Online Learning for Sparse PCA in High Dimensions: Exact Dynamics and Phase Transitions

E. Oja and J. Karhunen, “On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix,” J. Math. Anal. Appl. , vol. 106, no. 1, pp. 69–84, 1985

1985

Earlier work this paper cites.

H. Risken, The Fokker-Planck equation: Methods of solution and applications , 2nd ed. New York: Springer-Verlag, 1996

Original

1996

Earlier work this paper cites.

P. Billingsley, Convergence of probability measures , 2nd ed. New York: Wiley, 1999

1999

Earlier work this paper cites.

I. M. Johnstone, “On the distribution of the largest eigenvalue in principal components analysis,” Ann. Stat. , vol. 29, no. 2, pp. 295–327, Apr. 2001

2001

Earlier work this paper cites.

O. Kallenberg, Foundations of modern probability , 2nd ed. Springer, 2002

2002

Earlier work this paper cites.

I. T. Jolliffe, N. T. Trendafilov, and M. Uddin, “A modified principal component technique based on the LASSO,” J. Comp. Graph. Stat. , vol. 12, no. 3, pp. 531–547, Sep. 2003

2003

Earlier work this paper cites.

H. Zou, T. Hastie, and R. Tibshirani, “Sparse principal component analysis,” J. Comp. Graph. Stat. , vol. 15, no. 2, pp. 265–286, 2006

2006

Earlier work this paper cites.

A. d’Aspremont, L. El Ghaoui, M. I. Jordan, and G. R. G. Lanckriet, “A direct formulation for sparse PCA using semidefinite programming,” SIAM Rev. , vol. 49, no. 3, pp. 434–448, Jan. 2007

2007

Cited alongside, same era.

B. Nadler, “Finite sample approximation results for principal component analysis: A matrix perturbation approach,” Ann. Stat. , vol. 36, no. 6, pp. 2791–2817, 2008

2008

Cited alongside, same era.

H. Shen and J. Z. Huang, “Sparse principal component analysis via regularized low rank matrix approximation,” J. Maultivar. Anal. , vol. 99, no. 6, pp. 1015–1034, Jul. 2008

2008

Cited alongside, same era.

I. M. Johnstone and A. Y. Lu, “On consistency and sparsity for principal components analysis in high dimensions,” J. Am. Stat. Assoc. , vol. 104, no. 486, pp. 682–693, Jun. 2009

2009

Cited alongside, same era.

R. Arora, A. Cotter, K. Livescu, and N. Srebro, “Stochastic optimization for PCA and PLS,” in Proc. 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , Oct. 2012

2012

Later among the works it cites.

Z. Ma, “Sparse principal component analysis and iterative thresholding,” Ann. Stat. , vol. 41, no. 2, pp. 772–801, Apr. 2013

2013

Later among the works it cites.

A. Balsubramani, S. Dasgupta, and Y. Freund, “The fast convergence of incremental PCA,” in Adv. Neural Inf. Process. Syst. , 2013

2013

Later among the works it cites.

Y. Deshpande and A. Montanari, “Information-theoretically optimal sparse PCA,” in IEEE International Symposium on Information Theory , 2014

2014

Later among the works it cites.

N. Parikh and S. Boyd, “Proximal Algorithms,” Foundations and Trends in Optimization , vol. 1, no. 3, Jan. 2014

2014