REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS

By U. Grenander, M. I. Miller. 1994

Subfields: Knowledge Graphs & Representation

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Citations in the corpus

Score-Based Generative Modeling through Stochastic Differential Equations (2020, positive): “Since we have a score-based model s θ ˚ p x , t q « ∇ x log p t p x q , we can employ score-based MCMC approaches, such as Langevin MCMC (Parisi, 1981; Grenander & Miller, 1994) or HMC (Neal et al., 2011) to sample from p t directly, and correct the solution of a numerical SDE solver.”
Elucidating the Design Space of Diffusion-Based Generative Models (2022, background): “1 and a time-varying Langevin diffusion SDE [14] (see Appendix B.5): with discrete SDE solver steps introduces error in itself.”
Handbook of Markov Chain Monte Carlo (2011, neutral): “…without an accept/reject step can also be used (for a discussion of this, see Neal, 1993, Section 5.3) — as, for instance, in a paper on statistical inference for complex models by Grenander and Miller (1990), where also an accept/reject step is proposed in the discussion by J. Besag (p. 591).”
High-dimensional Bayesian inference via the unadjusted Langevin algorithm (2016, methodology): “r be held constant or be chosen to decrease to 0. This algorithm has been ﬁrst proposed by [16] and [35] for molecular dynamics applications. Then it has been popularized in machine learning by [20], [21] and computational statistics by [33] and [37]. Following [37], in the sequel this method will b”
Model choice using reversible jump Markov chain Monte Carlo (2012, unknown): “Predating reversible jump, Grenander and Miller (1994) proposed a sampling method they termed jump diffusion, involving between-model jumps and within-model diffusion according to a Langevin stochastic differential equation.”
Bayesian Methods for Hidden Markov Models (2002, methodology): “The growing list of VDMC algorithms that have been applied to (cid:142) nite mixture models includes jump diffusions (Grenander and Miller 1994; Phillips and Smith 1996), reversible-jump MCMC (Green 1995; Richardson and Green 1997), and birth–death sampling (Stephens 2000a).”
Bayesian Modelling and Inference on Mixtures of Distributions (2005, methodology): “2 Birth-and-death processes The Birth-and-death MCMC (BDMCMC) approach of Stephens (2000a) is already found in Ripley (1987), Grenander and Miller (1994), Phillips and Smith (1996).”
Convergence of Heavy‐tailed Monte Carlo Markov Chain Algorithms (2007, methodology): “It has then been proposed by, e.g. Besag (1994) to use the candidate transition kernel Q(x, ·)=N ( x + h 2 ∇ log (x), h ) , (42) where h > 0, N denotes the normal distribution and ∇ is the differential operator.”
Trans-dimensional Markov chain Monte Carlo (2000, background): “A continuous time Markov chain approach to simulating certain spatial point processes by regarding them as the invariant distributions of spatial birth-and-death processes was suggested and investigated by Preston (1977) and Ripley (1977).”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, background): “y community Langevin diusions and their equilibrium distributions had also been around for some time (Kent (1978)), it was the Roberts and Tweedie (1996a) paper (motivated by Besag (1994) comment on Grenander and Miller (1994)) that brought the approach to the centre of interest of the computational”
Handbook of Markov Chain Monte Carlo: Hardcover: 619 pages Publisher: Chapman and Hall/CRC Press (first edition, May 2011) Language: English ISBN-10: 1420079417 (2012, background): “For example, Keith et al. (2004) present a generalized Markov sampler, which includes the reversible jump sampler as a special case. Petris and Tardella (2003) demonstrate a geometric approach for sampling from nested models, formulated by drawing from a fixed-dimension auxiliary continuous distribu”
Sampling from a strongly log-concave distribution with the Unadjusted Langevin Algorithm (2016, methodology): “This method was originally proposed in the physics literature by [19] and introduced in the computational statistics community by [11] and [12].”
A Review of Geometric Transformations for Nonrigid Body Registration (2008, unknown): “[57] for fluid flow registration, were suitable to generate groups of computational anatomies [143]–[145].”
Exponential convergence of Langevin distributions and their discrete approximations (1996, methodology): “Any naive algorithm using (11) below might be constructed in this way, as in Parisi (1981) or Grenander and Miller (1994). We shall see that the algorithm may have some undesirable convergence properties, although since its implementation may involve less computational expense than some of its more ”