Corpus ID: 39177

Efficient Exact Inference in Planar Ising Models

@inproceedings{Schraudolph2008EfficientEI,
  title={Efficient Exact Inference in Planar Ising Models},
  author={Nicol N. Schraudolph and Dmitry Kamenetsky},
  booktitle={NIPS},
  year={2008}
}
We give polynomial-time algorithms for the exact computation of lowest-energy states, worst margin violators, partition functions, and marginals in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it does not impose any submodularity constraints; instead we require planarity to establish a correspondence with perfect matchings in an expanded dual graph. Maximum-margin parameter estimation for a boundary… Expand
Planar Cycle Covering Graphs
TLDR
This work describes a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field and shows that optimization of variational parameters achieves the same lower- bound as dual-decomposition into the set of all cycles of the original graph. Expand
Polynomial-Time Exact Inference in NP-Hard Binary MRFs via Reweighted Perfect Matching
TLDR
A new form of reweighting is developed 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. Expand
Learning Planar Ising Models
TLDR
This paper proposes a simple greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data) given the set of all pairwise correlations among variables. Expand
Ising Graphical Model
TLDR
The key to the construction is the complementary correspondence between graph cuts of the model graph and perfect matchings of its expanded dual, and it is shown that the exact algorithms are effective and efficient on a number of real-world machine learning problems. Expand
A Thorough View of Exact Inference in Graphs from the Degree-4 Sum-of-Squares Hierarchy
TLDR
This work applies a powerful hierarchy of relaxations, known as the sum-of-squares (SoS) hierarchy, to the combinatorial problem of exactly recovering an unknown groundtruth binary labeling of the nodes from a single corrupted observation of each edge. Expand
Inference and Sampling of K33-free Ising Models
TLDR
This work calls an Ising model tractable when it is possible to compute its partition function value in polynomial time, and extends the basic case of planar zero-field Ising models to models, whose triconnected components are either planar or graphs of $O(1)$ size. Expand
Inference in Sparse Graphs with Pairwise Measurements and Side Information
TLDR
A simple, efficient, algorithm that infers the ground truth with optimal Hamming error has optimal sample complexity and implies recovery results for all connected graphs and the power of this method is shown in several examples including hypergrids, ring lattices, and the Newman-Watts model for small world graphs. Expand
A New Family of Tractable Ising Models
We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components along with subsets of at most three verticesExpand
Spectral Bounds for the Ising Ferromagnet on an Arbitrary Given Graph
We revisit classical bounds of M. E. Fisher on the ferromagnetic Ising model, and show how to efficiently use them on an arbitrary given graph to rigorously upper-bound the partition function,Expand
Dynamic Planar-Cuts : Efficient Computation of Min-Marginals for OuterPlanar MRFs
This paper presents an algorithm for Dynamic MAP inference and the computation of min-marginals in boolean outer-planar MRFs. Our goal is to efficiently solve an instance of the MAP problem givenExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 62 REFERENCES
Approximate inference using planar graph decomposition
TLDR
This work base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field), and shows how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models. Expand
Computing Minimum-Weight Perfect Matchings
TLDR
A key feature in the implementation of Edmonds' blossom algorithm for solving minimum-weight perfect matching problems is the use of multiple search trees with an individual dual-change e for each tree. Expand
A new class of upper bounds on the log partition function
TLDR
A new class of upper bounds on the log partition function of a Markov random field (MRF) is introduced, based on concepts from convex duality and information geometry, and the Legendre mapping between exponential and mean parameters is exploited. Expand
Tree-based reparameterization framework for analysis of sum-product and related algorithms
We present a tree-based reparameterization (TRP) framework that provides a new conceptual view of a large class of algorithms for computing approximate marginals in graphs with cycles. This classExpand
Exact ground states of large two-dimensional planar Ising spin glasses.
  • G. Pardella, F. Liers
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
TLDR
This work presents an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction using Kasteleyn cities, and points out that the correctness of heuristically computed ground states can easily be verified. Expand
Minimizing Nonsubmodular Functions with Graph Cuts-A Review
  • V. Kolmogorov, C. Rother
  • Mathematics, Medicine
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • 2007
TLDR
This survey reviews some results that show that graph cuts can be applied to a much larger class of energy functions (in particular, nonsubmodular functions) and demonstrates the relevance of these results to vision on the problem of binary texture restoration. Expand
On the computational complexity of Ising spin glass models
In a spin glass with Ising spins, the problems of computing the magnetic partition function and finding a ground state are studied. In a finite two-dimensional lattice these problems can be solved byExpand
On the Dimer Solution of Planar Ising Models
Derivations of the partition function of the Ising model on a general planar lattice L, which proceed via an associated dimer problem and use Pfaffians, are simplified by constructing a lattice LΔExpand
From Fields to Trees
TLDR
It is proved that tree sampling exhibits lower variance than the naive Gibbs sampler and other naive partitioning schemes using the theoretical measure of maximal correlation. Expand
Implementation of O(nmlogn) weighted matchings in general graphs: the power of data structures
TLDR
The implementation of an algorithm which solves the weighted matching problem in general graphs with n vertices and m edges in time O(nm log n) is described, which is a variant of the algorithm of Galil, Micali and Gabow and extensively uses sophisticated data structures. Expand
...
1
2
3
4
5
...