Algorithmic thresholds for tensor PCA
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[1] I. J. Schoenberg. Positive definite functions on spheres , 1942 .
[2] D. W. Stroock,et al. Multidimensional Diffusion Processes , 1979 .
[3] p>2 spin glasses with first order ferromagnetic transitions , 1999, cond-mat/9912201.
[4] I. Johnstone. On the distribution of the largest principal component , 2000 .
[5] M. Ledoux. The concentration of measure phenomenon , 2001 .
[6] Elton P. Hsu. Stochastic analysis on manifolds , 2002 .
[7] J. Wellner,et al. High Dimensional Probability III , 2003 .
[8] S. Péché,et al. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices , 2004, math/0403022.
[9] Mylène Maïda,et al. Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles , 2006 .
[10] V. Koltchinskii,et al. High Dimensional Probability , 2006, math/0612726.
[11] S. Péché. The largest eigenvalue of small rank perturbations of Hermitian random matrices , 2006 .
[12] C. Donati-Martin,et al. The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations. , 2007, 0706.0136.
[13] A. Guionnet,et al. Large deviations of the extreme eigenvalues of random deformations of matrices , 2010, Probability Theory and Related Fields.
[14] Antonio Auffinger,et al. Random Matrices and Complexity of Spin Glasses , 2010, 1003.1129.
[15] Y. Gliklikh. Stochastic Analysis on Manifolds , 2011 .
[16] P. Rigollet,et al. Optimal detection of sparse principal components in high dimension , 2012, 1202.5070.
[17] Christopher J. Hillar,et al. Most Tensor Problems Are NP-Hard , 2009, JACM.
[18] Antonio Auffinger,et al. Complexity of random smooth functions on the high-dimensional sphere , 2011, 1110.5872.
[19] Andrea Montanari,et al. A statistical model for tensor PCA , 2014, NIPS.
[20] Jonathan Shi,et al. Tensor principal component analysis via sum-of-square proofs , 2015, COLT.
[21] Florent Krzakala,et al. Statistical physics of inference: thresholds and algorithms , 2015, ArXiv.
[22] Eliran Subag,et al. The complexity of spherical p-spin models - a second moment approach , 2015, 1504.02251.
[23] Tselil Schramm,et al. Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors , 2015, STOC.
[24] Ankur Moitra,et al. Noisy tensor completion via the sum-of-squares hierarchy , 2015, Mathematical Programming.
[25] Pravesh Kothari,et al. A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).
[26] Afonso S. Bandeira,et al. Statistical limits of spiked tensor models , 2016, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.
[27] Ankur Moitra,et al. Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization , 2016, ArXiv.
[28] Florent Krzakala,et al. Statistical and computational phase transitions in spiked tensor estimation , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).
[29] Andrea Montanari,et al. On the Limitation of Spectral Methods: From the Gaussian Hidden Clique Problem to Rank One Perturbations of Gaussian Tensors , 2014, IEEE Transactions on Information Theory.
[30] Michel X. Goemans,et al. Community detection in hypergraphs, spiked tensor models, and Sum-of-Squares , 2017, 2017 International Conference on Sampling Theory and Applications (SampTA).
[31] G. Ben Arous,et al. Spectral Gap Estimates in Mean Field Spin Glasses , 2017, 1705.04243.
[32] David Gamarnik,et al. High Dimensional Regression with Binary Coefficients. Estimating Squared Error and a Phase Transtition , 2017, COLT.
[33] Tengyu Ma,et al. On the optimization landscape of tensor decompositions , 2017, Mathematical Programming.
[34] Emmanuel Abbe,et al. Proof of the Achievability Conjectures for the General Stochastic Block Model , 2018 .
[35] Reza Gheissari,et al. On the spectral gap of spherical spin glass dynamics , 2016, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.
[36] Reza Gheissari,et al. Bounding Flows for Spherical Spin Glass Dynamics , 2018, Communications in Mathematical Physics.
[37] Wei-Kuo Chen,et al. Phase transition in the spiked random tensor with Rademacher prior , 2017, The Annals of Statistics.
[38] G. B. Arous,et al. The Landscape of the Spiked Tensor Model , 2017, Communications on Pure and Applied Mathematics.
[39] G. Biroli,et al. Complex Energy Landscapes in Spiked-Tensor and Simple Glassy Models: Ruggedness, Arrangements of Local Minima, and Phase Transitions , 2018, Physical Review X.