Timezone: »
Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic simulations. However, such stochastic gradient MCMC samplers have lagged behind their full-data counterparts in terms of the complexity of dynamics considered since proving convergence in the presence of the stochastic gradient noise is non-trivial. Even with simple dynamics, significant physical intuition is often required to modify the dynamical system to account for the stochastic gradient noise. In this paper, we provide a general recipe for constructing MCMC samplers--including stochastic gradient versions--based on continuous Markov processes specified via two matrices. We constructively prove that the framework is complete. That is, any continuous Markov process that provides samples from the target distribution can be written in our framework. We show how previous continuous-dynamic samplers can be trivially "reinvented" in our framework, avoiding the complicated sampler-specific proofs. We likewise use our recipe to straightforwardly propose a new state-adaptive sampler: stochastic gradient Riemann Hamiltonian Monte Carlo (SGRHMC). Our experiments on simulated data and a streaming Wikipedia analysis demonstrate that the proposed SGRHMC sampler inherits the benefits of Riemann HMC, with the scalability of stochastic gradient methods.
Author Information
Yi-An Ma (University of Washington)
Tianqi Chen (University of Washington)
Emily Fox (Washington)
More from the Same Authors
-
2019 : Emily Fox »
Emily Fox -
2018 : Plenary Talk 4 »
Emily Fox -
2018 : Poster Session (All Posters) »
Stephen Macke · Hongzi Mao · Caroline Lemieux · Saim Salman · Rishikesh Jha · Hanrui Wang · Shoumik P Palkar · Tianqi Chen · Thomas Pumir · Vaishnav Janardhan · adit bhardwaj · Ed Chi -
2018 Poster: Large-Scale Stochastic Sampling from the Probability Simplex »
Jack Baker · Paul Fearnhead · Emily Fox · Christopher Nemeth -
2018 Poster: Learning to Optimize Tensor Programs »
Tianqi Chen · Lianmin Zheng · Eddie Yan · Ziheng Jiang · Thierry Moreau · Luis Ceze · Carlos Guestrin · Arvind Krishnamurthy -
2018 Spotlight: Learning to Optimize Tensor Programs »
Tianqi Chen · Lianmin Zheng · Eddie Yan · Ziheng Jiang · Thierry Moreau · Luis Ceze · Carlos Guestrin · Arvind Krishnamurthy -
2017 : Updates from Current ML Systems (TensorFlow, PyTorch, Caffe2, CNTK, MXNet, TVM, Clipper, MacroBase, ModelDB) »
Rajat Monga · Soumith Chintala · Cha Zhang · Tianqi Chen · Daniel Crankshaw · Kai Sheng Tai · Andrew Tulloch · Manasi Vartak -
2016 : Emily Fox. Sparse Graphs via Exchangeable Random Measures. »
Emily Fox -
2016 : Emily Fox : Functional Connectivity in MEG via Graphical Models of Time Series »
Emily Fox -
2015 Workshop: Machine Learning Systems »
Alex Beutel · Tianqi Chen · Sameer Singh · Elaine Angelino · Markus Weimer · Joseph Gonzalez -
2015 : Bayesian Time Series: Structured Representations for Scalability »
Emily Fox -
2014 Workshop: High-energy particle physics, machine learning, and the HiggsML data challenge (HEPML) »
Glen Cowan · Balázs Kégl · Kyle Cranmer · Gábor Melis · Tim Salimans · Vladimir Vava Gligorov · Daniel Whiteson · Lester Mackey · Wojciech Kotlowski · Roberto Díaz Morales · Pierre Baldi · Cecile Germain · David Rousseau · Isabelle Guyon · Tianqi Chen -
2014 Poster: Expectation-Maximization for Learning Determinantal Point Processes »
Jennifer A Gillenwater · Alex Kulesza · Emily Fox · Ben Taskar -
2014 Poster: Stochastic variational inference for hidden Markov models »
Nick Foti · Jason Xu · Dillon Laird · Emily Fox -
2013 Poster: Approximate Inference in Continuous Determinantal Processes »
Raja Hafiz Affandi · Emily Fox · Ben Taskar -
2013 Spotlight: Approximate Inference in Continuous Determinantal Processes »
Raja Hafiz Affandi · Emily Fox · Ben Taskar -
2013 Session: Oral Session 4 »
Emily Fox -
2012 Poster: Multiresolution Gaussian Processes »
Emily Fox · David B Dunson -
2012 Poster: Effective Split-Merge Monte Carlo Methods for Nonparametric Models of Sequential Data »
Michael Hughes · Emily Fox · Erik Sudderth -
2011 Workshop: Bayesian Nonparametric Methods: Hope or Hype? »
Emily Fox · Ryan Adams -
2009 Poster: Sharing Features among Dynamical Systems with Beta Processes »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2009 Oral: Sharing Features among Dynamical Systems with Beta Processes »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2008 Poster: Nonparametric Bayesian Learning of Switching Linear Dynamical Systems »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky -
2008 Spotlight: Nonparametric Bayesian Learning of Switching Linear Dynamical Systems »
Emily Fox · Erik Sudderth · Michael Jordan · Alan S Willsky