networks. We show that, under mild assumptions, repeated interactions lead agents to successfully aggregate information and to learn the true underlying state of the world. This result holds in spite of the apparent naıvite of agents’ updating rule, the agents’ need for information from sources (i.e., other agents) the existence of which they may not be aware of, the possibility that the most persuasive agents in the network are precisely those least informed and with worst prior views, and the assumption that no agent can tell whether their own views or their neighbors’ views are more accurate.Social networks, learning, information aggregation
- …