Monte Carlo Sampling Methods Using Markov Chains and Their Applications

By W. Hastings. 1970

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, methodology): “In practice, for any proposal distribution, one can ensure detailed balance through a Metropolis-Hastings (Hastings, 1970) accept/reject step.”
A-NICE-MC: Adversarial Training for MCMC (2017, background): “Therefore, the resulting MH transition kernel can be expressed as T✓(x|x) = g✓(x|x)A✓(x|x) (if x 6= x0), and it can be shown that pd is stationary for T✓(·|x) [25].”
Foundation Posteriors for Approximate Probabilistic Inference (2022, neutral): “Markov Chain Monte Carlo (MCMC) [32, 24] and variational inference (VI) [37, 64, 8] are two widely used examples.”
The frontier of simulation-based inference (2019, methodology): “This challenge is commonly addressed with Markov Chain Monte Carlo (MCMC) methods (9, 10) or variational inference (VI) (11).”
Distributed Prioritized Experience Replay (2018, background): “Distributed Importance Sampling A complementary family of techniques for speeding up training is based on variance reduction by means of importance sampling (cf. Hastings, 1970).”
Annealed importance sampling (1998, methodology): “An alternative is to obtain a sample of dependent points by simulating a Markov chain that converges to the distribution of interest, as in the Metropolis-Hastings algorithm (Metropolis, et al 1953; Hastings 1970).”
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): “Fordecades, the dominant paradigm for approximate inference has been MCMC (Hastings 1970; Gelfand and Smith 1990).”
COLA: Decentralized Linear Learning (2018, methodology): “A desired mixing matrix can be constructed using Metropolis-Hastings weights [Hastings, 1970]:”
Uncertainty-guided Continual Learning with Bayesian Neural Networks (2019, methodology): “Markov Chain Monte Carlo (MCMC) sampling (Hastings, 1970) has been widely used and explored for this purpose, see (Robert & Casella, 2013) for different methods under this category.”
A deterministic and computable Bernstein-von Mises theorem (2019, methodology): “For example, it is straightforward to solve an optimization problem while accessing only subsets (or batches) of the data at any one time, thus minimizing the memory cost of the method while evaluation of the Metropolis-Hastings ratio on subsets of the data is much trickier. Furthermore, in the larg”
DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Corrections (2019, methodology): “Several methods to estimate these ratios have been proposed recently [12, 14, 21], all based on the steady-state property of stationary distributions of Markov processes [15].”
Handbook of Markov Chain Monte Carlo (2011, neutral): “Since this proposal is not symmetrical, it must be accepted or rejected based on both the ratio of the probability densities of q and q and on the ratio of the probability densities for proposing q from q and vice versa (Hastings, 1970).”
Beyond Data and Model Parallelism for Deep Neural Networks (2018, methodology): “This section briefly introduces the Metropolis-Hastings algorithm (Hastings, 1970) we use for MCMC sampling in the execution optimizer.”
An Explanation of In-context Learning as Implicit Bayesian Inference (2021, neutral): “Topic models and HMMs. Topic models such as LDA (Blei et al., 2003) also have document-level latent variables, but learning is typically relies on algorithms such as EM (Dempster et al., 1977), variational inference (Jordan et al., 1999), or MCMC (Metropolis et al., 1953; Hastings, 1970).”
Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo (2015, methodology): “Instead, we often rely on Markov Chain Monte Carlo methods, e.g., Metropolis-Hastings algorithm (Hastings, 1970) to generate samples.”
Edward: A library for probabilistic modeling, inference, and criticism (2016, methodology): “Black box algorithms are typically based on Monte Carlo methods, and make very few assumptions about the model (Metropolis and Ulam, 1949; Hastings, 1970; Geman and Geman, 1984).”
NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport (2019, background): “It introduces a set of auxiliary variables that let one generate Metropolis-Hastings proposals (Metropolis et al., 1953; Hastings, 1970) by simulating the dynamics of a fictional Hamiltonian physical system.”