Markov Random Fields in Computer Vision: MAP Inference and Learning

2015 ◽  
pp. 841-845
Author(s):  
Nikos Komodakis ◽  
M. Pawan Kumar ◽  
Nikos Paragios
Keyword(s):  
Computer Vision ◽  
Random Fields ◽  
Markov Random Fields ◽  
Map Inference ◽  
Markov Random

scholarly journals Lifted Hinge-Loss Markov Random Fields

2019 ◽  
Vol 33 ◽  
pp. 7975-7983 ◽  
Author(s):  
Sriram Srinivasan ◽  
Behrouz Babaki ◽  
Golnoosh Farnadi ◽  
Lise Getoor
Keyword(s):  
Convex Optimization ◽  
Graphical Models ◽  
Random Fields ◽  
Markov Random Fields ◽  
Optimization Problem ◽  
Convex Optimization Problem ◽  
Map Inference ◽  
Lifted Inference ◽  
Hinge Loss ◽  
Markov Random

Statistical relational learning models are powerful tools that combine ideas from first-order logic with probabilistic graphical models to represent complex dependencies. Despite their success in encoding large problems with a compact set of weighted rules, performing inference over these models is often challenging. In this paper, we show how to effectively combine two powerful ideas for scaling inference for large graphical models. The first idea, lifted inference, is a wellstudied approach to speeding up inference in graphical models by exploiting symmetries in the underlying problem. The second idea is to frame Maximum a posteriori (MAP) inference as a convex optimization problem and use alternating direction method of multipliers (ADMM) to solve the problem in parallel. A well-studied relaxation to the combinatorial optimization problem defined for logical Markov random fields gives rise to a hinge-loss Markov random field (HLMRF) for which MAP inference is a convex optimization problem. We show how the formalism introduced for coloring weighted bipartite graphs using a color refinement algorithm can be integrated with the ADMM optimization technique to take advantage of the sparse dependency structures of HLMRFs. Our proposed approach, lifted hinge-loss Markov random fields (LHL-MRFs), preserves the structure of the original problem after lifting and solves lifted inference as distributed convex optimization with ADMM. In our empirical evaluation on real-world problems, we observe up to a three times speed up in inference over HL-MRFs.

Sampling from Gaussian Markov random fields conditioned on linear constraints

2008 ◽  
Vol 48 ◽  
pp. 1041 ◽  
Author(s):  
Daniel Peter Simpson ◽  
Ian W. Turner ◽  
A. N. Pettitt
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Linear Constraints ◽  
Gaussian Markov Random Fields ◽  
Markov Random

scholarly journals A Methodology for Redesigning Networks by Using Markov Random Fields

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1389
Author(s):  
Julia García Cabello ◽  
Pedro A. Castillo ◽  
Maria-del-Carmen Aguilar-Luzon ◽  
Francisco Chiclana ◽  
Enrique Herrera-Viedma
Keyword(s):  
Decision Making ◽  
Random Fields ◽  
Markov Random Fields ◽  
Application Performance ◽  
Cross Border ◽  
Markov Random ◽  
User Groups ◽  
Universal Definition ◽  
Definition Of ◽  
Decision Making Model

Standard methodologies for redesigning physical networks rely on Geographic Information Systems (GIS), which strongly depend on local demographic specifications. The absence of a universal definition of demography makes its use for cross-border purposes much more difficult. This paper presents a Decision Making Model (DMM) for redesigning networks that works without geographical constraints. There are multiple advantages of this approach: on one hand, it can be used in any country of the world; on the other hand, the absence of geographical constraints widens the application scope of our approach, meaning that it can be successfully implemented either in physical (ATM networks) or non-physical networks such as in group decision making, social networks, e-commerce, e-governance and all fields in which user groups make decisions collectively. Case studies involving both types of situations are conducted in order to illustrate the methodology. The model has been designed under a data reduction strategy in order to improve application performance.

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