Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering

D. J. Thouless, P. W. Anderson, and R. G. Palmer, “Solution of’solvable model of a spin glass’,” Philosophical Magazine , vol. 35, no. 3, pp. 593–601, 1977

1977

Earlier work this paper cites.

S. P. Lloyd, “Least squares quantization in PCM,” IEEE Transactions on Information Theory , vol. 28, no. 2, pp. 129–137, 1982

1982

Earlier work this paper cites.

M. Mézard, G. Parisi, and M. A. Virasoro, Spin-Glass Theory and Beyond , ser. Lecture Notes in Physics. Singapore: World Scientific, 1987, vol. 9

1987

Earlier work this paper cites.

T. Watkin and J.-P. Nadal, “Optimal unsupervised learning,” Journal of Physics A: Mathematical and General , vol. 27, no. 6, p. 1899, 1994

1994

Earlier work this paper cites.

N. Barkai and H. Sompolinsky, “Statistical mechanics of the maximum-likelihood density estimation,” Physical Review E , vol. 50, no. 3, p. 1766, 1994

1994

Earlier work this paper cites.

M. Biehl and A. Mietzner, “Statistical mechanics of unsupervised structure recognition,” Journal of Physics A: Mathematical and General , vol. 27, no. 6, p. 1885, 1994

1994

Earlier work this paper cites.

A. Buhot and M. B. Gordon, “Phase transitions in optimal unsupervised learning,” Physical Review E , vol. 57, no. 3, p. 3326, 1998

1998

Earlier work this paper cites.

D. C. Hoyle and M. Rattray, “Principal-component-analysis eigenvalue spectra from data with symmetry-breaking structure,” Physical Review E , vol. 69, no. 2, p. 026124, 2004

2004

Earlier work this paper cites.

J. Baik, G. B. Arous, and S. Péché, “Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices,” The Annals of Probability , vol. 33, no. 5, pp. 1643–1697, 2005

2005

Cited alongside, same era.

M. Mézard and A. Montanari, Information, Physics, and Computation , ser. Oxford Graduate Texts. OUP Oxford, 2009

2009

Cited alongside, same era.

S. Korada and N. Macris, “Exact solution of the gauge symmetric p-spin glass model on a complete graph,” Journal of Statistical Physics , vol. 136, no. 2, pp. 205–230, 2009

2009

Cited alongside, same era.

M. Bayati and A. Montanari, “The dynamics of message passing on dense graphs, with applications to compressed sensing,” IEEE Transactions on Information Theory , vol. 57, no. 2, pp. 764–785, 2011

2011

Cited alongside, same era.

Y. Deshpande and A. Montanari, “Information-theoretically optimal sparse PCA,” in Information Theory (ISIT), 2014 IEEE International Symposium on . IEEE, 2014, pp. 2197–2201

2014

Later among the works it cites.

M. Bayati, M. Lelarge, A. Montanari et al. , “Universality in polytope phase transitions and message passing algorithms,” The Annals of Applied Probability , vol. 25, no. 2, pp. 753–822, 2015

2015

Later among the works it cites.

T. Lesieur, F. Krzakala, and L. Zdeborová, “Mmse of probabilistic low-rank matrix estimation: Universality with respect to the output channel,” in 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton) , 2015

2015

Later among the works it cites.

F. Krzakala, J. Xu, and L. Zdeborová, “Mutual information in rank-one matrix estimation,” ITW 2016, arXiv:1603.08447 , 2016

Original

2016

Closest in time.