Large scale machine learning, probabilistic inference, deep learning

I am a DPhil student in the OxWaSP centre for doctoral training supervised by Prof. Yee Whye Teh. I am interested in large scale Bayesian machine learning. For most of the last year I have been working on distributed Bayesian learning using stochastic natural gradient expectation propagation applied Bayesian neural networks. I am also interested in stochastic gradient Markov chain Monte Carlo methods.

Hamiltonian Monte Carlo (HMC) is a popular Markov chain Monte Carlo (MCMC) algorithm that generates proposals for a Metropolis-Hastings algorithm by simulating the dynamics of a Hamiltonian system. However, HMC is sensitive to large time discretizations and performs poorly if there is a mismatch between the spatial geometry of the target distribution and the scales of the momentum distribution. In particular the mass matrix of HMC is hard to tune well. In order to alleviate these problems we propose relativistic Hamiltonian Monte Carlo, a version of HMC based on relativistic dynamics that introduce a maximum velocity on particles. We also derive stochastic gradient versions of the algorithm and show that the resulting algorithms bear interesting relationships to gradient clipping, RMSprop, Adagrad and Adam, popular optimisation methods in deep learning. Based on this, we develop relativistic stochastic gradient descent by taking the zero-temperature limit of relativistic stochastic gradient Hamiltonian Monte Carlo. In experiments we show that the relativistic algorithms perform better than classical Newtonian variants and Adam.

@inproceedings{LuPerHas2016a,
author = {Lu, X. and Perrone, V. and Hasenclever, L. and Teh, Y. W. and Vollmer, S. J.},
booktitle = {Artificial Intelligence and Statistics (AISTATS)},
title = {Relativistic {M}onte {C}arlo},
year = {2017},
bdsk-url-1 = {https://arxiv.org/pdf/1609.04388v1.pdf}
}

2015

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}
}