MCMC Using Hamiltonian Dynamics

By Radford M. Neal. 2011

1,520 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Generative Modeling by Estimating Gradients of the Data Distribution (2019, methodology): “For sampling, any method based on scores is applicable, including Langevin dynamics and (potentially) Hamiltonian Monte Carlo [38].”
Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model (2019, methodology): “Generating synthesized examples x − i ∼ p θ ( x ) requires MCMC, such as Langevin dynamics (or Hamiltonian Monte Carlo) [36], which iterates where τ indexes the time, ∆ τ is the discretization of time, and ∼ If p θ is of low entropy or low temperature, the gradient term dominates the diffusion noise”
On the Anatomy of MCMC-based Maximum Likelihood Learning of Energy-Based Models (2019, background): “where zt ∼ N(0, IN ) and ε, τ > 0, has stationary distribution pθ [9, 27].”
Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, methodology): “This is an extreme version of an example from Neal (2011).”
A-NICE-MC: Adversarial Training for MCMC (2017, methodology): “The proposal first draws v from p(v) (typically a factored Gaussian distribution) and then obtains (x0, v0) by simulating the dynamics (and inverting v at the end of the simulation) corresponding to the Hamiltonian H(x, v) = v>v/2 + U(x) (8) where x and v are iteratively updated using the leapfrog i”
Variational Inference with Normalizing Flows (2015, methodology): “Hamiltonian Monte Carlo can also be described in terms of a normalizing ﬂow on an augmented space ˜ z = ( z , ω ) with dynamics resulting from the Hamiltonian H ( z , ω ) = −L ( z ) − ω (cid:62) M ω ; HMC is also widely used in machine learning, e.g., Neal (2011).”
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.”
Denoising Diffusion Implicit Models (2020, methodology): “Both use a denoising autoencoder objective for many noise levels, and both use a procedure similar to Langevin dynamics to produce samples (Neal et al., 2011).”
Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro (2019, methodology): “The No-U-Turn Sampler (NUTS) [14] is an extension of the Hamiltonian Monte Carlo (HMC) algorithm [15, 16], which can efﬁciently sample from high-dimensional continuous probability distributions.”
Kernel Sequential Monte Carlo (2015, background): “Random walk methods, which are the default choice for intractable likelihoods, scale badly in high dimensions themselves [16].”
Equivariant Hamiltonian Flows (2019, methodology): “The latter is the same interpretation as in HMC [22, 25, 21].”
Bayesian Model-Agnostic Meta-Learning (2018, methodology): “Gradient-based MCMC methods like HMC (Neal et al., 2011) or SGLD (Welling & Teh, 2011) are such methods.”
Stochastic Gradient Hamiltonian Monte Carlo (2014, methodology): “Such partial momentum refreshment was shown to not greatly improve HMC in the case of noise-free gradients (Neal, 2010).”
Adding Gradient Noise Improves Learning for Very Deep Networks (2015, methodology): “This use of gradient information in MCMC sampling for machine learning to allow faster exploration of state space was previously proposed by Neal (2011).”
Generative Modeling of Convolutional Neural Networks (2014, methodology): “In practical implementation, the leapfrog algorithm (Neal, 2011) is used to discretize the continuous Hamiltonian dynamics as follows, with (cid:15) being the step-size: that is, a half-step update of φ is performed ﬁrst and then it is used to compute x ( t + (cid:15) ) and φ ( t + (cid:15) ) .”
Learning Energy-Based Models by Diffusion Recovery Likelihood (2020, methodology): “After training the model by maximizing the diffusion recovery likelihood under setting T 1 k , we ﬁrst sample from the normal approximation as the ﬁrst sampling step, and then use Hamiltonian Monte Carlo (HMC) (Neal et al., 2011) with 2 leapfrog steps to perform the remaining sampling steps.”