Inference on graphical models, expectation propagation, particle methods

I am a fourth year DPhil student co-supervised by Prof. Yee Whye Teh and Prof. Arnaud Doucet. I am interested in inference on graphical models, from the computational as well as the application side. I have worked on using expectation propagation to help with particle belief propagation as well as to help with distributed learning. I am now looking at rejection free samplers.

Publications

2015

T. Lienart,
Y. W. Teh,
A. Doucet,
Expectation Particle Belief Propagation, in Advances in Neural Information Processing Systems (NIPS), 2015.

We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. The algorithm constructs adaptively efficient proposal distributions approximating the local beliefs at each note of the MRF. This is achieved by considering proposal distributions in the exponential family whose parameters are updated iterately in an Expectation Propagation (EP) framework. The proposed particle scheme provides consistent estimation of the LBP marginals as the number of particles increases. We demonstrate that it provides more accurate results than the Particle Belief Propagation (PBP) algorithm of Ihler and McAllester (2009) at a fraction of the computational cost and is additionally more robust empirically. The computational complexity of our algorithm at each iteration is quadratic in the number of particles. We also propose an accelerated implementation with sub-quadratic computational complexity which still provides consistent estimates of the loopy BP marginal distributions and performs almost as well as the original procedure.

@inproceedings{LieTehDou2015a,
author = {Lienart, T. and Teh, Y. W. and Doucet, A.},
booktitle = {Advances in Neural Information Processing Systems (NIPS)},
title = {Expectation Particle Belief Propagation},
year = {2015},
bdsk-url-1 = {http://papers.nips.cc/paper/5674-expectation-particle-belief-propagation},
bdsk-url-2 = {http://papers.nips.cc/paper/5674-expectation-particle-belief-propagation.pdf},
bdsk-url-3 = {http://papers.nips.cc/paper/5674-expectation-particle-belief-propagation-supplemental.zip}
}

L. Hasenclever,
S. Webb,
T. Lienart,
S. Vollmer,
B. Lakshminarayanan,
C. Blundell,
Y. W. Teh,
Distributed Bayesian Learning with Stochastic Natural-gradient Expectation Propagation and the Posterior Server, 2015.

This paper makes two contributions to Bayesian machine learning algorithms. Firstly, we propose stochastic natural gradient expectation propagation (SNEP), a novel alternative to expectation propagation (EP), a popular variational inference algorithm. SNEP is a black box variational algorithm, in that it does not require any simplifying assumptions on the distribution of interest, beyond the existence of some Monte Carlo sampler for estimating the moments of the EP tilted distributions. Further, as opposed to EP which has no guarantee of convergence, SNEP can be shown to be convergent, even when using Monte Carlo moment estimates. Secondly, we propose a novel architecture for distributed Bayesian learning which we call the posterior server. The posterior server allows scalable and robust Bayesian learning in cases where a dataset is stored in a distributed manner across a cluster, with each compute node containing a disjoint subset of data. An independent Monte Carlo sampler is run on each compute node, with direct access only to the local data subset, but which targets an approximation to the global posterior distribution given all data across the whole cluster. This is achieved by using a distributed asynchronous implementation of SNEP to pass messages across the cluster. We demonstrate SNEP and the posterior server on distributed Bayesian learning of logistic regression and neural networks.

@unpublished{HasWebLie2015a,
author = {Hasenclever, L. and Webb, S. and Lienart, T. and Vollmer, S. and Lakshminarayanan, B. and Blundell, C. and Teh, Y. W.},
note = {ArXiv e-prints: 1512.09327},
title = {Distributed {B}ayesian Learning with Stochastic Natural-gradient Expectation Propagation and the Posterior Server},
year = {2015},
bdsk-url-1 = {https://arxiv.org/pdf/1512.09327.pdf}
}

This paper makes two contributions to Bayesian machine learning algorithms. Firstly, we propose stochastic natural gradient expectation propagation (SNEP), a novel alternative to expectation propagation (EP), a popular variational inference algorithm. SNEP is a black box variational algorithm, in that it does not require any simplifying assumptions on the distribution of interest, beyond the existence of some Monte Carlo sampler for estimating the moments of the EP tilted distributions. Further, as opposed to EP which has no guarantee of convergence, SNEP can be shown to be convergent, even when using Monte Carlo moment estimates. Secondly, we propose a novel architecture for distributed Bayesian learning which we call the posterior server. The posterior server allows scalable and robust Bayesian learning in cases where a dataset is stored in a distributed manner across a cluster, with each compute node containing a disjoint subset of data. An independent Monte Carlo sampler is run on each compute node, with direct access only to the local data subset, but which targets an approximation to the global posterior distribution given all data across the whole cluster. This is achieved by using a distributed asynchronous implementation of SNEP to pass messages across the cluster. We demonstrate SNEP and the posterior server on distributed Bayesian learning of logistic regression and neural networks.

@software{HasWebLie2016a,
author = {Hasenclever, L. and Webb, S. and Lienart, T. and Vollmer, S. and Lakshminarayanan, B. and Blundell, C. and Teh, Y. W.},
title = {Posterior Server},
year = {2016},
bdsk-url-1 = {https://github.com/BigBayes/PosteriorServer}
}