Publications

Lost Relatives of the Gumbel Trick

Matej Balog, Nilesh Tripuraneni, Zoubin Ghahramani, Adrian Weller, August 2017. (In 34th International Conference on Machine Learning). Sydney, Australia.

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The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of related methods, of which the Gumbel trick is one member, and show that the new methods have superior properties in several settings with minimal additional computational cost. In particular, for the Gumbel trick to yield computational benefits for discrete graphical models, Gumbel perturbations on all configurations are typically replaced with so-called low-rank perturbations. We show how a subfamily of our new methods adapts to this setting, proving new upper and lower bounds on the log partition function and deriving a family of sequential samplers for the Gibbs distribution. Finally, we balance the discussion by showing how the simpler analytical form of the Gumbel trick enables additional theoretical results.

Comment: [arXiv] [Poster] [Slides] [Code]

Particle Gibbs for Infinite Hidden Markov Models

Nilesh Tripuraneni, Shixiang Gu, Hong Ge, Zoubin Ghahramani, May 2015. (In Advances in Neural Information Processing Systems 29). Montreal CANADA.

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Infinite Hidden Markov Models (iHMM’s) are an attractive, nonparametric gener- alization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of the transition dynamics, performing inference in the iHMM is difficult. In this paper, we present an infinite-state Particle Gibbs (PG) algorithm to re- sample state trajectories for the iHMM. The proposed algorithm uses an efficient proposal optimized for iHMMs and leverages ancestor sampling to improve the mixing of the standard PG algorithm. Our algorithm demonstrates significant con- vergence improvements on synthetic and real world data sets.

Magnetic Hamiltonian Monte Carlo

Nilesh Tripuraneni, Mark Rowland, Zoubin Ghahramani, Richard E. Turner, 2017. (In 34th International Conference on Machine Learning).

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Hamiltonian Monte Carlo (HMC) exploits Hamiltonian dynamics to construct efficient proposals for Markov chain Monte Carlo (MCMC). In this paper, we present a generalization of HMC which exploits non-canonical Hamiltonian dynamics. We refer to this algorithm as magnetic HMC, since in 3 dimensions a subset of the dynamics map onto the mechanics of a charged particle coupled to a magnetic field. We establish a theoretical basis for the use of non-canonical Hamiltonian dynamics in MCMC, and construct a symplectic, leapfrog-like integrator allowing for the implementation of magnetic HMC. Finally, we exhibit several examples where these non-canonical dynamics can lead to improved mixing of magnetic HMC relative to ordinary HMC.

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