4,634 research outputs found
Feedback message passing for inference in Gaussian graphical models
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Includes bibliographical references (p. 89-92).For Gaussian graphical models with cycles, loopy belief propagation often performs reasonably well, but its convergence is not guaranteed and the computation of variances is generally incorrect. In this paper, we identify a set of special vertices called a feedback vertex set whose removal results in a cycle-free graph. We propose a feedback message passing algorithm in which non-feedback nodes send out one set of messages while the feedback nodes use a different message update scheme. Exact inference results can be obtained in O(k²n), where k is the number of feedback nodes and n is the total number of nodes. For graphs with large feedback vertex sets, we describe a tractable approximate feedback message passing algorithm. Experimental results show that this procedure converges more often, faster, and provides better results than loopy belief propagation.by Ying Liu.S.M
Recursive FMP for distributed inference in Gaussian graphical models
For inference in Gaussian graphical models with cycles, loopy belief propagation (LBP) performs well for some graphs, but often diverges or has slow convergence. When LBP does converge, the variance estimates are incorrect in general. The feedback message passing (FMP) algorithm has been proposed to enhance the convergence and accuracy of inference. In FMP, standard LBP is run twice on the subgraph excluding the pseudo-FVS (a set of nodes that breaks most crucial cycles) while nodes in the pseudo-FVS use a different protocol. In this paper, we propose recursive FMP, a purely distributed extension of FMP, where all nodes use the same message-passing protocol. An inference problem on the entire graph is recursively reduced to those on smaller subgraphs in a distributed manner. One advantage of this recursive approach compared with FMP is that there is only one active feedback node at a time, so centralized communication among feedback nodes can be turned into message broadcasting from the single feedback node. We characterize this algorithm using walk-sum analysis and provide theoretical results for convergence and accuracy. We also demonstrate the performance using both simulated models on grids and large-scale sea surface height anomaly data.United States. Air Force Office of Scientific Research (Grant FA9550-12-1-0287
Learning Gaussian Graphical Models with Observed or Latent FVSs
Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely
used in many applications, and the trade-off between the modeling capacity and
the efficiency of learning and inference has been an important research
problem. In this paper, we study the family of GGMs with small feedback vertex
sets (FVSs), where an FVS is a set of nodes whose removal breaks all the
cycles. Exact inference such as computing the marginal distributions and the
partition function has complexity using message-passing algorithms,
where k is the size of the FVS, and n is the total number of nodes. We propose
efficient structure learning algorithms for two cases: 1) All nodes are
observed, which is useful in modeling social or flight networks where the FVS
nodes often correspond to a small number of high-degree nodes, or hubs, while
the rest of the networks is modeled by a tree. Regardless of the maximum
degree, without knowing the full graph structure, we can exactly compute the
maximum likelihood estimate in if the FVS is known or in
polynomial time if the FVS is unknown but has bounded size. 2) The FVS nodes
are latent variables, where structure learning is equivalent to decomposing a
inverse covariance matrix (exactly or approximately) into the sum of a
tree-structured matrix and a low-rank matrix. By incorporating efficient
inference into the learning steps, we can obtain a learning algorithm using
alternating low-rank correction with complexity per
iteration. We also perform experiments using both synthetic data as well as
real data of flight delays to demonstrate the modeling capacity with FVSs of
various sizes
Consensus Message Passing for Layered Graphical Models
Generative models provide a powerful framework for probabilistic reasoning.
However, in many domains their use has been hampered by the practical
difficulties of inference. This is particularly the case in computer vision,
where models of the imaging process tend to be large, loopy and layered. For
this reason bottom-up conditional models have traditionally dominated in such
domains. We find that widely-used, general-purpose message passing inference
algorithms such as Expectation Propagation (EP) and Variational Message Passing
(VMP) fail on the simplest of vision models. With these models in mind, we
introduce a modification to message passing that learns to exploit their
layered structure by passing 'consensus' messages that guide inference towards
good solutions. Experiments on a variety of problems show that the proposed
technique leads to significantly more accurate inference results, not only when
compared to standard EP and VMP, but also when compared to competitive
bottom-up conditional models.Comment: Appearing in Proceedings of the 18th International Conference on
Artificial Intelligence and Statistics (AISTATS) 201
Bayesian Nonparametric Hidden Semi-Markov Models
There is much interest in the Hierarchical Dirichlet Process Hidden Markov
Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous
Hidden Markov Model for learning from sequential and time-series data. However,
in many settings the HDP-HMM's strict Markovian constraints are undesirable,
particularly if we wish to learn or encode non-geometric state durations. We
can extend the HDP-HMM to capture such structure by drawing upon
explicit-duration semi-Markovianity, which has been developed mainly in the
parametric frequentist setting, to allow construction of highly interpretable
models that admit natural prior information on state durations.
In this paper we introduce the explicit-duration Hierarchical Dirichlet
Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for
efficient posterior inference. The methods we introduce also provide new
methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs
sampling methods can be embedded in samplers for larger hierarchical Bayesian
models, adding semi-Markov chain modeling as another tool in the Bayesian
inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference
methods on both synthetic and real experiments
High-Dimensional Gaussian Graphical Model Selection: Walk Summability and Local Separation Criterion
We consider the problem of high-dimensional Gaussian graphical model
selection. We identify a set of graphs for which an efficient estimation
algorithm exists, and this algorithm is based on thresholding of empirical
conditional covariances. Under a set of transparent conditions, we establish
structural consistency (or sparsistency) for the proposed algorithm, when the
number of samples n=omega(J_{min}^{-2} log p), where p is the number of
variables and J_{min} is the minimum (absolute) edge potential of the graphical
model. The sufficient conditions for sparsistency are based on the notion of
walk-summability of the model and the presence of sparse local vertex
separators in the underlying graph. We also derive novel non-asymptotic
necessary conditions on the number of samples required for sparsistency
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