Efficient inference with cardinality-based clique potentials

Gupta, Rahul; Diwan, Ajit A.; Sarawagi, Sunita

doi:10.1145/1273496.1273538

Cited by 29 publications

(33 citation statements)

References 16 publications

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“…operators PRMs, Friedman et al [12] mode [35] mode, count, exists Macskassy & Provost [36] prop Gupta, Diwan, & Sarawagi [21] mode, count McDowell, Gupta, & Aha [39] prop Table 2: A list of systems and the aggregation operators they use to aggregate neighborhood class labels. The systems include probabilistic relational models (PRMs), relational Markov networks (RMNs) and Markov logic networks (MLNs).…”

Section: Approximate Inference Algorithms For Approaches Based On Glomentioning

confidence: 99%

Collective Classification in Network Data

et al. 2008

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Numerous real-world applications produce networked data such as web data (hypertext documents connected via hyperlinks) and communication networks (people connected via communication links). A recent focus in machine learning research has been to extend traditional machine learning classification techniques to classify nodes in such data. In this report, we attempt to provide a brief introduction to this area of research and how it has progressed during the past decade. We introduce four of the most widely used inference algorithms for classifying networked data and empirically compare them on both synthetic and real-world data.

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Section: Approximate Inference Algorithms For Approaches Based On Glomentioning

confidence: 99%

Collective Classification in Network Data

et al. 2008

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“…The global minimum of any MPF in this (and therefore also the linear) class will generally, ignoring integrability, 8 produce delta function marginal statistics. This can be seen from the fact that a concave function k f k (h k ) defined over a simplex {{h k } : h k ≥ 0, k h k = const} attains a minimum at an extreme point of this simplex.…”

Section: Characterizing Cost Functionsmentioning

confidence: 99%

“…It is well-known that the minimum of (15) can be computed in O(n log n) time [8]. We need to sort values θ i in non-decreasing order, evaluate the cost of n + 1 labellings (0, .…”

Section: Case I: Binary Variablesmentioning

confidence: 99%

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A global perspective on MAP inference for low-level vision

Woodford

Rother

Kolmogorov

2009

2009 IEEE 12th International Conference on Computer Vision

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In recent years the Markov Random Field (MRF) has become the de facto probabilistic model for low-level vision applications. However, in a maximum a posteriori (MAP) framework, MRFs inherently encourage delta function marginal statistics. By contrast, many low-level vision problems have heavy tailed marginal statistics, making the MRF model unsuitable. In this paper we introduce a more general Marginal Probability Field (MPF), of which the MRF is a special, linear case, and show that convex energy MPFs can be used to encourage arbitrary marginal statistics. We introduce a flexible, extensible framework for effectively optimizing the resulting NP-hard MAP problem, based around dual-decomposition and a modified mincost flow algorithm, and which achieves global optimality in some instances. We use a range of applications, including image denoising and texture synthesis, to demonstrate the benefits of this class of MPF over MRFs.

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“…all algorithms in [49] can be used as soft GAC-propagators. We anticipate that in the future, more global constraints with tractable soft propagators and useful in applications will be discovered.…”

Section: Handling High-arity and Global Constraintsmentioning

confidence: 99%

Revisiting the Linear Programming Relaxation Approach to Gibbs Energy Minimization and Weighted Constraint Satisfaction

Werner

2010

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-We present a number of contributions to the LP relaxation approach to weighted constraint satisfaction (= Gibbs energy minimization). We link this approach to many works from constraint programming, which relation has so far been ignored in machine vision and learning. While the approach has been mostly considered only for binary constraints, we generalize it to n-ary constraints in a simple and natural way. This includes a simple algorithm to minimize the LP-based upper bound, n-ary max-sum diffusionhowever, we consider using other bound-optimizing algorithms as well. The diffusion iteration is tractable for a certain class of higharity constraints represented as a black-box, which is analogical to propagators for global constraints CSP. Diffusion exactly solves permuted n-ary supermodular problems. A hierarchy of gradually tighter LP relaxations is obtained simply by adding various zero constraints and coupling them in various ways to existing constraints. Zero constraints can be added incrementally, which leads to a cutting plane algorithm. The separation problem is formulated as finding an unsatisfiable subproblem of a CSP.

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Efficient inference with cardinality-based clique potentials

Cited by 29 publications

References 16 publications

Collective Classification in Network Data

Collective Classification in Network Data

A global perspective on MAP inference for low-level vision

Revisiting the Linear Programming Relaxation Approach to Gibbs Energy Minimization and Weighted Constraint Satisfaction

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