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We propose a Langevin diffusion-based algorithm for non-convex optimization and sampling on a product manifold of spheres.
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Robert C Griffiths, Diffusion processes and coalescent trees , arXiv preprint arXiv:1003.4650 (2010)
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2017
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Maxim Raginsky, Alexander Rakhlin, and Matus Telgarsky, Non-convex learning via stochastic gradient langevin dynamics: a nonasymptotic analysis , Proceedings of the 30th Conference on Learning Theory, COLT 2017, Amsterdam, The Netherlands, 7-10 July 2017, 2017, pp. 1674–1703
2017
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Sébastien Bubeck, Ronen Eldan, and Joseph Lehec, Sampling from a log-concave distribution with projected langevin monte carlo , Discrete & Computational Geometry 59
2018
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Xiang Cheng and Peter Bartlett, Convergence of langevin mcmc in kl-divergence , Algorithmic Learning Theory, PMLR, 2018, pp. 186–211
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David Steurer, Fast sdp algorithms for constraint satisfaction problems , Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms, SIAM, 2010, pp. 684–697
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2013
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2018
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Andrew Holbrook, Shiwei Lan, Alexander Vandenberg-Rodes, and Babak Shahbaba, Geodesic lagrangian monte carlo over the space of positive definite matrices: with application to bayesian spectral density estimation , Journal of statistical computation and simulation 88
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2019
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2019
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Arnak S Dalalyan and Avetik Karagulyan, User-friendly guarantees for the langevin monte carlo with inaccurate gradient , Stochastic Processes and their Applications 129
2019
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Alain Durmus, Szymon Majewski, and Błażej Miasojedow, Analysis of langevin monte carlo via convex optimization , The Journal of Machine Learning Research 20
2019
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Jiang Hu, Xin Liu, Zai-Wen Wen, and Ya-Xiang Yuan, A brief introduction to manifold optimization , Journal of the Operations Research Society of China (2019), 1–50
2019
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J.M. Lee, Introduction to riemannian manifolds , Graduate Texts in Mathematics, Springer International Publishing, 2019
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2019
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Xuechen Li, Yi Wu, Lester Mackey, and Murat A Erdogdu, Stochastic runge-kutta accelerates langevin monte carlo and beyond , Advances in Neural Information Processing Systems, 2019, pp. 7748–7760
2019
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2019
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2019
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Martin J Wainwright, High-dimensional statistics: A non-asymptotic viewpoint , vol. 48, Cambridge University Press, 2019
2019
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2019
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2020
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2020
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