High-dimensional Bayesian inference via the unadjusted Langevin algorithm

Supplementary material to the paper available at https://arxiv.org/abs/1605.01559 or https://hal.archives-ouvertes.fr/hal-01304430

[1]  D. Ermak.  A computer simulation of charged particles in solution. I. Technique and equilibrium properties , 1975 .

[2]  D. Ermak.  A computer simulation of charged particles in solution. II. Polyion diffusion coefficient , 1975 .

[3]  J. D. Doll,et al.  Brownian dynamics as smart Monte Carlo simulation , 1978 .

[4]  G. Parisi.  Correlation functions and computer simulations (II) , 1981 .

[5]  L. Rogers,et al.  Coupling of Multidimensional Diffusions by Reflection , 1986 .

[6]  Mu-Fa Chen,et al.  Coupling Methods for Multidimensional Diffusion Processes , 1989 .

[7]  D. Talay,et al.  Expansion of the global error for numerical schemes solving stochastic differential equations , 1990 .

[8]  Radford M. Neal.  Bayesian Learning via Stochastic Dynamics , 1992, NIPS.

[9]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[10]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[11]  Michael I. Miller,et al.  REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS , 1994 .

[12]  A. Borodin,et al.  Handbook of Brownian Motion - Facts and Formulae , 1996 .

[13]  R. Tweedie,et al.  Exponential convergence of Langevin distributions and their discrete approximations , 1996 .

[14]  Martin E. Dyer,et al.  An elementary analysis of a procedure for sampling points in a convex body , 1998, Random Struct. Algorithms.

[15]  Jonathan C. Mattingly,et al.  Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise , 2002 .

[16]  G. Pagès,et al.  RECURSIVE COMPUTATION OF THE INVARIANT DISTRIBUTION OF A DIFFUSION: THE CASE OF A WEAKLY MEAN REVERTING DRIFT , 2003 .

[17]  Gábor Lugosi,et al.  Concentration Inequalities , 2008, COLT.

[18]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[19]  C. Holmes,et al.  Bayesian auxiliary variable models for binary and multinomial regression , 2006 .

[20]  P. Cattiaux,et al.  Trends to equilibrium in total variation distance , 2007, math/0703451.

[21]  D. Bakry,et al.  Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré , 2007, math/0703355.

[22]  B. Klartag.  A central limit theorem for convex sets , 2006, math/0605014.

[23]  Xiongzhi Chen.  Brownian Motion and Stochastic Calculus , 2008 .

[24]  C. Villani.  Optimal Transport: Old and New , 2008 .

[25]  Nicholas G. Polson,et al.  Simulation-based Regularized Logistic Regression , 2010, 1005.3430.

[26]  Y. Ollivier,et al.  CURVATURE, CONCENTRATION AND ERROR ESTIMATES FOR MARKOV CHAIN MONTE CARLO , 2009, 0904.1312.

[27]  S. Frühwirth-Schnatter,et al.  Data Augmentation and MCMC for Binary and Multinomial Logit Models , 2010 .

[28]  Leonhard Held,et al.  Hyper-$g$ priors for generalized linear models , 2010, 1008.1550.

[29]  M. Wand,et al.  Variational Bayesian Inference for Parametric and Nonparametric Regression With Missing Data , 2011 .

[30]  Yee Whye Teh,et al.  Bayesian Learning via Stochastic Gradient Langevin Dynamics , 2011, ICML.

[31]  S. Glotzer,et al.  Time-course gait analysis of hemiparkinsonian rats following 6-hydroxydopamine lesion , 2004, Behavioural Brain Research.

[32]  W. Marsden.  I and J , 2012 .

[33]  James G. Scott,et al.  Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables , 2012, 1205.0310.

[34]  Hee Min Choi,et al.  The Polya-Gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic , 2013 .

[35]  Adam J. Branscum,et al.  Informative g-Priors for Logistic Regression , 2014 .

[36]  A. Dalalyan.  Theoretical guarantees for approximate sampling from smooth and log‐concave densities , 2014, 1412.7392.

[37]  James Ridgway,et al.  Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation , 2015, 1506.08640.

[38]  Sébastien Bubeck,et al.  Finite-Time Analysis of Projected Langevin Monte Carlo , 2015, NIPS.

[39]  A. Eberle.  Couplings, distances and contractivity for diffusion processes revisited , 2013 .

[40]  Arnak S. Dalalyan,et al.  Further and stronger analogy between sampling and optimization: Langevin Monte Carlo and gradient descent , 2017, COLT.

[41]  A. Eberle,et al.  Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes , 2016, Transactions of the American Mathematical Society.

[42]  J. Vince.  Curvature , 2019, Calculus for Computer Graphics.