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In many problems in modern statistics and machine learning, it is often of interest to establish that a first order method on a non-convex risk function eventually enters a region of parameter space in which the risk is locally convex.
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2019
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Michael Celentano, Andrea Montanari, and Yuchen Wu, The estimation error of general first order methods , Proceedings of Thirty Third Conference on Learning Theory (Jacob Abernethy and Shivani Agarwal, eds.), Proceedings of Machine Learning Research, vol. 125, PMLR, 09–12 Jul 2020, pp. 1078–1141
2020
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Francesca Mignacco, Florent Krzakala, Pierfrancesco Urbani, and Lenka Zdeborová, Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification , Advances in Neural Information Processing Systems (H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, eds.), vol. 33, Curran Associates, Inc., 2020, pp. 9540–9550
2020
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2015
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T. Tony Cai, Xiaodong Li, and Zongming Ma, Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow , The Annals of Statistics 44
2016
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Yash Deshpande, Emmanuel Abbe, and Andrea Montanari, Asymptotic mutual information for the balanced binary stochastic block model , Information and Inference: A Journal of the IMA 6
2016
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Sujay Sanghavi, Rachel Ward, and Chris D. White, The local convexity of solving systems of quadratic equations , Results in Mathematics 71
2017
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Raphaël Berthier, Andrea Montanari, and Phan-Minh Nguyen, State evolution for approximate message passing with non-separable functions , Information and Inference: A Journal of the IMA 9
2019
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Yuxin Chen, Yuejie Chi, Jianqing Fan, and Cong Ma, Gradient descent with random initialization: fast global convergence for nonconvex phase retrieval , Mathematical Programming 176
2019
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Sebastian Goldt, Madhu Advani, Andrew M Saxe, Florent Krzakala, and Lenka Zdeborová, Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup , Advances in Neural Information Processing Systems (H. Wallach, H. Larochelle, A. Beygelzimer, F. Alché-Buc, E. Fox, and R. Garnett, eds.), vol. 32, Curran Associates, Inc., 2019
2019
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Stefano Sarao Mannelli, Florent Krzakala, Pierfrancesco Urbani, and Lenka Zdeborova, Passed and spurious: Descent algorithms and local minima in spiked matrix-tensor models , Proceedings of the 36th International Conference on Machine Learning (Kamalika Chaudhuri and Ruslan Salakhutdinov, eds.), Proceedings of Machine Learning Research, vol. 97, PMLR, 09–15 Jun 2019, pp. 4333–4342
2019
Cited alongside, same era.
Ahmed El Alaoui, Andrea Montanari, and Mark Sellke, Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization
Cited in the paper.
Cong Ma, Kaizheng Wang, Yuejie Chi, and Yuxin Chen, Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution , Foundations of Computational Mathematics 20
2020
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Stefano Sarao Mannelli and Lenka Zdeborová, Thresholds of descending algorithms in inference problems , Journal of Statistical Mechanics: Theory and Experiment 2020
2020
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Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Pierfrancesco Urbani, and Lenka Zdeborová, Complex dynamics in simple neural networks: Understanding gradient flow in phase retrieval , Advances in Neural Information Processing Systems (H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, eds.), vol. 33, Curran Associates, Inc., 2020, pp. 3265–3274
2020
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Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Pierfrancesco Urbani, and Lenka Zdeborová, Marvels and pitfalls of the Langevin algorithm in noisy high-dimensional inference , Phys. Rev. X 10
2020
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Zhou Fan, Song Mei, and Andrea Montanari, TAP free energy, spin glasses and variational inference , The Annals of Probability 49
2021
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Léo Miolane and Andrea Montanari, The distribution of the Lasso: Uniform control over sparse balls and adaptive parameter tuning , The Annals of Statistics 49
2021
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Andrea Montanari and Ramji Venkataramanan, Estimation of low-rank matrices via approximate message passing , The Annals of Statistics 49
2021
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Andrea Montanari and Yuchen Wu, Statistically optimal first order algorithms: A proof via orthogonalization , 2022
2022
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