Markov Random Fields and Their Applications

By Ross P. Kindermann, L. Snell, W. H. Graves, Claude Schochet. 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 [35], (restricted) Boltzmann machines [62, 24, 29], and conditional random fields [40].”
The Factor Graph Approach to Model-Based Signal Processing (2007, background): “In many respects, the different notation systems for graphical models (Bayesian networks [7], [8], Markov random fields [7], [9], junction graphs [10], [11], etc.”
Visual-Based Defect Detection and Classification Approaches for Industrial Applications—A SURVEY (2020, background): “Markov random fields approaches [121] combine both statistical and structural information of context dependent entities, such as pixels depending on their neighbor pixels, and can be used in texture segmentation [122,123] and classification problems [124,125].”
Parsing the Hand in Depth Images (2014, methodology): “The Markov Random Fields [16] can be used to refine the classification results, which can well model the constraints from the neighboring states and the image observations [17].”
Statistical reconstruction of two-phase random media (2014, background): “The joint probability distribution of Markov random fields is the Gibbs distribution [14], which is exactly the probability distribution that maximizes the entropy under expectation-type confinements (e.”
Discovering molecular pathways from protein interaction and gene expression data (2003, methodology): “To model this assumption, we use the framework of Markov networks or Markov random ﬁelds (Kindeman and Snell, 1980), very common in statistical physics, e.g. to represent correlations between spins of neighboring electrons.”
Exact Optimization for Markov Random Fields with Convex Priors (2003, background): “A theorem(Besag[3], Kinderman and Snell[15]) connects it to a joint probability model: a probability distribution P onX is an MRF exactly when it is a Gibbs distribution relative to G: P (X) ∼ e−E(X), E(X) = ∑”
Statistical Inverse Ray Tracing for Image-Based 3D Modeling (2014, methodology): “Putting the values in, we further get M uv!x o i ¼ Àw o uv : (14) 4.1.2 Pair-Wise Message The pair-wise clique is the standard clique used in 3D Ising models [38].”
Self-Avoiding Random Dynamics on Integer Complex Systems (2011, methodology): “Ising models, also known as Boltzmann machines, are ubiquitous models in physics, machine learning and spatial statistics [Ackley et al. 1985; Besag 1974; Hopfield 1984; Kindermann and Snell 1980; Newman and Barkema 1999].”
Methodologies for Cross-Domain Data Fusion: An Overview (2015, methodology): “Two branches of graphical representations of distributions are commonly used , namely , Bayesian Networks and Mar - kov Networks ( also called Markov Random Field [ 34 ] ) .”
Pattern Recognition and Machine Learning (2006, unknown): “A Markov random field, also known as a Markov network or an undirected graphical model (Kindermann and Snell, 1980), has a set of nodes each of which corresponds to a variable or group of variables, as well as a set of links each of which connects a pair of nodes.”
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].”
Turbo Decoding as an Instance of Pearl's "Belief Propagation" Algorithm (1998, background): “4 if (4.4) A set of random variables whose density functions factor according to a given DAG is called a directed Markov field [35], [32], [65].”
A convex relaxation approach for computing minimal partitions (2009, background): “In the discrete setting, respective optimization problems can be addressed on a graph with nodes and edges in the framework of Markov Random Field (MRF) theory [19].”
Opinion Fraud Detection in Online Reviews by Network Effects (2013, methodology): “We propose to use an objective function that utilizes pairwise Markov Random Fields (pMRF) (Kindermann and Snell 1980) , which we adapt to our problem setting as fol- lows.”
Graph Signal Processing: Overview, Challenges, and Applications (2017, background): “Acyclic graphs [31], [32] represent Bayesian networks, and undirected graphs represent Markov random fields [33], [34], [35].”
Asymptotically exact inference in differentiable generative models (2016, methodology): “latent and observed variables, often via a graphical model such as a Bayesian network [74], Markov random field [45] or factor graph [32].”
Limit measures for affine cellular automata II (2001, background): “μ ∈ M[AM] is a (non-stationary) Markov random field [2, 9] with interaction range U (or ‘U-MRF’) if, for any W ⊂ M and any a ∈ A∂(W), events occurring ‘inside’ W are independent of those occurring ‘outside’, relative to the conditional measure μa.”