Fetching the paper…
Reading the bibliography…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced.
[author] Hotelling, HaroldH. (1936). Relations between two sets of variates. Biometrika 28 321–377
1936
Earlier work this paper cites.
[author] Bartlett, Maurice SM. S. (1937). The statistical conception of mental factors. British journal of Psychology 28 97
1937
Earlier work this paper cites.
[author] Thomson, GodfreyG. (1939). THE FACTORIAL ANALYSIS OF HUMAN ABILITY. British Journal of Educational Psychology 9 188–195
1939
Earlier work this paper cites.
[author] Lawley, Derrick NormanD. N. and Maxwell, Albert ErnestA. E. (1962). Factor analysis as a statistical method. Journal of the Royal Statistical Society. Series D (The Statistician) 12 209–229
1962
Earlier work this paper cites.
[author] Davis, ChandlerC. and Kahan, William MortonW. M. (1970). The rotation of eigenvectors by a perturbation. III. SIAM Journal on Numerical Analysis 7 1–46
1970
Earlier work this paper cites.
[author] Wedin, Per-AkeP.-A. (1972). Perturbation bounds in connection with singular value decomposition. BIT Numerical Mathematics 12 99–111
1972
Earlier work this paper cites.
[author] Yu, BinB. (1997). Assouad, fano, and le cam. In Festschrift for Lucien Le Cam 423–435. Springer
1997
Earlier work this paper cites.
[author] Tipping, Michael EM. E. and Bishop, Christopher MC. M. (1999). Probabilistic principal component analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61 611–622
1999
Earlier work this paper cites.
[author] De Lathauwer, LievenL., De Moor, BartB. and Vandewalle, JoosJ. (2000). On the best rank-1 and rank-(r 1, r 2,…, rn) approximation of higher-order tensors. SIAM journal on Matrix Analysis and Applications 21 1324–1342
2000
Earlier work this paper cites.
[author] Johnstone, Iain MI. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Annals of statistics 295–327
2001
Earlier work this paper cites.
Collins, M
2002
Earlier work this paper cites.
[author] Katznelson, YitzhakY. (2004). An introduction to harmonic analysis. Cambridge University Press
2004
Earlier work this paper cites.
[author] Baik, JinhoJ., Arous, Gérard BenG. B. and Péché, SandrineS. (2005). Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. The Annals of Probability 33 1643–1697
2005
Earlier work this paper cites.
[author] Baik, JinhoJ. and Silverstein, Jack WJ. W. (2006). Eigenvalues of large sample covariance matrices of spiked population models. Journal of multivariate analysis 97 1382–1408
2006
Earlier work this paper cites.
[author] Massart, PascalP. (2007). Concentration inequalities and model selection
2007
Earlier work this paper cites.
[author] Paul, DebashisD. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statistica Sinica 1617–1642
2007
Earlier work this paper cites.
2008
Earlier work this paper cites.
2008
Earlier work this paper cites.
[author] Nadler, BoazB. (2008). Finite sample approximation results for principal component analysis: A matrix perturbation approach. The Annals of Statistics 36 2791–2817
2008
Earlier work this paper cites.
[author] Candès, Emmanuel JE. J. and Recht, BenjaminB. (2009). Exact matrix completion via convex optimization. Foundations of Computational mathematics 9 717
2009
Earlier work this paper cites.
[author] Ghosh, JoyeeJ. and Dunson, David BD. B. (2009). Default prior distributions and efficient posterior computation in Bayesian factor analysis. Journal of Computational and Graphical Statistics 18 306–320
2009
Earlier work this paper cites.
Mohamed, S
2009
Earlier work this paper cites.
[author] Fortunato, SantoS. (2010). Community detection in graphs. Physics reports 486 75–174
2010
Earlier work this paper cites.
[author] Keshavan, Raghunandan HR. H., Montanari, AndreaA. and Oh, SewoongS. (2010). Matrix completion from a few entries. IEEE Transactions on Information Theory 56 2980–2998
2010
Cited alongside, same era.
[author] Mazumder, RahulR., Hastie, TrevorT. and Tibshirani, RobertR. (2010). Spectral regularization algorithms for learning large incomplete matrices. Journal of machine learning research 11 2287–2322
2010
Cited alongside, same era.
2010
Cited alongside, same era.
[author] Koltchinskii, VladimirV., Lounici, KarimK. and Tsybakov, Alexandre BA. B. (2011). Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. The Annals of Statistics 39 2302–2329
2011
Cited alongside, same era.
Florescu, L
2016
Later among the works it cites.
[author] Owen, Art BA. B. and Wang, JingshuJ. (2016). Bi-cross-validation for factor analysis. Statistical Science 31 119–139
2016
Later among the works it cites.
Vaswani, N
2016
Later among the works it cites.
[author] Gavish, MatanM. and Donoho, David LD. L. (2017). Optimal shrinkage of singular values. IEEE Transactions on Information Theory 63 2137–2152
2017
Later among the works it cites.
Vaswani, N
2017
Later among the works it cites.
[author] Wang, WeichenW. and Fan, JianqingJ. (2017). Asymptotics of empirical eigenstructure for high dimensional spiked covariance. Annals of statistics 45 1342
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
[author] Martin, Andrew DA. D., Quinn, Kevin MK. M. and Park, Jong HeeJ. H. (2011). MCMCpack: Markov Chain Monte Carlo in R. Journal of Statistical Software 42
2011
Cited alongside, same era.
[author] Recht, BenjaminB. (2011). A simpler approach to matrix completion. Journal of Machine Learning Research 12 3413–3430
2011
Cited alongside, same era.
[author] Vershynin, RomanR. (2011). Spectral norm of products of random and deterministic matrices. Probability theory and related fields 150 471–509
2011
Cited alongside, same era.
[author] Bai, JushanJ. and Li, KunpengK. (2012). Statistical analysis of factor models of high dimension. The Annals of Statistics 40 436–465
2012
Cited alongside, same era.
[author] Bai, ZhidongZ. and Yao, JianfengJ. (2012). On sample eigenvalues in a generalized spiked population model. Journal of Multivariate Analysis 106 167–177
2012
Cited alongside, same era.
[author] Keshavan, Raghunandan HulikalR. H. (2012). Efficient algorithms for collaborative filtering, PhD thesis, Stanford University
2012
Cited alongside, same era.
[author] Boucheron, StéphaneS., Lugosi, GáborG. and Massart, PascalP. (2013). Concentration inequalities: A nonasymptotic theory of independence. Oxford university press
2013
Cited alongside, same era.
[author] Candes, Emmanuel JE. J., Sing-Long, Carlos AC. A. and Trzasko, Joshua DJ. D. (2013). Unbiased risk estimates for singular value thresholding and spectral estimators. IEEE transactions on signal processing 61 4643–4657
2013
Cited alongside, same era.
[author] Cai, Jian-FengJ.-F. and Wei, KeK. (2018). Exploiting the Structure Effectively and Efficiently in Low-Rank Matrix Recovery. Processing, Analyzing and Learning of Images, Shapes, and Forms 19 21
2018
Closest in time.
[author] Cai, T TonyT. T. and Zhang, AnruA. (2018). Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics. The Annals of Statistics 46 60–89
2018
Closest in time.
[author] Donoho, David LD. L., Gavish, MatanM. and Johnstone, Iain MI. M. (2018). Optimal shrinkage of eigenvalues in the spiked covariance model. Annals of statistics 46 1742
2018
Closest in time.
[author] Hong, DavidD., Balzano, LauraL. and Fessler, Jeffrey AJ. A. (2018). Asymptotic performance of PCA for high-dimensional heteroscedastic data. Journal of Multivariate Analysis
2018
Closest in time.
2018
Closest in time.
[author] Liu, Lydia TL. T., Dobriban, EdgarE. and Singer, AmitA. (2018). e e PCA: high dimensional exponential family PCA. Annals of Applied Statistics 12 2121–2150
2018
Closest in time.
Vaswani, N
2018
Closest in time.
[author] Zhang, AnruA., Cai, T. TonyT. T. and Wu, YihongY. (2018). Supplement to “Heteroskedastic PCA: Algorithm, Optimality, and Applications". Technical Report
2018
Closest in time.
[author] Zhang, AnruA. and Xia, DongD. (2018). Tensor SVD: Statistical and computational limits. IEEE Transactions on Information Theory 64 7311–7338
2018
Closest in time.
[author] Robin, GenevièveG., Josse, JulieJ., Moulines, ÉricÉ. and Sardy, SylvainS. (2019). Low-rank model with covariates for count data with missing values. Journal of Multivariate Analysis 173 416–434
2019
Closest in time.
[author] Cao, YuanpeiY., Zhang, AnruA. and Li, HongzheH. (2020). Multisample estimation of bacterial composition matrices in metagenomics data. Biometrika 107 75–92
2020
Closest in time.
[author] Hao, BotaoB., Zhang, AnruA. and Cheng, GuangG. (2020). Sparse and Low-Rank Tensor Estimation via Cubic Sketchings. IEEE Transactions on Information Theory 66 5927–5964
2020
Closest in time.
[author] Vaswani, NamrataN. and Narayanamurthy, PraneethP. (2020). Fast Robust Subspace Tracking via PCA in Sparse Data-dependent Noise. IEEE Journal on Selected Areas in Information Theory 1 723-744
2020
Closest in time.
[author] Zhou, ZhixinZ. and Amini, Arash AA. A. (2020). Optimal Bipartite Network Clustering. Journal of Machine Learning Research 21 1–68
2020
Closest in time.
[author] Keshavan, Raghunandan HR. H., Montanari, AndreaA. and Oh, SewoongS. (2010). Matrix completion from noisy entries. Journal of Machine Learning Research 11 2057–2078
2078
Closest in time.
[author] Candès, Emmanuel JE. J. and Tao, TerenceT. (2010). The power of convex relaxation: Near-optimal matrix completion. IEEE Transactions on Information Theory 56 2053–2080
2080
Closest in time.