Efficient stochastic optimisation by unadjusted Langevin Monte Carlo

[1]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[2]  E.J. Candes Compressive Sampling , 2022 .

[3]  Richard J. Boys,et al.  Discussion to "Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by Girolami and Calderhead , 2011 .

[4]  Alexander Shapiro,et al.  Stochastic Approximation approach to Stochastic Programming , 2013 .

[5]  G. Casella Empirical Bayes Gibbs sampling. , 2001, Biostatistics.

[6]  Vishal Monga,et al.  Handbook of Convex Optimization Methods in Imaging Science , 2017, Springer International Publishing.

[7]  G. Pólya,et al.  Problems and theorems in analysis , 1983 .

[8]  M. Ledoux,et al.  Analysis and Geometry of Markov Diffusion Operators , 2013 .

[9]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.

[10]  S. Meyn,et al.  Stability of Markovian processes I: criteria for discrete-time Chains , 1992, Advances in Applied Probability.

[11]  Antonin Chambolle,et al.  An introduction to continuous optimization for imaging , 2016, Acta Numerica.

[12]  H. Kushner,et al.  Stochastic Approximation and Recursive Algorithms and Applications , 2003 .

[13]  É. Moulines,et al.  Convergence of a stochastic approximation version of the EM algorithm , 1999 .

[14]  Gersende Fort,et al.  Convergence of the Monte Carlo expectation maximization for curved exponential families , 2003 .

[15]  Michael B. Wakin,et al.  An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition] , 2008 .

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

[17]  Evgueni A. Haroutunian,et al.  Information Theory and Statistics , 2011, International Encyclopedia of Statistical Science.

[18]  S. Schweitzer A Course In Differential Geometry , 2016 .

[19]  Gersende Fort,et al.  On Perturbed Proximal Gradient Algorithms , 2014, J. Mach. Learn. Res..

[20]  Eric Moulines,et al.  Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau , 2016, SIAM J. Imaging Sci..

[21]  Jon Wakefield,et al.  Bayesian and Frequentist Regression Methods , 2013 .

[22]  G. Fort,et al.  Convergence of adaptive and interacting Markov chain Monte Carlo algorithms , 2011, 1203.3036.

[23]  D. Vere-Jones Markov Chains , 1972, Nature.

[24]  C. Andrieu,et al.  On the ergodicity properties of some adaptive MCMC algorithms , 2006, math/0610317.

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

[26]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[27]  Mathews Jacob,et al.  A blind compressive sensing frame work for accelerated dynamic MRI , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[28]  M. Girolami,et al.  Riemann manifold Langevin and Hamiltonian Monte Carlo methods , 2011, Journal of the Royal Statistical Society: Series B (Statistical Methodology).

[29]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[30]  Alain Durmus,et al.  Convergence of diffusions and their discretizations: from continuous to discrete processes and back , 2019, 1904.09808.

[31]  Yoram Singer,et al.  Adaptive Subgradient Methods for Online Learning and Stochastic Optimization , 2011, J. Mach. Learn. Res..

[32]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[33]  É. Moulines,et al.  On the convergence of Hamiltonian Monte Carlo , 2017, 1705.00166.

[34]  Pierre Priouret,et al.  Adaptive Algorithms and Stochastic Approximations , 1990, Applications of Mathematics.

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

[36]  David Williams,et al.  Probability with Martingales , 1991, Cambridge mathematical textbooks.

[37]  A. Eberle,et al.  Couplings and quantitative contraction rates for Langevin dynamics , 2017, The Annals of Probability.

[38]  M. Yor,et al.  Continuous martingales and Brownian motion , 1990 .

[39]  O. Kallenberg Foundations of Modern Probability , 2021, Probability Theory and Stochastic Modelling.

[40]  S. F. Jarner,et al.  Geometric ergodicity of Metropolis algorithms , 2000 .

[41]  G. Casella An Introduction to Empirical Bayes Data Analysis , 1985 .

[42]  H. Robbins A Stochastic Approximation Method , 1951 .

[43]  Mateusz B. Majka,et al.  Quantitative contraction rates for Markov chains on general state spaces , 2018, Electronic Journal of Probability.

[44]  S. Meyn,et al.  Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes , 1993, Advances in Applied Probability.

[45]  Yuichi Mori,et al.  Handbook of computational statistics : concepts and methods , 2004 .

[46]  D. W. Stroock,et al.  Multidimensional Diffusion Processes , 1979 .

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

[48]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[49]  Yuichi Mori,et al.  Handbook of Computational Statistics , 2004 .

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

[51]  T. Louis,et al.  Empirical Bayes: Past, Present and Future , 2000 .

[52]  É. Moulines,et al.  Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm , 2015, 1507.05021.

[53]  V. V. Buldygin,et al.  Brunn-Minkowski inequality , 2000 .

[54]  C. Robert,et al.  Computational methods for Bayesian model choice , 2009, 0907.5123.

[55]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[56]  Marcelo Pereyra,et al.  Maximum Likelihood Estimation of Regularisation Parameters , 2018, 2018 25th IEEE International Conference on Image Processing (ICIP).