3,510 research outputs found
Cutset Sampling for Bayesian Networks
The paper presents a new sampling methodology for Bayesian networks that
samples only a subset of variables and applies exact inference to the rest.
Cutset sampling is a network structure-exploiting application of the
Rao-Blackwellisation principle to sampling in Bayesian networks. It improves
convergence by exploiting memory-based inference algorithms. It can also be
viewed as an anytime approximation of the exact cutset-conditioning algorithm
developed by Pearl. Cutset sampling can be implemented efficiently when the
sampled variables constitute a loop-cutset of the Bayesian network and, more
generally, when the induced width of the networks graph conditioned on the
observed sampled variables is bounded by a constant w. We demonstrate
empirically the benefit of this scheme on a range of benchmarks
Loop corrections in spin models through density consistency
Computing marginal distributions of discrete or semidiscrete Markov random
fields (MRFs) is a fundamental, generally intractable problem with a vast
number of applications in virtually all fields of science. We present a new
family of computational schemes to approximately calculate the marginals of
discrete MRFs. This method shares some desirable properties with belief
propagation, in particular, providing exact marginals on acyclic graphs, but it
differs with the latter in that it includes some loop corrections; i.e., it
takes into account correlations coming from all cycles in the factor graph. It
is also similar to the adaptive Thouless-Anderson-Palmer method, but it differs
with the latter in that the consistency is not on the first two moments of the
distribution but rather on the value of its density on a subset of values. The
results on finite-dimensional Isinglike models show a significant improvement
with respect to the Bethe-Peierls (tree) approximation in all cases and with
respect to the plaquette cluster variational method approximation in many
cases. In particular, for the critical inverse temperature of the
homogeneous hypercubic lattice, the expansion of
around of the proposed scheme is exact up to the order,
whereas the two latter are exact only up to the order.Comment: 12 pages, 3 figures, 1 tabl
Interactive Music Generation with Positional Constraints using Anticipation-RNNs
Recurrent Neural Networks (RNNS) are now widely used on sequence generation
tasks due to their ability to learn long-range dependencies and to generate
sequences of arbitrary length. However, their left-to-right generation
procedure only allows a limited control from a potential user which makes them
unsuitable for interactive and creative usages such as interactive music
generation. This paper introduces a novel architecture called Anticipation-RNN
which possesses the assets of the RNN-based generative models while allowing to
enforce user-defined positional constraints. We demonstrate its efficiency on
the task of generating melodies satisfying positional constraints in the style
of the soprano parts of the J.S. Bach chorale harmonizations. Sampling using
the Anticipation-RNN is of the same order of complexity than sampling from the
traditional RNN model. This fast and interactive generation of musical
sequences opens ways to devise real-time systems that could be used for
creative purposes.Comment: 9 pages, 7 figure
Predicting epidemic evolution on contact networks from partial observations
The massive employment of computational models in network epidemiology calls
for the development of improved inference methods for epidemic forecast. For
simple compartment models, such as the Susceptible-Infected-Recovered model,
Belief Propagation was proved to be a reliable and efficient method to identify
the origin of an observed epidemics. Here we show that the same method can be
applied to predict the future evolution of an epidemic outbreak from partial
observations at the early stage of the dynamics. The results obtained using
Belief Propagation are compared with Monte Carlo direct sampling in the case of
SIR model on random (regular and power-law) graphs for different observation
methods and on an example of real-world contact network. Belief Propagation
gives in general a better prediction that direct sampling, although the quality
of the prediction depends on the quantity under study (e.g. marginals of
individual states, epidemic size, extinction-time distribution) and on the
actual number of observed nodes that are infected before the observation time
A Review of Inference Algorithms for Hybrid Bayesian Networks
Hybrid Bayesian networks have received an increasing attention during the last years. The difference with respect to standard Bayesian networks is that they can host discrete and continuous variables simultaneously, which extends the applicability of the Bayesian network framework in general. However, this extra feature also comes at a cost: inference in these types of models is computationally more challenging and the underlying models and updating procedures may not even support closed-form solutions. In this paper we provide an overview of the main trends and principled approaches for performing inference in hybrid Bayesian networks. The methods covered in the paper are organized and discussed according to their methodological basis. We consider how the methods have been extended and adapted to also include (hybrid) dynamic Bayesian networks, and we end with an overview of established software systems supporting inference in these types of models
Learning loopy graphical models with latent variables: Efficient methods and guarantees
The problem of structure estimation in graphical models with latent variables
is considered. We characterize conditions for tractable graph estimation and
develop efficient methods with provable guarantees. We consider models where
the underlying Markov graph is locally tree-like, and the model is in the
regime of correlation decay. For the special case of the Ising model, the
number of samples required for structural consistency of our method scales
as , where p is the
number of variables, is the minimum edge potential, is
the depth (i.e., distance from a hidden node to the nearest observed nodes),
and is a parameter which depends on the bounds on node and edge
potentials in the Ising model. Necessary conditions for structural consistency
under any algorithm are derived and our method nearly matches the lower bound
on sample requirements. Further, the proposed method is practical to implement
and provides flexibility to control the number of latent variables and the
cycle lengths in the output graph.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1070 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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