NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
By Matthew D. Hoffman, Pavel Sountsov, Joshua V. Dillon, Ian Langmore, Dustin Tran, Srinivas Vasudevan. 2019
125 citations recorded by the source corpus.
Hamiltonian Monte Carlo is a powerful algorithm for sampling from difficult-to-normalize posterior distributions. However, when the geometry of the posterior is unfavorable, it may take many expensive evaluations of the target distribution and its gradient to converge and mix. We propose neural transport (NeuTra) HMC, a technique for learning to correct this sort of unfavorable geometry using inverse autoregressive flows (IAF), a powerful neural variational inference technique. The IAF is trained to minimize the KL divergence from an isotropic Gaussian to the warped posterior, and then HMC sampling is performed in the warped space. We evaluate NeuTra HMC on a variety of synthetic and real problems, and find that it significantly outperforms vanilla HMC both in time to reach the stationary distribution and asymptotic effective-sample-size rates.
Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability, Probabilistic & Bayesian Methods
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In Artificial Intelligence
- Yoshua Bengio
- Song-Chun Zhu
- Sergey Levine
- Stefano Ermon
- Ying Nian Wu
- Quoc V. Le
- Mohit Bansal
- Ruslan Salakhutdinov
In Statistical and Nonlinear Physics
- Yoshua Bengio
- Danilo Jimenez Rezende
- Erik Nijkamp
- Shakir Mohamed
- Stefano Ermon
- Balaji Lakshminarayanan
- Max Welling
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In Statistics and Probability
- Shakir Mohamed
- Balaji Lakshminarayanan
- Eric T. Nalisnick
- Jascha Narain Sohl-Dickstein
- Bo Pang
- Song-Chun Zhu
- Danilo Jimenez Rezende
- Yoshua Bengio
In Probabilistic & Bayesian Methods
- Danilo Jimenez Rezende
- Yoshua Bengio
- Ying Nian Wu
- Song-Chun Zhu
- Erik Nijkamp
- Stefano Ermon
- Diederik P. Kingma
- Max Welling
Citations in the corpus
- Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling (2020, background): “One solution to the problem of slow-sampling Markov Chains is to perform sampling using a carfefully crafted latent space [15, 16].”
- Normalizing Flows for Probabilistic Modeling and Inference (2019, methodology): “Tran et al. (2019) take this approach, showing performance in character-level language modeling competitive to RNNs while having superior generation runtime.”
- Learning Energy-based Model with Flow-based Backbone by Neural Transport MCMC (2020, methodology): “Our work is inspired by neural transport sampling [24].”
- Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models (2021, background): “samplers with neural networks can also improve the efficiency of sampling [62], [88], [134], [199], [215].”