Markov Random Fields and Their Applications

By Ross P. Kindermann, J. L. Snell. 1980

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Energy-Inspired Models: Learning with Sampler-Induced Distributions (2019, neutral): “Different choices of energy function recover well-known probabilistic models including Markov random fields [36], (restricted) Boltzmann machines [64, 24, 30], and conditional random fields [41].”
Mining the network value of customers (2001, background): “The set of variables X u, with joint probability conditioned on X k, Y and M described by Equation 2, is an instance of a Markov random field [2, 25, 7].”
Mental Disorders as Causal Systems (2015, background): “Such models are known as Markov random fields (Kindermann & Snell, 1980).”
No free lunch theorems for optimization (1997, background): “For example, Markov or Gibbs random field descriptions [10] of families of optimization problems express exactly.”
Factor graphs and the sum-product algorithm (2001, methodology): “A Markov random field (see, e.g., [ 18 ]) is a graphical model based on an undirected graph in which each node corresponds to a random variable.”
Segmentation of X‐ray computed tomography images of porous materials: A crucial step for characterization and quantitative analysis of pore structures (2009, methodology): “The most promising methods within this category are based on Markov random fields (MRF), a multidimensional extension of Markov chains [Kindermann and Snell, 1980; Chellappa and Jain, 1993].”
Collective Opinion Spam Detection: Bridging Review Networks and Metadata (2015, background): “In their formulation, the domain of class labels is L = { spammer } for users and L = { quality, bad - quality for products. the To formally deﬁne classiﬁcation problem, the network is represented as a pair-wise Markov Random Field (MRF) [11].”
Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields (1999, background): “Such problems have a rich history in statistics, where they arise naturally from formalisms such as the theory of Markov random fields [4, 14, 28 , 29, 33]; they have formed some of the core analytical frameworks in areas including image processing [5, 15, 20, 23] and biometric analysis [4], and th”
A survey of MRI-based brain tumor segmentation methods (2014, unknown): “MRF had been proposed as it can provide a way to integrate spatial information into the clustering or classification process[89].”
Exponential Family Estimation via Adversarial Dynamics Embedding (2019, methodology): “ommonly used distributions, and the notably powerful undirected graphical models (Wainwright and Jordan, 2008) and energy-based models (LeCun et al., 2006; Wu et al., 2018), e.g., Markov random elds (Kinderman and Snell, 1980), conditional random elds (Laerty et al., 2001), and language models (Mnih”
Exact Optimization for Markov Random Fields with Convex Priors (2003, background): “and Snell[ 15 ]) connects it to a joint probability model: a probability distribution P on X is an”
A survey of MRI-based medical image analysis for brain tumor studies (2013, methodology): “In most case, this is performed with a random field method, either Markov random fields (MRFs) (Kindermann and Snell 1980) or Conditional Random Fields (CRFs) (Lafferty et al 2001, Kumar and Hebert 2006).”