On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach

[1]  James Hensman,et al.  Banded Matrix Operators for Gaussian Markov Models in the Automatic Differentiation Era , 2019, AISTATS.

[2]  Robert Kohn,et al.  The Block-Poisson Estimator for Optimally Tuned Exact Subsampling MCMC , 2016, J. Comput. Graph. Stat..

[3]  Gareth O. Roberts,et al.  Examples of Adaptive MCMC , 2009 .

[4]  David M. Blei,et al.  Variational Inference: A Review for Statisticians , 2016, ArXiv.

[5]  Zoubin Ghahramani,et al.  Gaussian Process Volatility Model , 2014, NIPS.

[6]  A. Doucet,et al.  Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator , 2012, 1210.1871.

[7]  A. Gelfand,et al.  Bayesian Model Choice: Asymptotics and Exact Calculations , 1994 .

[8]  G. Roberts,et al.  MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster , 2012, 1202.0709.

[9]  S. Geisser,et al.  A Predictive Approach to Model Selection , 1979 .

[10]  Daniel B. Williamson,et al.  Diagnostics-Driven Nonstationary Emulators Using Kernel Mixtures , 2018, SIAM/ASA J. Uncertain. Quantification.

[11]  A. Gelfand,et al.  Gaussian predictive process models for large spatial data sets , 2008, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[12]  Yves F. Atchad'e,et al.  On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods , 2013, 1306.4032.

[13]  Mark Girolami,et al.  Posterior inference for sparse hierarchical non-stationary models , 2018, Comput. Stat. Data Anal..

[14]  Václav Šmídl,et al.  Adaptive multiple importance sampling for Gaussian processes , 2015, 1508.01050.

[15]  A. Doucet,et al.  Particle Markov chain Monte Carlo methods , 2010 .

[16]  Volker Tresp,et al.  A Bayesian Committee Machine , 2000, Neural Computation.

[17]  G. Matheron The intrinsic random functions and their applications , 1973, Advances in Applied Probability.

[18]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[19]  Yaming Yu,et al.  To Center or Not to Center: That Is Not the Question—An Ancillarity–Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Efficiency , 2011 .

[20]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[21]  Faming Liang,et al.  Statistical and Computational Inverse Problems , 2006, Technometrics.

[22]  Jouni Helske,et al.  Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo , 2016, Scandinavian Journal of Statistics.

[23]  James Hensman,et al.  MCMC for Variationally Sparse Gaussian Processes , 2015, NIPS.

[24]  Carl E. Rasmussen,et al.  Infinite Mixtures of Gaussian Process Experts , 2001, NIPS.

[25]  Radford M. Neal Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification , 1997, physics/9701026.

[26]  Ryan P. Adams,et al.  Firefly Monte Carlo: Exact MCMC with Subsets of Data , 2014, UAI.

[27]  M. Beaumont Estimation of population growth or decline in genetically monitored populations. , 2003, Genetics.

[28]  Mark A. Girolami,et al.  Bat Call Identification with Gaussian Process Multinomial Probit Regression and a Dynamic Time Warping Kernel , 2014, AISTATS.

[29]  Peter W. Glynn,et al.  Unbiased Estimation with Square Root Convergence for SDE Models , 2015, Oper. Res..

[30]  R. Kohn,et al.  Speeding Up MCMC by Efficient Data Subsampling , 2014, Journal of the American Statistical Association.

[31]  A. Doucet,et al.  The correlated pseudomarginal method , 2015, Journal of the Royal Statistical Society: Series B (Statistical Methodology).

[32]  Ryan P. Adams,et al.  Elliptical slice sampling , 2009, AISTATS.

[33]  Iain Murray,et al.  Pseudo-Marginal Slice Sampling , 2015, AISTATS.

[34]  Giovanni Monegato,et al.  Error estimates for Gauss-Laguerre and Gauss-Hermite quadrature formulas , 1994 .

[35]  Anders Kirk Uhrenholt,et al.  Probabilistic selection of inducing points in sparse Gaussian processes , 2020, ArXiv.

[36]  C. Rasmussen,et al.  Approximations for Binary Gaussian Process Classification , 2008 .

[37]  Paul Marjoram,et al.  Markov chain Monte Carlo without likelihoods , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[38]  Zoubin Ghahramani,et al.  Sparse Gaussian Processes using Pseudo-inputs , 2005, NIPS.

[39]  Carl E. Rasmussen,et al.  Rates of Convergence for Sparse Variational Gaussian Process Regression , 2019, ICML.

[40]  Neil D. Lawrence,et al.  Parallelizable sparse inverse formulation Gaussian processes (SpInGP) , 2016, 2017 IEEE 27th International Workshop on Machine Learning for Signal Processing (MLSP).

[41]  Daniel Hernández-Lobato,et al.  Robust Multi-Class Gaussian Process Classification , 2011, NIPS.

[42]  Arnaud Doucet,et al.  On Markov chain Monte Carlo methods for tall data , 2015, J. Mach. Learn. Res..

[43]  A. Raftery,et al.  Probabilistic Weather Forecasting for Winter Road Maintenance , 2010 .

[44]  Neil D. Lawrence,et al.  Fast Forward Selection to Speed Up Sparse Gaussian Process Regression , 2003, AISTATS.

[45]  Robert J. Elliott,et al.  Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature , 2007, Proceedings of the IEEE.

[46]  W. Gautschi A Survey of Gauss-Christoffel Quadrature Formulae , 1981 .

[47]  Dorit Hammerling,et al.  A Case Study Competition Among Methods for Analyzing Large Spatial Data , 2017, Journal of Agricultural, Biological and Environmental Statistics.

[48]  Maurizio Filippone Bayesian Inference for Gaussian Process Classifiers with Annealing and Pseudo-Marginal MCMC , 2014, 2014 22nd International Conference on Pattern Recognition.

[49]  P. Fearnhead,et al.  Particle filters for partially observed diffusions , 2007, 0710.4245.

[50]  Maurizio Filippone,et al.  Pseudo-Marginal Bayesian Inference for Gaussian Processes , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[51]  Neil D. Lawrence,et al.  Deep Gaussian Processes for Multi-fidelity Modeling , 2019, ArXiv.

[52]  Neil D. Lawrence,et al.  Gaussian Processes for Big Data , 2013, UAI.

[53]  N. Cressie,et al.  Fixed rank kriging for very large spatial data sets , 2008 .

[54]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[55]  Robert Kohn,et al.  Hamiltonian Monte Carlo with Energy Conserving Subsampling , 2017, J. Mach. Learn. Res..

[56]  Jonas Wallin,et al.  Infinite dimensional adaptive MCMC for Gaussian processes. , 2018 .

[57]  Neil D. Lawrence,et al.  Deep Gaussian Processes , 2012, AISTATS.

[58]  Andrew M. Stuart,et al.  How Deep Are Deep Gaussian Processes? , 2017, J. Mach. Learn. Res..

[59]  Charles W. L. Gadd,et al.  Enriched mixtures of generalised Gaussian process experts , 2020, AISTATS.

[60]  James Hensman,et al.  On Sparse Variational Methods and the Kullback-Leibler Divergence between Stochastic Processes , 2015, AISTATS.

[61]  P. Fearnhead,et al.  Random‐weight particle filtering of continuous time processes , 2010 .

[62]  Aki Vehtari,et al.  Bayesian Modeling with Gaussian Processes using the GPstuff Toolbox , 2012, 1206.5754.

[63]  C. Andrieu,et al.  The pseudo-marginal approach for efficient Monte Carlo computations , 2009, 0903.5480.

[64]  Surya T. Tokdar,et al.  Computer Emulation with Nonstationary Gaussian Processes , 2016, SIAM/ASA J. Uncertain. Quantification.

[65]  Christopher J Paciorek,et al.  Spatial modelling using a new class of nonstationary covariance functions , 2006, Environmetrics.

[66]  B. Mallick,et al.  Analyzing Nonstationary Spatial Data Using Piecewise Gaussian Processes , 2005 .

[67]  A. W. van der Vaart,et al.  Adaptive Bayesian credible bands in regression with a Gaussian process prior , 2015, Sankhya A.

[68]  Michalis K. Titsias,et al.  Variational Learning of Inducing Variables in Sparse Gaussian Processes , 2009, AISTATS.

[69]  Maurizio Filippone,et al.  Sparse Gaussian Processes Revisited: Bayesian Approaches to Inducing-Variable Approximations , 2020, AISTATS.

[70]  Akeel Shah,et al.  Pseudo-marginal Bayesian inference for supervised Gaussian process latent variable models , 2018, ArXiv.