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@string{IEEECT   = {IEEE Trans. Circ. Theory}}
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@string{IEEEPAMI = {IEEE Trans. Pattern Anal. Mach. Intell.}}
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@string{IEEEPAMI = {IEEE Trans. Patt. Anal. Mach. Intell.}}
@string{IEEEIP   = {IEEE Trans. Image Process.}}
@string{IEEEGRS  = {IEEE Trans. Geosci. Remote Sens.}}
@string{IEEESAP  = {IEEE Trans. Speech, Audio Proc.}}
@string{IEEESMC  = {IEEE Trans. Systems, Man, Cybernet.}}
@string{IEEEVT   = {IEEE Trans. Veh. Technol.}}
@string{IEEEPROC = {Proc. IEEE}}
@string{JASA     = {J. Acoust. Soc. Amer.}}
@string{JAMS     = {J. Amer. Math. Soc.}}
@string{JAT      = {J. Approx. Theory}}
@string{JAES     = {J. Audio Eng. Soc.}}
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@string{JCP      = {J. Comput. Phys.}}
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@string{JMIV     = {J. Math. Imag. Vision}}
@string{JMP      = {J. Math. Phys.}}
@string{JMPA     = {J. Math. Pure Appl.}}
@string{JOS      = {J. Opt. Soc.}}
@string{JROYSA   = {J. Roy. Stat. Soc. Ser. A}}
@string{JROYSB   = {J. Roy. Stat. Soc. Ser. B}}
@string{JROYSC   = {J. Roy. Stat. Soc. Ser. C}}
@string{JROYSD   = {J. Roy. Stat. Soc. Ser. D}}
@string{JSV      = {J. Sound Vib.}}
@string{LNM      = {Lecture Notes in Math.}}
@string{LINALG   = {Linear Algebra and its Applications}}
@string{MC       = {Math. Comp.}}
@string{MEDI     = {IEEE Trans. Med. Imag.}}
@string{MM       = {Monatsh. Math.}}
@string{MN       = {Math. Nach.}}
@string{MS       = {Math. Scand.}}
@string{NM       = {Numer. Math.}}
@string{NA       = {Numer. Algor.}}
@string{OE       = {Opt. Eng.}}
@string{OPT      = {Journal of Optimization Theory Applications}}
@string{PJR      = {Philips J. Research}}
@string{PAMS     = {Proc. Amer. Math. Soc.}}
@string{PR       = {Phys. Rev.}}
@string{PRA      = {Phys. Rev. A}}
@string{PRL      = {Phys. Rev. Lett.}}
@string{PRP      = {Phys. Rep.}}
@string{PTP      = {Prog. Theor. Phys.}}
@string{RMI      = {Rev. Mat. Iberoamericana}}
@string{SIAMAM   = {SIAM J. Appl. Math.}}
@string{SIAMMA   = {SIAM J. Math. Anal.}}
@string{SIMAT    = {SIAM J. Matrix Anal. Appl.}}
@string{SIAMNA   = {SIAM J. Numer. Anal.}}
@string{SIJSC    = {SIAM J. Sci. Comp.}}
@string{SIJSSC   = {SIAM J. Sci. Statist. Comp.}}
@string{SIAMR    = {SIAM Rev.}}
@string{EUSP     = {Signal Processing}}
@string{TAMS     = {Trans. Amer. Math. Soc.}}
@string{ASILOMAR = {Asilomar Conf. Signals, Systems, Computers}}
@string{CISS     = {Proc. Conf. Information Sciences and Systems}}
@string{ICASSP   = {Proc. IEEE Int. Conf. Acoust., Speech, and Signal Proc. (ICASSP)}}
@string{ICASSP83 = {Proc. IEEE ICASSP-83}}
@string{ICASSP84 = {Proc. IEEE ICASSP-84}}
@string{ICASSP85 = {Proc. IEEE ICASSP-85}}
@string{ICASSP86 = {Proc. IEEE ICASSP-83}}
@string{ICASSP87 = {Proc. IEEE ICASSP-87}}
@string{ICASSP88 = {Proc. IEEE ICASSP-83}}
@string{ICASSP89 = {Proc. IEEE ICASSP-83}}
@string{ICASSP90 = {Proc. IEEE ICASSP-90}}
@string{ICASSP91 = {Proc. IEEE ICASSP-83}}
@string{ICASSP92 = {Proc. IEEE ICASSP-92}}
@string{ICASSP93 = {Proc. IEEE ICASSP-93}}
@string{ICASSP94 = {Proc. IEEE ICASSP-94}}
@string{ICASSP95 = {Proc. IEEE ICASSP-95}}
@string{ICASSP96 = {Proc. IEEE ICASSP-96}}
@string{ICASSP97 = {Proc. IEEE ICASSP-97}}
@string{ICASSP98 = {Proc. IEEE ICASSP-98}}
@string{ICASSP99 = {Proc. IEEE ICASSP-99}}
@string{ICIP   = {Proc. IEEE Int. Conf. Image Proc. (ICIP)}}
@string{ISCAS92  = {Proc. IEEE ISCAS-92}}
@string{ISCAS    = {Proc. IEEE Int. Conf. Circuits and Systems}}
@string{TFTS     = {Proc. IEEE-SP Int. Sympos. Time-Frequency Time-Scale Analysis}}
@string{SSAP     = {Proc. IEEE-SP Workshop Stat. Signal and Array Processing}}
@string{TU       = {Vienna University of Technology}}
@string{INTHFT   = {Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology}}
@string{jan      = {Jan.}}
@string{feb      = {Feb.}}
@string{mar      = {March}}
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@string{dec      = {Dec.}}
@string{academic = {Academic Press}}
@string{addwes   = {Addison Wesley}}
@string{artech   = {Artech House}}
@string{dover    = {Dover Publications}}
@string{elsevier = {Elsevier}}
@string{kluwer   = {Kluwer}}
@string{dekker   = {Marcel Dekker}}
@string{mcgraw   = {McGraw-Hill}}
@string{pergamon = {Pergamon Press}}
@string{prent    = {Prentice Hall}}
@string{spring   = {Springer}}
@string{wiley    = {Wiley}}

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@article{Dobigeon2010boca,
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@ARTICLE{Bali2008,
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	abstract ={Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis-Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.},
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	keywords={Gibbs sampling strategy;Markov chain Monte Carlo;additive white Gaussian noise;hierarchical Bayesian sparse image reconstruction;linear transformation;magnetic resonance force microscopy imaging;positive exponential distribution;posterior distribution estimation;synthetic data;tobacco virus sample;Markov processes;Monte Carlo methods;biomedical MRI;exponential distribution;image reconstruction;microscopy;Algorithms;Artificial Intelligence;Bayes Theorem;Image Processing, Computer-Assisted;Magnetic Resonance Spectroscopy;Markov Chains;Microscopy, Atomic Force;Monte Carlo Method;Tobacco Mosaic Virus;},
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@ARTICLE{Kayabol2009,
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	year={2009},
	month=may ,
	volume={18},
	number={5},
	pages={982 -994},
	keywords={Bayesian framework;ICA;MCMC;Markov random field;a posteriori distribution;astrophysical image;gradient image;iterated conditional mode;joint maximization;modified-Gibbs sampling;numerical method;source estimation;source separation;statistical model;texture image;Bayes methods;Markov processes;Monte Carlo methods;image sampling;independent component analysis;iterative methods;maximum likelihood estimation;random processes;source separation;statistical distributions;},
	doi={10.1109/TIP.2009.2012905},
	ISSN={1057-7149},
}

@ARTICLE{Mignotte2007,
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	title={Image Denoising by Averaging of Piecewise Constant Simulations of Image Partitions},
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	month=feb ,
	volume={16},
	number={2},
	pages={523 -533},
	keywords={Markov Chain Monte-Carlo simulations;additive white Gaussian noise;constant-value regions;image denoising;image partitions;least square sense;mean square sense error;piecewise constant simulations;spatial adaptive denoising method;unsupervised Markovian framework;wavelet-based denoising methods;AWGN;Markov processes;Monte Carlo methods;image denoising;least mean squares methods;wavelet transforms;Algorithms;Artifacts;Artificial Intelligence;Computer Simulation;Image Enhancement;Image Interpretation, Computer-Assisted;Imaging, Three-Dimensional;Information Storage and Retrieval;Markov Chains;Models, Statistical;Pattern Recognition, Automated;},
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@ARTICLE{Noble2006,
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@article{PereyraTMIC2011,
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	title = {Segmentation of skin lesions in 2{D} and 3{D} ultrasound images using a spatially coherent generalized {R}ayleigh mixture model},
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%IP journals - MRF
@ARTICLE{Cordero2012,
	author={Cordero-Grande, L. and Vegas-Sanchez-Ferrero, G. and Casaseca-de-la-Higuera, P. and Alberola-Lopez, C.},
	journal=IEEEIP,
	title={A {M}arkov Random Field Approach for Topology-Preserving Registration: Application to Object-Based Tomographic Image Interpolation},
	year={2012},
	month=apr,
	volume={21},
	number={4},
	pages={2047 -2061},
}

@ARTICLE{Mahapatra2012,
	author={Mahapatra, D. and Ying Sun},
	journal=IEEEIP,
	title={Integrating Segmentation Information for Improved {MRF}-Based Elastic Image Registration},
	year={2012},
	month=jan,
	volume={21},
	number={1},
	pages={170 -183},
}

@ARTICLE{Katsuki2012,
	author={Katsuki, T. and Torii, A. and Inoue, M.},
	journal=IEEEIP,
	title={Posterior Mean Super-resolution with a Causal {G}aussian {M}arkov Random Field Prior},
	year={2012},
	month=apr,
	volume={21},
	number={4},
	pages={2187-2197},
	keywords={},
}

@ARTICLE{Jain2012,
	author={Jain, S. and Papadakis, M. and Upadhyay, S. and Azencott, R.},
	journal={IEEE Trans. Image Process.},
	title={Rigid Motion Invariant Classification of $3${D}-Textures},
	year={2012},
	month=may,
	volume={21},
	number={5},
	pages={2449-2463},
}

%IP journals - MCMC
@ARTICLE{Mignotte2010,
	author={Mignotte, M.},
	journal=IEEEIP,
	title={A Label Field Fusion {B}ayesian Model and Its Penalized Maximum Rand Estimator for Image Segmentation},
	year={2010},
	month=jun,
	volume={19},
	number={6},
	pages={1610 -1624},
}

@ARTICLE{Kayabol2010,
	author={Kayabol, K. and Kuruoglu, E.E. and Sanz, J.L. and Sankur, B. and Salerno, E. and Herranz, D.},
	journal=IEEEIP,
	title={Adaptive Langevin Sampler for Separation of  t-Distribution Modelled Astrophysical Maps},
	year={2010},
	month=sep,
	volume={19},
	number={9},
	pages={2357-2368},
}

@ARTICLE{Zhou2012,
	author={Xiuzhuang Zhou and Yao Lu and Jiwen Lu and Jie Zhou},
	journal=IEEEIP,
	title={Abrupt Motion Tracking Via Intensively Adaptive {M}arkov-Chain {M}onte {C}arlo Sampling},
	year={2012},
	month=feb,
	volume={21},
	number={2},
	pages={789 -801},
}

@article{Laplace,
	title = {Memoir on the Probability of the Causes of Events},
	author = {Pierre Simon Laplace},
	journal = {Statistical Science},
	volume = {1},
	number = {3},
	pages = {364--378},
	year = {1986},
	month = aug,
}

@ARTICLE{Destrempes2006,
	author={Destrempes, F. and Angers, J.-F. and Mignotte, M.},
	journal=IEEEIP,
	title={Fusion of Hidden {M}arkov Random Field Models and Its {B}ayesian Estimation},
	year={2006},
	month=oct,
	volume={15},
	number={10},
	pages={2920 -2935},
}

@ARTICLE{Nikou2010,
	author={Nikou, C. and Likas, A.C. and Galatsanos, N.P.},
	journal=IEEEIP,
	title={A {B}ayesian Framework for Image Segmentation With Spatially Varying Mixtures},
	year={2010},
	month=sep,
	volume={19},
	number={9},
	pages={2278 -2289},
}

@ARTICLE{Orieux2012,
	author={Orieux, F. and Sepulveda, E. and Loriette, V. and Dubertret, B. and Olivo-Marin, J.-C.},
	journal=IEEEIP,
	title={Bayesian Estimation for Optimized Structured Illumination Microscopy},
	year={2012},
	month=feb,
	volume={21},
	number={2},
	pages={601 - 614},
}

%IP journals - Kuruoglu

@ARTICLE{Kuruoglu2004,
	author={Kuruoglu, E.E. and Zerubia, J.},
	journal=IEEEIP,
	title={Modeling {SAR} images with a generalization of the Rayleigh distribution},
	year={2004},
	month=apr,
	volume={13},
	number={4},
	pages={527-533},
}

@ARTICLE{Achim2006,
	author={Achim, A. and Kuruoglu, E.E. and Zerubia, J.},
	journal=IEEEIP,
	title={{SAR} image filtering based on the heavy-tailed Rayleigh model},
	year={2006},
	month=sep,
	volume={15},
	number={9},
	pages={2686-2693},
}

@inproceedings{pereyra2014maximum,
	title={Maximum marginal likelihood estimation of the granularity coefficient of a Potts-Markov random field within an mcmc algorithm},
	author={Pereyra, Marcelo and Whiteley, Nick and Andrieu, Christophe and Tourneret, Jean-Yves},
	booktitle={Statistical Signal Processing (SSP), 2014 IEEE Workshop on},
	pages={121--124},
	year={2014},
	organization={IEEE}
}

@article{salsa2010fast,
	title={Fast image recovery using variable splitting and constrained optimization},
	author={Afonso, Manya V and Bioucas-Dias, Jos{\'e} M and Figueiredo, M{\'a}rio AT},
	journal={IEEE Transactions on Image Processing},
	volume={19},
	number={9},
	pages={2345--2356},
	year={2010},
	publisher={IEEE}
}

@article{sugar2014stein,
	title={Stein Unbiased GrAdient estimator of the Risk (SUGAR) for multiple parameter selection},
	author={Deledalle, Charles-Alban and Vaiter, Samuel and Fadili, Jalal and Peyr{\'e}, Gabriel},
	journal={SIAM Journal on Imaging Sciences},
	volume={7},
	number={4},
	pages={2448--2487},
	year={2014},
	publisher={SIAM}
}

@article{stein1981estimation,
	title={Estimation of the mean of a multivariate normal distribution},
	author={Stein, Charles M},
	journal={The annals of Statistics},
	pages={1135--1151},
	year={1981},
	publisher={JSTOR}
}

@article{pesquet2009sure,
	title={A SURE approach for digital signal/image deconvolution problems},
	author={Pesquet, Jean-Christophe and Benazza-Benyahia, Amel and Chaux, Caroline},
	journal={IEEE Transactions on Signal Processing},
	volume={57},
	number={12},
	pages={4616--4632},
	year={2009},
	publisher={IEEE}
}

@article{fort2017stochastic,
	title={Stochastic Proximal Gradient Algorithms for Penalized Mixed Models},
	author={Fort, Gersende and Ollier, Edouard and Samson, Adeline},
	journal={arXiv preprint arXiv:1704.08891},
	year={2017}
}

@article{molina1999bayesian,
	title={Bayesian and regularization methods for hyperparameter estimation in image restoration},
	author={Molina, Rafael and Katsaggelos, Aggelos K and Mateos, Javier},
	journal={IEEE Transactions on Image Processing},
	volume={8},
	number={2},
	pages={231--246},
	year={1999},
	publisher={IEEE}
}

@article{thompson1991study,
	title={A study of methods of choosing the smoothing parameter in image restoration by regularization},
	author={Thompson, Alan M and Brown, John C and Kay, Jim W and Titterington, D Michael},
	journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume={13},
	number={4},
	pages={326--339},
	year={1991},
	publisher={IEEE Computer Society}
}

@article{ramani2008suremontecarlo,
	title={Monte-Carlo SURE: A black-box optimization of regularization parameters for general denoising algorithms},
	author={Ramani, Sathish and Blu, Thierry and Unser, Michael},
	journal={IEEE Transactions on Image Processing},
	volume={17},
	number={9},
	pages={1540--1554},
	year={2008},
	publisher={IEEE}
}

@article{durmus2016efficient,
	title={Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau},
	author={Durmus, Alain and Moulines, Eric and Pereyra, Marcelo},
	journal={SIAM Journal on Imaging Sciences},
	volume={11},
	number={1},
	pages={473--506},
	year={2018},
	publisher={SIAM}
}

@article {durmus2017nonasymp,
    AUTHOR = {Durmus, Alain and Moulines, \'{E}ric},
     TITLE = {Nonasymptotic convergence analysis for the unadjusted
              {L}angevin algorithm},
   JOURNAL = {The Annals of Applied Probability},
  FJOURNAL = {The Annals of Applied Probability},
    VOLUME = {27},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {1551--1587},
}

@incollection{combettes2011proximalsplitting,
	title={Proximal splitting methods in signal processing},
	author={Combettes, Patrick L and Pesquet, Jean-Christophe},
	booktitle={Fixed-point algorithms for inverse problems in science and engineering},
	pages={185--212},
	year={2011},
	publisher={Springer}
}

@article{green2015bayesian,
	title={Bayesian computation: a summary of the current state, and samples backwards and forwards},
	author={Green, Peter J and {\L}atuszy{\'n}ski, Krzysztof and Pereyra, Marcelo and Robert, Christian P},
	journal={Statistics and Computing},
	volume={25},
	number={4},
	pages={835--862},
	year={2015},
	publisher={Springer}
}

@article{bonettini2013new,
	title={A new semiblind deconvolution approach for Fourier-based image restoration: an application in astronomy},
	author={Bonettini, Silvia and Cornelio, Anastasia and Prato, Marco},
	journal={SIAM Journal on Imaging Sciences},
	volume={6},
	number={3},
	pages={1736--1757},
	year={2013},
	publisher={SIAM}
}


@article{amizic2013compressive,
	title={Compressive blind image deconvolution},
	author={Amizic, Bruno and Spinoulas, Leonidas and Molina, Rafael and Katsaggelos, Aggelos K},
	journal={IEEE Transactions on Image Processing},
	volume={22},
	number={10},
	pages={3994--4006},
	year={2013},
	publisher={IEEE}
}

@article{donoho2006compressed,
	title={Compressed sensing},
	author={Donoho, David L},
	journal={IEEE Transactions on information theory},
	volume={52},
	number={4},
	pages={1289--1306},
	year={2006},
	publisher={IEEE}
}

@article{candes2006robust,
	title={Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information},
	author={Cand{\`e}s, Emmanuel J and Romberg, Justin and Tao, Terence},
	journal={IEEE Transactions on information theory},
	volume={52},
	number={2},
	pages={489--509},
	year={2006},
	publisher={IEEE}
}

@article{babacan2011variational,
	title={Variational Bayesian super resolution},
	author={Babacan, S Derin and Molina, Rafael and Katsaggelos, Aggelos K},
	journal={IEEE Transactions on Image Processing},
	volume={20},
	number={4},
	pages={984--999},
	year={2011},
	publisher={IEEE}
}

@article{morgenshtern2016super,
	title={Super-resolution of positive sources: The discrete setup},
	author={Morgenshtern, Veniamin I and Candes, Emmanuel J},
	journal={SIAM Journal on Imaging Sciences},
	volume={9},
	number={1},
	pages={412--444},
	year={2016},
	publisher={SIAM}
}

@article{bioucas2007new,
	title={A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration},
	author={Bioucas-Dias, Jos{\'e} M and Figueiredo, M{\'a}rio AT},
	journal={IEEE Transactions on Image processing},
	volume={16},
	number={12},
	pages={2992--3004},
	year={2007},
	publisher={IEEE}
}

@article{lustig2007sparse,
	title={Sparse MRI: The application of compressed sensing for rapid MR imaging},
	author={Lustig, Michael and Donoho, David and Pauly, John M},
	journal={Magnetic resonance in medicine},
	volume={58},
	number={6},
	pages={1182--1195},
	year={2007},
	publisher={Wiley Online Library}
}

@article{chan2011alternating,
	title={Alternating direction method for image inpainting in wavelet domains},
	author={Chan, Raymond H and Yang, Junfeng and Yuan, Xiaoming},
	journal={SIAM Journal on Imaging Sciences},
	volume={4},
	number={3},
	pages={807--826},
	year={2011},
	publisher={SIAM}
}

@article{mairal2008sparse,
	title={Sparse representation for color image restoration},
	author={Mairal, Julien and Elad, Michael and Sapiro, Guillermo},
	journal={IEEE Transactions on image processing},
	volume={17},
	number={1},
	pages={53--69},
	year={2008},
	publisher={IEEE}
}

@article{nascimento2005vertex,
	title={Vertex component analysis: A fast algorithm to unmix hyperspectral data},
	author={Nascimento, Jos{\'e} MP and Dias, Jos{\'e} MB},
	journal={IEEE transactions on Geoscience and Remote Sensing},
	volume={43},
	number={4},
	pages={898--910},
	year={2005},
	publisher={IEEE}
}

@article{xing2012dictionary,
	title={Dictionary learning for noisy and incomplete hyperspectral images},
	author={Xing, Zhengming and Zhou, Mingyuan and Castrodad, Alexey and Sapiro, Guillermo and Carin, Lawrence},
	journal={SIAM Journal on Imaging Sciences},
	volume={5},
	number={1},
	pages={33--56},
	year={2012},
	publisher={SIAM}
}

@article{simoes2015convex,
	title={A convex formulation for hyperspectral image superresolution via subspace-based regularization},
	author={Sim{\~o}es, Miguel and Bioucas-Dias, Jos{\'e} and Almeida, Luis B and Chanussot, Jocelyn},
	journal={IEEE Transactions on Geoscience and Remote Sensing},
	volume={53},
	number={6},
	pages={3373--3388},
	year={2015},
	publisher={IEEE}
}

@article{haro2012photographing,
	title={Photographing paintings by image fusion},
	author={Haro, Gloria and Buades, Antoni and Morel, Jean-Michel},
	journal={SIAM Journal on Imaging Sciences},
	volume={5},
	number={3},
	pages={1055--1087},
	year={2012},
	publisher={SIAM}
}

@article{candes2015phase,
	title={Phase retrieval via matrix completion},
	author={Candes, Emmanuel J and Eldar, Yonina C and Strohmer, Thomas and Voroninski, Vladislav},
	journal={SIAM review},
	volume={57},
	number={2},
	pages={225--251},
	year={2015},
	publisher={SIAM}
}

@article{bioucas2007phase,
	title={Phase unwrapping via graph cuts},
	author={Bioucas-Dias, Jos M and Valadao, Gonalo},
	journal={IEEE Transactions on Image processing},
	volume={16},
	number={3},
	pages={698--709},
	year={2007},
	publisher={IEEE}
}

@book{kaipio2006statistical,
	title={Statistical and computational inverse problems},
	author={Kaipio, Jari and Somersalo, Erkki},
	volume={160},
	year={2006},
	publisher={Springer Science \& Business Media}
}

@book{robert2007bayesian,
	title={The Bayesian choice: from decision-theoretic foundations to computational implementation},
	author={Robert, Christian},
	year={2007},
	publisher={Springer Science \& Business Media}
}

@article{pereyra2016proximal,
	title={Proximal markov chain monte carlo algorithms},
	author={Pereyra, Marcelo},
	journal={Statistics and Computing},
	volume={26},
	number={4},
	pages={745--760},
	year={2016},
	publisher={Springer}
}

@article{pereyra2014computing,
	title={Computing the Cramer--Rao bound of Markov random field parameters: application to the Ising and the Potts models},
	author={Pereyra, Marcelo and Dobigeon, Nicolas and Batatia, Hadj and Tourneret, Jean-Yves},
	journal={IEEE Signal Processing Letters},
	volume={21},
	number={1},
	pages={47--50},
	year={2014},
	publisher={IEEE}
}

@article{atchade2017perturbed,
	title={On perturbed proximal gradient algorithms},
	author={Atchad{\'e}, Yves F and Fort, Gersende and Moulines, Eric},
	journal={J. Mach. Learn. Res},
	volume={18},
	number={1},
	pages={310--342},
	year={2017}
}

@InProceedings{EUSIPCO,
	title="Maximum-a-posteriori estimation with unknown regularisation parameters",
	author="Pereyra, Marcelo and Bioucas-Dias, Jos{\'e} M and Figueiredo, M{\'a}rio AT",
	booktitle="Signal Processing Conference (EUSIPCO), 2015 23rd European",
	pages="230--234",
	year="2015",
	organization="IEEE"
}


@article{andrieu2006ergodicity,
	title="On the ergodicity properties of some adaptive MCMC algorithms",
	author="Andrieu, Christophe and Moulines, {\'E}ric",
	journal="The Annals of Applied Probability",
	volume="16",
	number="3",
	pages="1462--1505",
	year="2006",
	publisher="Institute of Mathematical Statistics"
}



@Book{bakry:gentil:ledoux:2014,
  Title                    = {Analysis and Geometry of {M}arkov Diffusion Operators},
  Author                   = {Bakry, D. and Gentil, I. and Ledoux, M.},
  Publisher                = {Springer},
  Year                     = {2014},
  Volume                   = {348},
  Doi                      = {10.1007/978-3-319-00227-9},
  ISBN                     = {978-3-319-00226-2; 978-3-319-00227-9},
  Mrclass                  = {60J25 (58J65 60J35 60J60)},
  Mrnumber                 = {3155209},
  Mrreviewer               = {Ming Liao},
  Pages                    = {xx+552},
  Url                      = {http://dx.doi.org/10.1007/978-3-319-00227-9}
}



@article{debortoli:durmus:pereyra:vidal:2018,
author = {De Bortoli V. and Durmus A. and Pereyra M. and Vidal A.},
title = {Supplementary to "...."},
year = {2018}
}



@article{douc:fort:moulines:soulier:2004,
    AUTHOR = {Douc, R. and Fort, G. and Moulines, E. and
              Soulier, P.},
     TITLE = {Practical drift conditions for subgeometric rates of
              convergence},
   JOURNAL = {Ann. Appl. Probab.},
  FJOURNAL = {The Annals of Applied Probability},
    VOLUME = {14},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {1353--1377},
      ISSN = {1050-5164},
   MRCLASS = {60J10},
  MRNUMBER = {2071426},
MRREVIEWER = {M. G. Shur},
       DOI = {10.1214/105051604000000323},
       URL = {https://doi.org/10.1214/105051604000000323},
}
		

@book{douc:moulines:priouret:soulier:2018,
  author =       {Douc, R. and Moulines, \'E. and Priouret, P. and Soulier, P.},
  editor =       {Springer},
  title =        {Markov Chains},
  publisher =    {Springer},
  year = {2019},
}


@Article{doucet:godsill:robert:2002,
author="Doucet, A.
and Godsill, S. J.
and Robert, C. P.",
title="Marginal maximum a posteriori estimation using Markov chain Monte Carlo",
journal="Statistics and Computing",
year=2002,
month="Jan",
day=01,
volume=12,
number=1,
pages="77--84",
abstract="Markov chain Monte Carlo (MCMC) methods, while facilitating the solution of many complex problems in Bayesian inference, are not currently well adapted to the problem of marginal maximum a posteriori (MMAP) estimation, especially when the number of parameters is large. We present here a simple and novel MCMC strategy, called State-Augmentation for Marginal Estimation (SAME), which leads to MMAP estimates for Bayesian models. We illustrate the simplicity and utility of the approach for missing data interpolation in autoregressive time series and blind deconvolution of impulsive processes.",
issn="1573-1375",
doi="10.1023/A:1013172322619",
url="https://doi.org/10.1023/A:1013172322619"
}



@ARTICLE{durmus:moulines:2016,
   author = {{Durmus}, A. and {Moulines}, E.},
    title = "{High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1605.01559},
 primaryClass = "math.ST",
 keywords = {Mathematics - Statistics Theory, Statistics - Methodology, Statistics - Machine Learning},
     year = 2016,
    month = may,
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160501559D},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article {meyn1993criteria_iii,
    AUTHOR = {Meyn, Sean P. and Tweedie, R. L.},
     TITLE = {Stability of {M}arkovian processes. {III}. {F}oster-{L}yapunov
              criteria for continuous-time processes},
   JOURNAL = {Advances in Applied Probability},
  FJOURNAL = {Advances in Applied Probability},
    VOLUME = {25},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {518--548},
      ISSN = {0001-8678},
   MRCLASS = {60J27},
  MRNUMBER = {1234295},
MRREVIEWER = {Esa Nummelin},
       DOI = {10.2307/1427522},
       URL = {https://doi.org/10.2307/1427522},
}

@article {meyn1993criteria_i,
    AUTHOR = {Meyn, Sean P. and Tweedie, R. L.},
     TITLE = {Stability of {M}arkovian processes. {I}. {C}riteria for
              discrete-time chains},
   JOURNAL = {Adv. in Appl. Probab.},
  FJOURNAL = {Advances in Applied Probability},
    VOLUME = {24},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {542--574},
      ISSN = {0001-8678},
   MRCLASS = {60J10},
  MRNUMBER = {1174380},
MRREVIEWER = {Esa Nummelin},
       DOI = {10.2307/1427479},
       URL = {https://doi.org/10.2307/1427479},
}

@article {meyn1993criteria_ii,
    AUTHOR = {Meyn, Sean P. and Tweedie, R. L.},
     TITLE = {Stability of {M}arkovian processes. {II}. {C}ontinuous-time
              processes and sampled chains},
   JOURNAL = {Adv. in Appl. Probab.},
  FJOURNAL = {Advances in Applied Probability},
    VOLUME = {25},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {487--517},
      ISSN = {0001-8678},
   MRCLASS = {60J27},
  MRNUMBER = {1234294},
MRREVIEWER = {Esa Nummelin},
       DOI = {10.2307/1427521},
       URL = {https://doi.org/10.2307/1427521},
}


@book {villani2009optimal,
    AUTHOR = {Villani, C\'{e}dric},
     TITLE = {Optimal transport},
    SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental
              Principles of Mathematical Sciences]},
    VOLUME = {338},
      NOTE = {Old and new},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2009},
     PAGES = {xxii+973},
      ISBN = {978-3-540-71049-3},
   MRCLASS = {49-02 (28A75 37J50 49Q20 53C23 58E30)},
  MRNUMBER = {2459454},
MRREVIEWER = {Dario Cordero-Erausquin},
       DOI = {10.1007/978-3-540-71050-9},
       URL = {https://doi.org/10.1007/978-3-540-71050-9},
}
@book {meyn1993markov,
    AUTHOR = {Meyn, S. P. and Tweedie, R. L.},
     TITLE = {Markov chains and stochastic stability},
    SERIES = {Communications and Control Engineering Series},
 PUBLISHER = {Springer-Verlag London, Ltd., London},
      YEAR = {1993},
     PAGES = {xvi+ 548},
      ISBN = {3-540-19832-6},
   MRCLASS = {60J05},
  MRNUMBER = {1287609},
MRREVIEWER = {Esa Nummelin},
       DOI = {10.1007/978-1-4471-3267-7},
       URL = {https://doi.org/10.1007/978-1-4471-3267-7},
}


@book{khasminskii2011stochastic,
  title={Stochastic stability of differential equations},
  author={Khasminskii, R.},
  volume={66},
  year={2011},
  publisher={Springer Science \& Business Media}
}

@unpublished{debortoli2019souk,
  TITLE = {{Stochastic Optimization with Unadjusted Kernel: the SOUK Algorithm}},
  AUTHOR = {De Bortoli, Valentin and Durmus, Alain and Pereyra, Marcelo and Fernandez Vidal, Ana},
  URL = {https://hal.archives-ouvertes.fr/hal-01978999},
  NOTE = {working paper or preprint},
  YEAR = {2019},
  MONTH = Jan,
  PDF = {https://hal.archives-ouvertes.fr/hal-01978999/file/main.pdf},
  HAL_ID = {hal-01978999},
  HAL_VERSION = {v1},
}

@article {nummelin1978geometric,
    AUTHOR = {Nummelin, E. and Tweedie, R. L.},
     TITLE = {Geometric ergodicity and {$R$}-positivity for general {M}arkov
              chains},
   JOURNAL = {Ann. Probability},
    VOLUME = {6},
      YEAR = {1978},
    NUMBER = {3},
     PAGES = {404--420},
   MRCLASS = {60J05 (60J10 60J15)},
  MRNUMBER = {0474504},
MRREVIEWER = {Dean Isaacson},
}

@article{brosse2018tamed,
title = "The tamed unadjusted Langevin algorithm",
journal = "Stochastic Processes and their Applications",
year = "2018",
issn = "0304-4149",
doi = "https://doi.org/10.1016/j.spa.2018.10.002",
url = "http://www.sciencedirect.com/science/article/pii/S0304414918305635",
author = "Nicolas Brosse and Alain Durmus and Éric Moulines and Sotirios Sabanis",
keywords = "Tamed unadjusted Langevin algorithm, Markov chain Monte Carlo, Total variation distance, Wasserstein distance",
abstract = "In this article, we consider the problem of sampling from a probability measure π having a density on Rd proportional to x↦e−U(x). The Euler discretization of the Langevin stochastic differential equation (SDE) is known to be unstable, when the potential U is superlinear. Based on previous works on the taming of superlinear drift coefficients for SDEs, we introduce the Tamed Unadjusted Langevin Algorithm (TULA) and obtain non-asymptotic bounds in V-total variation norm and Wasserstein distance of order 2 between the iterates of TULA and π, as well as weak error bounds. Numerical experiments are presented which support our findings."
}

@article {nummelin1983rate,
    AUTHOR = {Nummelin, Esa and Tuominen, Pekka},
     TITLE = {The rate of convergence in {O}rey's theorem for {H}arris
              recurrent {M}arkov chains with applications to renewal theory},
   JOURNAL = {Stochastic Process. Appl.},
  FJOURNAL = {Stochastic Processes and their Applications},
    VOLUME = {15},
      YEAR = {1983},
    NUMBER = {3},
     PAGES = {295--311},
      ISSN = {0304-4149},
   MRCLASS = {60J05 (60K05)},
  MRNUMBER = {711187},
MRREVIEWER = {Martin Jacobsen},
       DOI = {10.1016/0304-4149(83)90037-6},
       URL = {https://doi.org/10.1016/0304-4149(83)90037-6},
}
		
@article {nummelin1982geometric,
    AUTHOR = {Nummelin, Esa and Tuominen, Pekka},
     TITLE = {Geometric ergodicity of {H}arris recurrent {M}arkov chains
              with applications to renewal theory},
   JOURNAL = {Stochastic Process. Appl.},
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%3 8  22 32

%7 13 23 32


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}


@article {veretennikov:1997,
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   MRCLASS = {60H10 (60J60)},
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}

@article {chan:1993,
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   MRCLASS = {60J10 (62F15)},
  MRNUMBER = {1212494},
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}

@article {chen:tsay:1991,
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@ARTICLE{roberts:polson:1994,
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    year = {1994},
    volume = {56},
    pages = {377--384}
}



@article {rosenthal:2002,
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  FJOURNAL = {Electronic Communications in Probability},
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      ISSN = {1083-589X},
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       DOI = {10.1214/ECP.v7-1054},
       URL = {https://doi.org/10.1214/ECP.v7-1054},
}

@article {roberts:tweedie:1999,
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    VOLUME = {80},
      YEAR = {1999},
    NUMBER = {2},
     PAGES = {211--229},
      ISSN = {0304-4149},
   MRCLASS = {60J10 (60K15)},
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MRREVIEWER = {Mark R. Jerrum},
       DOI = {10.1016/S0304-4149(98)00085-4},
       URL = {https://doi.org/10.1016/S0304-4149(98)00085-4},
}

@article {jones:hobert:2004,
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       URL = {https://doi.org/10.1214/009053604000000184},
}

@article{eberle:guillin:zimmer:2018,
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  journal={Transactions of the American Mathematical Society},
  year={2018}
}


@article{butkovsky:scheutzow:2017,
author = "Butkovsky, O. and Scheutzow, M.",
doi = "10.1214/17-EJP122",
fjournal = "Electronic Journal of Probability",
journal = "Electron. J. Probab.",
pages = "23 pp.",
pno = "98",
publisher = "The Institute of Mathematical Statistics and the Bernoulli Society",
title = "Invariant measures for stochastic functional differential equations",
url = "https://doi.org/10.1214/17-EJP122",
volume = "22",
year = "2017"
}



@article{eberle:guillin:zimmer:2017b,
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  author={Eberle, A. and Guillin, A. and Zimmer, R.},
  journal={arXiv preprint arXiv:1703.01617},
  year={2017}
}


@article{durmus:eberle:guillin:zimmer:2018,
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  journal={arXiv preprint arXiv:1805.11387},
  year={2018}
}


@article{qin:hobert:2019,
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  journal={arXiv preprint arXiv:1902.02964},
  year=2019
}



@article {roberts:rosenthal:1996,
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}



@article {jones:hobert:2001,
    AUTHOR = {Jones, G. L. and Hobert, J. P.},
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  publisher={Institute of Mathematical Statistics}
}

@article{debortoli2019supplementary,
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  year={2017}  
}

@article{debortoli2019back,
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  author={De Bortoli, V. and Durmus, A.},
  journal={arXiv preprint arXiv:tocomplete},
  year={2017}  
}


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}


@article{dalalyan2019user,
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  year={2019},
  publisher={Elsevier}
}


@inproceedings{chatterji2018theory,
  title={On the Theory of Variance Reduction for Stochastic Gradient Monte Carlo},
  author={Chatterji, Niladri and Flammarion, Nicolas and Ma, Yian and Bartlett, Peter and Jordan, Michael},
  booktitle={International Conference on Machine Learning},
  pages={763--772},
  year={2018}
}


@article{baker2017control,
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  journal={Statistics and Computing},
  pages={1--17},
  publisher={Springer}
}

@article{qin2018wasserstein,
  title={Wasserstein-based methods for convergence complexity analysis of MCMC with application to Albert and Chib's algorithm},
  author={Qin, Qian and Hobert, James P},
  journal={arXiv preprint arXiv:1810.08826},
  year={2018}
}

@article {steinsaltz1999locally,
    AUTHOR = {Steinsaltz, David},
     TITLE = {Locally contractive iterated function systems},
   JOURNAL = {Ann. Probab.},
  FJOURNAL = {The Annals of Probability},
    VOLUME = {27},
      YEAR = {1999},
    NUMBER = {4},
     PAGES = {1952--1979},
      ISSN = {0091-1798},
   MRCLASS = {26A18 (28A80 60K99)},
  MRNUMBER = {1742896},
MRREVIEWER = {M. Iosifescu},
       DOI = {10.1214/aop/1022677556},
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}

@article {madras2010quantitative,
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MRREVIEWER = {Thomas R. Boucher},
       DOI = {10.3150/09-BEJ238},
       URL = {https://doi.org/10.3150/09-BEJ238},
}

@incollection {hairer2011yet,
    AUTHOR = {Hairer, Martin and Mattingly, Jonathan C.},
     TITLE = {Yet another look at {H}arris' ergodic theorem for {M}arkov
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 BOOKTITLE = {Seminar on {S}tochastic {A}nalysis, {R}andom {F}ields and
              {A}pplications {VI}},
    SERIES = {Progr. Probab.},
    VOLUME = {63},
     PAGES = {109--117},
 PUBLISHER = {Birkh\"{a}user/Springer Basel AG, Basel},
      YEAR = {2011},
   MRCLASS = {60J05 (37A30 37A50 47D07)},
  MRNUMBER = {2857021},
MRREVIEWER = {Wojciech Bartoszek},
       DOI = {10.1007/978-3-0348-0021-1_7},
       URL = {https://doi.org/10.1007/978-3-0348-0021-1_7},
}
@article {vaisala:2005,
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    VOLUME = {23},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {187--231},
      ISSN = {0723-0869},
   MRCLASS = {53C23 (20F67)},
  MRNUMBER = {2164775},
MRREVIEWER = {Michel Coornaert},
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       URL = {https://doi.org/10.1016/j.exmath.2005.01.010},
}


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    AUTHOR = {Rogers, L. C. G. and Williams, David},
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      NOTE = {It\^{o} calculus,
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 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2000},
     PAGES = {xiv+480},
      ISBN = {0-521-77593-0},
   MRCLASS = {60J60 (60G07 60H05 60J25)},
  MRNUMBER = {1780932},
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}


@article{gadat,
  title={Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity},
  author={Gadat, S{\'e}bastien and Panloup, Fabien},
  journal={arXiv preprint arXiv:1709.03342},
  year={2017}
}


@article{bottou:lecun:2005,
title = "On-line learning for very large data sets",
abstract = "The design of very large learning systems presents many unsolved challenges. Consider, for instance, a system that 'watches' television for a few weeks and learns to enumerate the objects present in these images. Most current learning algorithms do not scale well enough to handle such massive quantities of data. Experience suggests that the stochastic learning algorithms are best suited to such tasks. This is at first surprising because stochastic learning algorithms optimize the training error rather slowly. Our paper reconsiders the convergence speed in terms of how fast a learning algorithm optimizes the testing error. This reformulation shows the superiority of the well designed stochastic learning algorithm.",
keywords = "Convergence speed, Learning, Online learning, Stochastic optimization",
author = "L. Bottou and Y. LeCun",
year = "2005",
month = "3",
doi = "10.1002/asmb.538",
language = "English (US)",
volume = "21",
pages = "137--151",
journal = "Applied Stochastic Models in Business and Industry",
issn = "1524-1904",
publisher = "John Wiley and Sons Ltd",
number = "2",
}

@article{polyak:juditsky:1992,
author = {Polyak, B. T. and Juditsky, A. B.},
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journal = {SIAM Journal on Control and Optimization},
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number = {4},
pages = {838-855},
year = {1992},
doi = {10.1137/0330046},
URL = { 
        https://doi.org/10.1137/0330046
},
eprint = { 
        https://doi.org/10.1137/0330046
}
}

@article{kingma:ba:2014,
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  year={2014}
}


@book{karatzas1991brownian,
    AUTHOR = {Karatzas, Ioannis and Shreve, Steven E.},
     TITLE = {Brownian motion and stochastic calculus},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {113},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag, New York},
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   MRCLASS = {60J65 (35K99 35R60 60G44 60H10 60J60)},
  MRNUMBER = {1121940},
       DOI = {10.1007/978-1-4612-0949-2},
       URL = {https://doi.org/10.1007/978-1-4612-0949-2},
}


@book{milstein1995numerical,
    AUTHOR = {Milstein, G. N.},
     TITLE = {Numerical integration of stochastic differential equations},
    SERIES = {Mathematics and its Applications},
    VOLUME = {313},
      NOTE = {Translated and revised from the 1988 Russian original},
 PUBLISHER = {Kluwer Academic Publishers Group, Dordrecht},
      YEAR = {1995},
     PAGES = {viii+169},
      ISBN = {0-7923-3213-X},
   MRCLASS = {65C05 (60H10 65D30 65L99 65P05 65U05)},
  MRNUMBER = {1335454},
MRREVIEWER = {Eckhard Platen},
       DOI = {10.1007/978-94-015-8455-5},
       URL = {https://doi.org/10.1007/978-94-015-8455-5},
}

@book{kushneryin,
  title={Stochastic approximation and recursive algorithms and applications},
  author={Kushner, Harold and Yin, G George},
  volume={35},
  year={2003},
  publisher={Springer Science \& Business Media}
}

@article{gadat,
  title={Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity},
  author={Gadat, S{\'e}bastien and Panloup, Fabien},
  journal={arXiv preprint arXiv:1709.03342},
  year={2017}
}






@article {ljung:1977,
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}

@book {kushner:clark:1978,
    AUTHOR = {Kushner, H. J. and Clark, D. S.},
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}

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}



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      YEAR = {1987},
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     PAGES = {403--428},
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MRREVIEWER = {G. Pflug},
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       URL = {https://doi.org/10.1007/BF00699098},
}

@book {benveniste:metivier:priouret:1990,
    AUTHOR = {Benveniste, A. and M\'etivier, M. and Priouret, P.},
     TITLE = {Adaptive algorithms and stochastic approximations},
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    VOLUME = {22},
      NOTE = {Translated from the French by Stephen S. Wilson},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1990},
     PAGES = {xii+365},
      ISBN = {3-540-52894-6},
   MRCLASS = {62L20 (60G35 93E35)},
  MRNUMBER = {1082341},
MRREVIEWER = {G. Pflug},
       DOI = {10.1007/978-3-642-75894-2},
       URL = {https://doi.org/10.1007/978-3-642-75894-2},
}


@article {tadic:doucet:2017,
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   JOURNAL = {Ann. Appl. Probab.},
  FJOURNAL = {The Annals of Applied Probability},
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}


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}

@book{kushneryin,
  title={Stochastic approximation and recursive algorithms and applications},
  author={Kushner, Harold and Yin, G George},
  volume={35},
  year={2003},
  publisher={Springer Science \& Business Media}
}

@article{gadat,
  title={Optimal non-asymptotic bound of the Ruppert-Polyak averaging without strong convexity},
  author={Gadat, S{\'e}bastien and Panloup, Fabien},
  journal={arXiv preprint arXiv:1709.03342},
  year={2017}
}

@inproceedings{shamirzhang,
  title={Stochastic gradient descent for non-smooth optimization: Convergence results and optimal averaging schemes},
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  booktitle={International Conference on Machine Learning},
  pages={71--79},
  year={2013}
}

@article{bertsekas,
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  year={1997},
  publisher={Taylor \& Francis}
}

@book {nesterov2004introductory,
    AUTHOR = {Nesterov, Yurii},
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    SERIES = {Applied Optimization},
    VOLUME = {87},
      NOTE = {A basic course},
 PUBLISHER = {Kluwer Academic Publishers, Boston, MA},
      YEAR = {2004},
     PAGES = {xviii+236},
      ISBN = {1-4020-7553-7},
   MRCLASS = {90-02 (90-01 90C25)},
  MRNUMBER = {2142598},
       DOI = {10.1007/978-1-4419-8853-9},
       URL = {https://doi.org/10.1007/978-1-4419-8853-9},
}


@book {pachpatte1998ineq,
    AUTHOR = {Pachpatte, B. G.},
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@inproceedings{mirrorzhou,
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author = {Karimi, Hamed and Nutini, Julie and Schmidt, Mark},
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year = {2016},
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publisher = {Springer-Verlag},
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booktitle = {European Conference on Machine Learning and Knowledge Discovery in Databases - Volume 9851},
pages = {795--811},
numpages = {17},
keywords = {Coordinate descent, Support vector machines, Gradient descent, Variance-reduction, L1-regularization, Boosting, Stochastic gradient},
location = {Riva del Garda, Italy},
series = {ECML PKDD 2016}
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@article{debortoli2019souk,
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@book{casella2002,
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% TRUC

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},
eprint = { 
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  keywords = {MSc _checked character_recognition mnist network neural},
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  timestamp = {2016-07-12T19:25:30.000+0200},
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