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Efficient Exact Inference in Planar Ising Models
[article]
2008
arXiv
pre-print
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graphical models. ...
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected ...
NICTA is building capabilities in ICT research, research training and commercialisation for the generation of national benefit. ...
arXiv:0810.4401v2
fatcat:ktqa5j6z4ng2xasd7ugwuj4fem
Recursive sum–product algorithm for generalized outer-planar graphs
2012
Information Processing Letters
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Inference on cyclic graphs is one of the most important problems in the applications of graphical models. ...
While exact inference is NP-hard on general cyclic graphs, it has been found that exact inference can be achieved with a computational complexity as low as O(Nm 3 ) on the outer-planar graph, which is ...
However, for some special cyclic graphs, exact inference can be done with efficient algorithms. ...
doi:10.1016/j.ipl.2012.03.001
fatcat:srjqth3jtbdujcpfq6hnnifdc4
Beyond trees: MRF inference via outer-planar decomposition
2010
2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
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Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NP-hard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate ...
We leverage a new class of graphs amenable to exact inference, called outerplanar graphs, and propose an approximate inference algorithm called Outer-Planar Decomposition (OPD). ...
We thank Pedro Felzenszwalb for pointing out the connections between outer-planar graphs and k-trees, and Carlos Guestrin and Ramin Zabih for helpful discussions. ...
doi:10.1109/cvpr.2010.5539951
dblp:conf/cvpr/BatraGPC10
fatcat:zpodxtnqabbm7c6w5ozwgfq7qe
Approximate inference on planar graphs using Loop Calculus and Belief Propagation
[article]
2014
arXiv
pre-print
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We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. ...
We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians ...
Such a model is known in statistical physics as the Ising model without external field. Notice that exact inference for a general binary graphical model on a planar graph (i.e. ...
arXiv:1408.2034v1
fatcat:sdgayr33u5eiznrnhndnv4sqyu
Tractable Minor-free Generalization of Planar Zero-field Ising Models
[article]
2019
arXiv
pre-print
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of an efficient (for planar) or brute-force (for O(1)-sized) inference and sampling to the components as a black box. ...
Second, we demonstrate empirically an improvement in the approximation quality of the NP-hard problem of inference over the square-grid Ising model in a node-dependent non-zero "magnetic" field. ...
In this manuscript, we, first of all, compile results that were scattered over the literature on (at least) O(N 3 2 )-efficient exact sampling and exact inference in the zero-field Ising model over planar ...
arXiv:1910.11142v1
fatcat:y6xyighwafdlxbrvlqr6pyfgwy
Approximate inference on planar graphs using Loop Calculus and Belief Propagation
[article]
2009
arXiv
pre-print
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We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. ...
We develop an algorithm for the approach presented in (Certkov et al., 2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians ...
Notice that exact inference for a general binary graphical model on a planar graph (that is Ising model with external field) is intractable (Barahona, 1982) . ...
arXiv:0901.0786v3
fatcat:ejzvd4lzurgebdw6tf75nmrzmi
Inference and Sampling of K_33-free Ising Models
[article]
2019
arXiv
pre-print
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2018 pre-print arXiv:1812.09587v1 fatcat:4i7stksedjgkhdrrb2hmxwlnhy
We call an Ising model tractable when it is possible to compute its partition function value (statistical inference) in polynomial time. ...
In particular, it results in a polynomial-time inference and sampling algorithms for K_33 (minor) free topologies of zero-field Ising models - a generalization of planar graphs with a potentially unbounded ...
This concludes construction of an efficient inference algorithm for computing PF of a planar ZFI model. ...
arXiv:1812.09587v2
fatcat:svunt7ttdvhvjnrnnlh5worqnu
Complexity of Inference in Graphical Models
[article]
2012
arXiv
pre-print
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It is well-known that inference in graphical models is hard in the worst case, but tractable for models with bounded treewidth. ...
In other words, is there some class of structures with unbounded treewidth in which inference is tractable? ...
MAIN RESULTS We present our main results for graphical models with binary-valued variables in this section.
EXACT INFERENCE Theorem 5.1. ...
arXiv:1206.3240v1
fatcat:vvsrqsamyfghbpqqxk6a2z2eii
Model Reductions for Inference: Generality of Pairwise, Binary, and Planar Factor Graphs
2013
Neural Computation
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We characterize the reducibility of each class, showing in particular that the class of binary pairwise factor graphs is able to simply reduce only positive models. ...
We offer a solution to the problem of efficiently translating algorithms between different types of discrete statistical model. ...
When the calculation is exact (to machine precision), the problem is often called exact inference. ...
doi:10.1162/neco_a_00441
pmid:23547951
fatcat:at7uw6ftafdbhkr3jzbjgwrypa
Learning Planar Ising Models
[article]
2010
arXiv
pre-print
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In this paper, we focus our attention on the class of planar Ising models, for which inference is tractable using techniques of statistical physics [Kac and Ward; Kasteleyn]. ...
However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical ...
The algorithm is simple to implement with the help of known methods for tractable inference in planar Ising models, efficient methods for planarity testing and embedding of planar graphs. ...
arXiv:1011.3494v1
fatcat:xjwcfomqsbgstdsjzusdxgk7we
Multi-task Planar Reconstruction with Feature Warping Guidance
[article]
2023
arXiv
pre-print
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However, most existing planar reconstruction models either neglect semantic predictions or do not run efficiently enough for real-time applications. ...
Our model simultaneously predicts semantics using single images at inference time, while achieving real-time predictions at 43 FPS. ...
The structure of the scene is easier to predict than the exact depth, a challenge presented when using a single image for inference. ...
arXiv:2311.14981v2
fatcat:yrvpgrwfsbdqhmoeosjfuv6e4m
Polynomial-Time Exact Inference in NP-Hard Binary MRFs via Reweighted Perfect Matching
2010
Journal of machine learning research
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., 2005b) to leverage the relationship between Ising spin glasses and perfect matchings into a novel technique for the exact computation of MAP states in hitherto intractable binary Markov random fields ...
It empirically scales as O(n 3 ) even though this problem is NP-hard and nonapproximable in polynomial time. We discuss limitations of our current implementation and propose ways to overcome them. ...
Much work in graphical models therefore proceeds via the following route: 1. identify a tractable class of graphs (distributions); 2. develop efficient, exact inference methods for it; 3. leverage these ...
dblp:journals/jmlr/Schraudolph10
fatcat:jkzd6mciv5f6hkf6o77avic5ma
Single-Image Piece-wise Planar 3D Reconstruction via Associative Embedding
[article]
2019
arXiv
pre-print
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Then, the plane instances are obtained by grouping the embedding vectors in planar regions via an efficient mean shift clustering algorithm. ...
Code is available at https://github.com/svip-lab/PlanarReconstruction. ...
The number of iterations T is set to 5 in training and set to 10 in testing. Our model is trained in an end-to-end manner. ...
arXiv:1902.09777v3
fatcat:fpego7f2lvfmjnhr4jrigukhm4
An Efficient Approximate Method for Scattering Response from Infinite Arrays of Nonlinearly Loaded Antenna in the Frequency Domain
2022
Advanced Electromagnetics
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In this paper, different arrangements of infinite arrays of nonlinearly loaded antennas are analyzed in the frequency domain by an efficient approximate method and compared with the exact one which are ...
In one hand, although the exact method is suitable for strongly nonlinear load, it is suffering from gradient operation and initial guess in the iteration process especially under multi-tone excitations ...
This paper is organized as follows. In section II, modeling principles of exact and approximate methods are briefly explained. ...
doaj:fb551eb80e9744a1b9c3a6c1085d5b25
fatcat:jk5wgfmi2bcqzopbumcapmmgna
Inference for Stereological Extremes
2007
Journal of the American Statistical Association
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The issue of inference is more difficult, since likelihood calculation is not feasible for the ellipsoidal model. ...
Our objectives in this article are two-fold: to assess the robustness of such inferences with respect to the assumption of spherical inclusions, and to develop an inference procedure that is valid for ...
of the inclusion shape and measurement process that we have included in the discussion. ...
doi:10.1198/016214506000000988
fatcat:cdaktztnf5duvbr6c6v27u46yu
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