Hamiltonian Annealed Importance Sampling for partition function estimation

By Jascha Narain Sohl-Dickstein, Benjamin Jackson Culpepper. 2012

40 citations recorded by the source corpus.

We introduce an extension to annealed importance sampling that uses Hamiltonian dynamics to rapidly estimate normalization constants. We demonstrate this method by computing log likelihoods in directed and undirected probabilistic image models. We compare the performance of linear generative models with both Gaussian and Laplace priors, product of experts models with Laplace and Student's t experts, the mc-RBM, and a bilinear generative model. We provide code to compare additional models.

Subfields: Artificial Intelligence, Statistics and Probability, 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 Artificial Intelligence

1. Ruslan Salakhutdinov
2. Jascha Narain Sohl-Dickstein
3. Yoshua Bengio
4. Roger Baker Grosse
5. Matthew D. Hoffman
6. Quoc V. Le
7. Sergey Levine
8. Stefano Ermon

In Statistics and Probability

1. Jascha Narain Sohl-Dickstein
2. Ruslan Salakhutdinov
3. Roger Baker Grosse
4. Matthew D. Hoffman
5. Daniel Lévy
6. Mayur Mudigonda
7. Michael Robert DeWeese
8. Daniel Zoran

In Probabilistic & Bayesian Methods

1. Jascha Narain Sohl-Dickstein
2. Matthew D. Hoffman
3. Ruslan Salakhutdinov
4. Roger Baker Grosse
5. Chris J. Maddison
6. Stefano Ermon
7. David M. Blei
8. Yoshua Bengio

Citations in the corpus

• Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, methodology): “…Berger et al., 2015); with the use of non-canonical Hamiltonian dynamics (Tripuraneni et al., 2016); with variants of AIS adapted to HMC proposals (Sohl-Dickstein & Culpepper, 2012); with the extension of HMC to discrete state spaces (Zhang et al., 2012); and with the use of alternative…”
• "Natural Images, Gaussian Mixtures and Dead Leaves" (2012, methodology): “HAIS allows us to estimate likelihoods for these models accurately, and we have verified that the approximation given by HAIS is relatively accurate in cases where exact calculations are feasible (see supplementary material for details).”
• Annealing between distributions by averaging moments (2013, background): “AIS has enabled precise quantitative comparisons of powerful generative models in image statistics [7, 8] and deep learning [9, 10, 11].”
• A Markov Jump Process for More Efficient Hamiltonian Monte Carlo (2015, methodology): “tion techniques [16], Hamiltonian annealed importance sampling [17], split HMC [18], tempered trajectories [9], novel discrete time transition rules [10, 19, 20], stochastic gradient variants on HMC [21], HMC for approximate Bayesian computation [22], and new approximate Hamiltonian integrators [23]”