Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images

By Stuart Geman, Donald Geman. 1984

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model (2019, methodology): “To sample from the current EBM, we need to use Markov chain Monte Carlo (MCMC), such as the Gibbs sampler [12], Langevin dynamics, or Hamiltonian Monte Carlo [33].”
On the Anatomy of MCMC-based Maximum Likelihood Learning of Energy-Based Models (2019, background): “where Z` ∼ N(0, IN ) and ε > 0, has stationary distribution pθ (Geman and Geman 1984; Neal 2011).”
GAN Inversion: A Survey (2021, methodology): “It has been widely adopted in computer vision tasks, including MRF [196], [197], [198], dark channel prior [199] and total variation regularizer [200], which all model correlation among neighboring pixels via Gibbs distribution.”
An Introduction to Probabilistic Programming (2018, background): “Gibbs sampling algorithms (Geman and Geman, 1984) are an important special case of MH, which cycle through all the latent variables in the model and iteratively sample from the so-called full conditional distributions”
Stochastic variational inference (2012, methodology): “In MCMC sampling, we construct a Markov chain over the hidden variables whose stationary distribution is the posterior of interest (Metropolis et al., 1953; Hastings, 1970; Geman and Geman, 1984; Gelfand and Smith, 1990; Robert and Casella, 2004).”
Variational Inference: A Review for Statisticians (2016, methodology): “This approach closely connects to the classical Gibbs sampler (Geman and Geman 1984; Gelfand and Smith 1990).”
How to Represent Part-Whole Hierarchies in a Neural Network (2021, methodology): “Pioneering work on using Markov Random Fields for image segmentation [Geman and Geman, 1984] used the presence of a boundary between pixel x and pixel y to prevent x from attending to y .”
Incorporating Non-local Information into Information Extraction Systems by Gibbs Sampling (2005, methodology): “One such algorithm isGibbs sampling , a simple Monte Carlo algorithm that is appropriate for inference in any factored probabilistic model, including sequence models and probabilistic context free grammars (Geman and Geman, 1984).”
Mean Field Theory for Sigmoid Belief Networks (1996, methodology): “One approach to dealing with such networks has been to use Gibbs sampling (Pearl, 1988), astochastic simulation methodology with roots in statistical mechanics (Geman & Geman, 1984).”
Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling (1998, methodology): “To draw a typical sample image from p.II3K; SK/, we use the Gibbs sampler ( Geman and Geman, 1984 ) which simulates a Markov chain in the image space LjDj.”
Divergence Triangle for Joint Training of Generator Model, Energy-Based Model, and Inferential Model (2018, methodology): “Both expectations can be approximated by MCMC, such as Gibbs sampling [1], Langevin dynamics, or Hamiltonian Monte Carlo (HMC) [2].”
Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo (2015, methodology): “, Metropolis-Hastings algorithm (Hastings, 1970) to generate samples. This is often prohibitively expensive when the data is large. One recent approach to scale up Bayesian learning is to combine stochastic gradient estimation as in Robbins & Monro (1951) and Monte Carlo methods that simulates stoch”
Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser (2020, background): “Since the family of observation densities, pσ(y) forms a scale-space representation of p(x), the algorithm may be viewed as an adaptive form of coarse-to-fine optimization [35–38].”
Edward: A library for probabilistic modeling, inference, and criticism (2016, methodology): “This extends to many algorithms: for example, classical message passing, which performs exact local inferences; Gibbs sampling, which draws samples from conditionally conjugate inferences (Geman and Geman, 1984); expectation propagation, which locally minimizes KL(p||q) over exponential families (Mi”
Deep Exponential Families (2014, background): “Unfortunately DEFs are a nonconjugate model—their local conditional distributions are difficult to compute—and so they are not amenable to simple inference algorithms like Gibbs sampling [9] or variational message passing [10].”
Variational inference for Dirichlet process mixtures (2006, background): “This yields a chain with the desired stationary distribution ( Geman and Geman, 1984; Gelfand and Smith, 1990; Neal, 1993).”
High-dimensional Ising model selection using ℓ1-regularized logistic regression (2010, neutral): “Setting δ = αλn4(2−α) , we obtain P [ 2 − α λn |Wnu | > α 4 ] ≤ 2 exp ( − α 2λ2n 128(2 − α)2 n ) .”