Probabilistic Inference Using Markov Chain Monte Carlo Methods

By Radford M. Neal. 2011

1,297 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Probabilistic & Bayesian Methods

Citations in the corpus

Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, methodology): “Markov chain Monte Carlo (MCMC) methods (Neal, 1993) aim to provide samples from p.”
VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models (2020, methodology): “1In principle one would require an accept/reject step to make it a rigorous MCMC algorithm, but for sufficiently small stepsizes this is not necessary in practice (Neal, 1993).”
Representation Learning: A Review and New Perspectives (2012, methodology): “Ngiam et al. (2011) have used Hybrid Monte Carlo (Neal, 1993), but other options include contrastive divergence (Hinton, 1999; Hinton et al., 2006), score matching (Hyvärinen, 2005; Hyvärinen, 2008), denoising score matching (Kingma and LeCun, 2010; Vincent, 2011), ratio-matching (Hyvärinen, 2007”
BERT has a Mouth, and It Must Speak: BERT as a Markov Random Field Language Model (2019, methodology): “is Markov-chain Monte-Carlo (MCMC) sampling (Neal, 1993; Swendsen and Wang, 1986; Salakhutdinov, 2009; Desjardins et al., 2010; Cho et al., 2010).”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “MCMC is a classical technique for estimating the expectations in approximate Bayesian inference (Robert and Casella 2005, Neal 1993).”
Handbook of Markov Chain Monte Carlo (2011, neutral): “I also provided a statistically-oriented tutorial on HMC in a review of MCMC methods (Neal, 1993, Chapter 5).”
The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo (2011, methodology): “Worse, if L is chosen so that the parameters jump from one side of the space to the other each iteration, then the Markov chain may not even be ergodic (Neal, 2011).”
Stochastic Back-propagation and Variational Inference in Deep Latent Gaussian Models (2014, background): “…of the true posterior p ( ξ | v ), (40) can be seen as an approximation of the Kernel The kernel (41 We apply the fundamental theorem for Markov chains (Neal, 1993, pp. 38) and conclude that given the above properties, a Markov chain generated by (41) is guaranteed to generate samples from the…”
Minimum Probability Flow Learning (2009, background): “Although CD is not guaranteed to converge to the right answer, or even to a fixed point, it has proven to be an effective and fast heuristic for parameter estimation (MacKay, 2001; Yuille, 2005).”
Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring (2012, neutral): “We compare the algorithm to Hamiltonian Monte Carlo sampling (Neal, 1993) and to SGLD (Welling & Teh, 2011).”
Fast Gradient-Based Inference with Continuous Latent Variable Models in Auxiliary Form (2013, background): “) [Min01]). When it is not reasonable or possible to make assumptions about the posterior (which is often the case), one needs to resort to sampling approaches such as Markov Chain Monte Carlo (MCMC) [Nea93]. In highdimensional spaces, gradient-based samplers such as Hybrid Monte Carlo [DKPR87] are ”
Quantum machine learning: a classical perspective (2017, methodology): “Sampling methods are a common technique to compute approximations to these intractable quantities [82].”
Factor Graphs for Robot Perception (2017, background): “Markov chain Monte Carlo (MCMC) and Gibbs sampling provide a way to sample over high-dimensional state-spaces as described by factor graphs, and are discussed in [151, 82, 55].”
Nonlinear Models Using Dirichlet Process Mixtures (2007, methodology): “We used Hamiltonian dynamics (Neal, 1993) for updating the regression parameters, α ’s and β ’s.”
Pseudo-Marginal Bayesian Inference for Gaussian Processes (2013, methodology): “Another way to efficiently sample latent variables in GP models is by means of a variant of hybrid Monte Carlo (HMC) [33], [34] where the inverse mass matrix is set to the GP covariance K, as described in detail in [21].”
The flip-the-state transition operator for restricted Boltzmann machines (2013, background): “Both G and T are (local) Metropolis algorithms (Neal 1993).”