{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:09:00Z","timestamp":1766268540977},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,12,19]],"date-time":"2018-12-19T00:00:00Z","timestamp":1545177600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci. China Inf. Sci."],"published-print":{"date-parts":[[2019,1]]},"DOI":"10.1007\/s11432-018-9656-y","type":"journal-article","created":{"date-parts":[[2018,12,23]],"date-time":"2018-12-23T12:29:05Z","timestamp":1545568145000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A convergence analysis for a class of practical variance-reduction stochastic gradient MCMC"],"prefix":"10.1007","volume":"62","author":[{"given":"Changyou","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenlin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yizhe","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinliang","family":"Su","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lawrence","family":"Carin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,12,19]]},"reference":[{"key":"9656_CR1","volume-title":"Proceedings of International Conference on Machine Learning","author":"Z Gan","year":"2015","unstructured":"Gan Z, Chen C Y, Henao R, et al. Scalable deep Poisson factor analysis for topic modeling. In: Proceedings of International Conference on Machine Learning, 2015"},{"key":"9656_CR2","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"C Liu","year":"2016","unstructured":"Liu C, Zhu J, Song Y. Stochastic gradient geodesic MCMC methods. In: Proceedings of Conference on Neural Information Processing System, 2016"},{"key":"9656_CR3","volume-title":"Proceedings of International Conference on Machine Learning","author":"T Chen","year":"2014","unstructured":"Chen T, Fox E B, Guestrin C. Stochastic gradient Hamiltonian Monte Carlo. In: Proceedings of International Conference on Machine Learning, 2014"},{"key":"9656_CR4","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"N Ding","year":"2014","unstructured":"Ding N, Fang Y H, Babbush R, et al. Bayesian sampling using stochastic gradient thermostats. In: Proceedings of Conference on Neural Information Processing System, 2014"},{"key":"9656_CR5","volume-title":"Proceedings of International Conference on Machine Learning","author":"U \u015eim\u015fekli","year":"2016","unstructured":"\u015eim\u015fekli U, Badeau R, Cemgil A T, et al. Stochastic quasi-Newton Langevin Monte Carlo. In: Proceedings of International Conference on Machine Learning, 2016"},{"key":"9656_CR6","volume-title":"Proceedings of International Conference on Machine Learning","author":"Y X Wang","year":"2015","unstructured":"Wang Y X, Fienberg S E, Smola A. Privacy for free: posterior sampling and stochastic gradient Monte Carlo. In: Proceedings of International Conference on Machine Learning, 2015"},{"key":"9656_CR7","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"J T Springenberg","year":"2016","unstructured":"Springenberg J T, Klein A, Falkner S, et al. Bayesian optimization with robust Bayesian neural networks. In: Proceedings of Conference on Neural Information Processing System, 2016"},{"key":"9656_CR8","volume-title":"Proceedings of AAAI Conference on Artificial Intelligence","author":"C Y Li","year":"2016","unstructured":"Li C Y, Chen C Y, Carlson D, et al. Preconditioned stochastic gradient Langevin dynamics for deep neural networks. In: Proceedings of AAAI Conference on Artificial Intelligence, 2016"},{"key":"9656_CR9","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"C Y Chen","year":"2015","unstructured":"Chen C Y, Ding N, Carin L. On the convergence of stochastic gradient MCMC algorithms with high-order integrators. In: Proceedings of Conference on Neural Information Processing System, 2015"},{"key":"9656_CR10","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"A Dubey","year":"2016","unstructured":"Dubey A, Reddi S J, P\u00f3czos B, et al. Variance reduction in stochastic gradient Langevin dynamics. In: Proceedings of Conference on Neural Information Processing System, 2016"},{"key":"9656_CR11","volume-title":"Proceedings of International Conference on Machine Learning","author":"M Welling","year":"2011","unstructured":"Welling M, Teh Y W. Bayesian learning via stochastic gradient Langevin dynamics. In: Proceedings of International Conference on Machine Learning, 2011"},{"key":"9656_CR12","first-page":"193","volume":"17","author":"Y W Teh","year":"2016","unstructured":"Teh Y W, Thiery A H, Vollmer S J. Consistency and fluctuations for stochastic gradient Langevin dynamics. J Mach Learn Res, 2016, 17: 193\u2013225","journal-title":"J Mach Learn Res"},{"key":"9656_CR13","first-page":"5504","volume":"17","author":"S J Vollmer","year":"2016","unstructured":"Vollmer S J, Zygalakis K C, Teh Y W. Exploration of the (Non-)asymptotic bias and variance of stochastic gradient Langevin dynamics. J Mach Learn Res, 2016, 17: 5504\u20135548","journal-title":"J Mach Learn Res"},{"key":"9656_CR14","volume-title":"Proceedings of International Conference on Machine Learning","author":"Y A Ma","year":"2015","unstructured":"Ma Y A, Chen T Q, Fox E B. A complete recipe for stochastic gradient MCMC. In: Proceedings of International Conference on Machine Learning, 2015"},{"key":"9656_CR15","volume-title":"Wiley Encyclopedia of Operations Research and Management Science","author":"A P Ghosh","year":"2011","unstructured":"Ghosh A P. Backward and forward equations for diffusion processes. Wiley Encyclopedia of Operations Research and Management Science, 2011. doi: 10.1002\/9780470400531.eorms0080"},{"key":"9656_CR16","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s10107-016-1030-6","volume":"162","author":"M L Schmidt","year":"2017","unstructured":"Schmidt M, Le Roux N, Bach F. Minimizing finite sums with the stochastic average gradient. Math Program, 2017, 162: 83\u2013112","journal-title":"Math Program"},{"key":"9656_CR17","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"R Johnson","year":"2013","unstructured":"Johnson R, Zhang T. Accelerating stochastic gradient descent using predictive variance reduction. In: Proceedings of Conference on Neural Information Processing System, 2013"},{"key":"9656_CR18","volume-title":"Proceedings of International Conference on Machine Learning","author":"S J Reddi","year":"2016","unstructured":"Reddi S J, Hefny A, Sra S, et al. Stochastic variance reduction for nonconvex optimization. In: Proceedings of International Conference on Machine Learning, 2016"},{"key":"9656_CR19","volume-title":"Proceedings of International Conference on Machine Learning","author":"Z Allen-Zhu","year":"2016","unstructured":"Allen-Zhu Z, Hazan E. Variance reduction for faster non-convex optimization. In: Proceedings of International Conference on Machine Learning, 2016"},{"key":"9656_CR20","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"C Y Chen","year":"2016","unstructured":"Chen C Y, Ding N, Li C Y, et al. Stochastic gradient MCMC with stale gradients. In: Proceedings of Conference on Neural Information Processing System, 2016"},{"key":"9656_CR21","volume-title":"Minimizing finite sums with the stochastic average gradient","author":"M Schmidt","year":"2013","unstructured":"Schmidt M, Roux N L, Bach F. Minimizing finite sums with the stochastic average gradient. 2013. ArXiv:1309.2388"},{"key":"9656_CR22","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"L J Zhang","year":"2013","unstructured":"Zhang L J, Mahdavi M, Jin R. Linear convergence with condition number independent access of full gradients. In: Proceedings of Conference on Neural Information Processing System, 2013"},{"key":"9656_CR23","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"A Defazio","year":"2014","unstructured":"Defazio A, Bach F, Lacoste-Julien S. SAGA: a fast incremental gradient method with support for non-strongly convex composite objectives. In: Proceedings of Conference on Neural Information Processing System, 2014"},{"key":"9656_CR24","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"S J Reddi","year":"2016","unstructured":"Reddi S J, Sra S, P\u00f3czos B. Fast stochastic methods for nonsmooth nonconvex optimization. In: Proceedings of Conference on Neural Information Processing System, 2016"},{"key":"9656_CR25","volume-title":"Proceedings of International Conference on Machine Learning","author":"Z Allen-Zhu","year":"2016","unstructured":"Allen-Zhu Z, Richt\u00e1rik P, Qu Z, et al. Even faster accelerated coordinate descent using non-uniform sampling. In: Proceedings of International Conference on Machine Learning, 2016"},{"key":"9656_CR26","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"S J Reddi","year":"2015","unstructured":"Reddi S J, Hefny A, Sra S, et al. On variance reduction in stochastic gradient descent and its asynchronous variants. In: Proceedings of Conference on Neural Information Processing System, 2015"},{"key":"9656_CR27","volume-title":"Proceedings of International Conference on Machine Learning","author":"Y T Chen","year":"2016","unstructured":"Chen Y T, Ghahramani Z. Scalable discrete sampling as a multi-armed bandit problem. In: Proceedings of International Conference on Machine Learning, 2016"},{"key":"9656_CR28","first-page":"1","volume":"18","author":"R Bardenet","year":"2017","unstructured":"Bardenet R, Doucet A, Holmes C. On Markov chain Monte Carlo methods for tall data. J Mach Learn Res, 2017, 18: 1\u201343","journal-title":"J Mach Learn Res"},{"key":"9656_CR29","volume-title":"Control variates for stochastic gradient MCMC","author":"J Baker","year":"2017","unstructured":"Baker J, Fearnhead P, Fox E B, et al. Control variates for stochastic gradient MCMC. 2017. ArXiv:1706.05439"},{"key":"9656_CR30","volume-title":"Proceedings of International Conference on Machine Learning","author":"N S Chatterji","year":"2018","unstructured":"Chatterji N S, Flammarion N, Ma Y A, et al. On the theory of variance reduction for stochastic gradient Monte Carlo. In: Proceedings of International Conference on Machine Learning, 2018"},{"key":"9656_CR31","volume-title":"Proceedings of Conference on Uncertainty in Artificial Intelligence","author":"D F Zou","year":"2018","unstructured":"Zou D F, Xu P, Gu Q Q. Subsampled stochastic variance-reduced gradient Langevin dynamics. In: Proceedings of Conference on Uncertainty in Artificial Intelligence, 2018"},{"key":"9656_CR32","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"R Harikandeh","year":"2015","unstructured":"Harikandeh R, Ahmed M O, Virani A, et al. Stop wasting my gradients: practical SVRG. In: Proceedings of Conference on Neural Information Processing System, 2015"},{"key":"9656_CR33","volume-title":"Proceedings of Conference on Learning Theory","author":"R Frostig","year":"2015","unstructured":"Frostig R, Ge R, Kakade S M, et al. Competing with the empirical risk minimizer in a single pass. In: Proceedings of Conference on Learning Theory, 2015"},{"key":"9656_CR34","volume-title":"Trading-off variance and complexity in stochastic gradient descent","author":"V Shah","year":"2016","unstructured":"Shah V, Asteris M, Kyrillidis A, et al. Trading-off variance and complexity in stochastic gradient descent. 2016. ArXiv:1603.06861"},{"key":"9656_CR35","volume-title":"Proceedings of Conference on Neural Information Processing System","author":"L H Lei","year":"2016","unstructured":"Lei L H, Jordan M I. Less than a single pass: stochastically controlled stochastic gradient method. In: Proceedings of Conference on Neural Information Processing System, 2016"},{"key":"9656_CR36","volume-title":"Proceedings of International Conference on Artificial Intelligence and Statistics","author":"X R Lian","year":"2017","unstructured":"Lian X R, Wang M D, J Liu. Finite-sum composition optimization via variance reduced gradient descent. In: Proceedings of International Conference on Artificial Intelligence and Statistics, 2017"},{"key":"9656_CR37","volume-title":"Proceedings of International Conference on Machine Learning","author":"J M Hern\u00e1ndez-Lobato","year":"2015","unstructured":"Hern\u00e1ndez-Lobato J M, Adams R P. Probabilistic backpropagation for scalable learning of Bayesian neural networks. In: Proceedings of International Conference on Machine Learning, 2015"},{"key":"9656_CR38","volume-title":"Proceedings of International Conference on Machine Learning","author":"C Blundell","year":"2015","unstructured":"Blundell C, Cornebise J, Kavukcuoglu K, et al. Weight uncertainty in neural networks. In: Proceedings of International Conference on Machine Learning, 2015"},{"key":"9656_CR39","volume-title":"Proceedings of International Conference on Machine Learning","author":"C Louizos","year":"2016","unstructured":"Louizos C, Welling M. Structured and efficient variational deep learning with matrix Gaussian posteriors. In: Proceedings of International Conference on Machine Learning, 2016"},{"key":"9656_CR40","volume-title":"Proceedings of IEEE Conference on Computer Vision and Pattern Recognition","author":"K M He","year":"2016","unstructured":"He K M, Zhang X Y, Ren S Q, et al. Deep residual learning for image recognition. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2016"},{"key":"9656_CR41","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","volume":"9","author":"S Hochreiter","year":"1997","unstructured":"Hochreiter S, Schmidhuber J. Long short-term memory. Neural Comput, 1997, 9: 1735\u20131780","journal-title":"Neural Comput"},{"key":"9656_CR42","volume-title":"Pointer sentinel mixture models","author":"S Merity","year":"2016","unstructured":"Merity S, Xiong C M, Bradbury J, et al. Pointer sentinel mixture models. 2016. ArXiv:1609.07843"},{"key":"9656_CR43","volume-title":"Recurrent neural network regularization","author":"W Zaremba","year":"2014","unstructured":"Zaremba W, Sutskever I, Vinyals O. Recurrent neural network regularization. 2014. ArXiv:1409.2329"},{"key":"9656_CR44","volume-title":"Proceedings of International Conference on Machine Learning","author":"Y Z Zhang","year":"2017","unstructured":"Zhang Y Z, Chen C Y, Gan Z, et al. Stochastic gradient monomial Gamma sampler. In: Proceedings of International Conference on Machine Learning, 2017"}],"container-title":["Science China Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-018-9656-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11432-018-9656-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-018-9656-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,19]],"date-time":"2020-02-19T14:17:25Z","timestamp":1582121845000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11432-018-9656-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,19]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["9656"],"URL":"https:\/\/doi.org\/10.1007\/s11432-018-9656-y","relation":{},"ISSN":["1674-733X","1869-1919"],"issn-type":[{"value":"1674-733X","type":"print"},{"value":"1869-1919","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,19]]},"assertion":[{"value":"26 June 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 August 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 December 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"12101"}}