Fetching the paper…
Reading the bibliography…
This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix.
Hoeffding, WassilyW. (1951). A combinatorial central limit theorem. Ann. Math. Statistics 22 558–566
1951
Earlier work this paper cites.
Hoeffding, WassilyW. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 13–30
1963
Earlier work this paper cites.
Rosenthal, Haskell P.H. P. (1970). On the subspaces of L p ( p > 2 ) L_{p}\ (p>2) spanned by sequences of independent random variables. Israel J. Math. 8 273–303
1970
Earlier work this paper cites.
Stein, CharlesC. (1972). A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability Theory 583–602. Univ. California Press, Berkeley, CA
1971
Earlier work this paper cites.
Burkholder, D. L.D. L. (1973). Distribution function inequalities for martingales. Ann. Probab. 1 19–42
1973
Earlier work this paper cites.
Lieb, Elliott H.E. H. (1973). Convex trace functions and the Wigner–Yanase–Dyson conjecture. Adv. Math. 11 267–288
1973
Earlier work this paper cites.
Nagaev, S. V.S. V. andPinelis, I. F.I. F. (1977). Some inequalities for the distributions of sums of independent random variables. Theory Probab. Appl. 22 248–256
1977
Earlier work this paper cites.
Lust-Piquard, FrançoiseF. (1986). Inégalités de Khintchine dans C p ( 1 < p < ∞ ) C_{p}\ (1<p<\infty) . C. R. Acad. Sci. Paris Sér. I Math. 303 289–292
1986
Earlier work this paper cites.
McDiarmid, ColinC. (1989). On the method of bounded differences. In Surveys in Combinatorics, 1989 (Norwich, 1989). London Mathematical Society Lecture Note Series 141 148–188. Cambridge Univ. Press, Cambridge
1989
Earlier work this paper cites.
Lust-Piquard, FrançoiseF. andPisier, GillesG. (1991). Noncommutative Khintchine and Paley inequalities. Ark. Mat. 29 241–260
1991
Earlier work this paper cites.
Petz, DénesD. (1994). A survey of certain trace inequalities. In Functional Analysis and Operator Theory (Warsaw, 1992). Banach Center Publ. 30 287–298. Polish Acad. Sci., Warsaw
1992
Earlier work this paper cites.
Pinelis, IosifI. (1994). Optimum bounds for the distributions of martingales in Banach spaces. Ann. Probab. 22 1679–1706
1994
Earlier work this paper cites.
Bhatia, RajendraR. (1997). Matrix Analysis. Graduate Texts in Mathematics 169. Springer, New York
1997
Earlier work this paper cites.
Pisier, GillesG. andXu, QuanhuaQ. (1997). Noncommutative martingale inequalities. Comm. Math. Phys. 189 667–698
1997
Earlier work this paper cites.
Rudelson, M.M. (1999). Random vectors in the isotropic position. J. Funct. Anal. 164 60–72
1999
Earlier work this paper cites.
Buchholz, ArturA. (2001). Operator Khintchine inequality in noncommutative probability. Math. Ann. 319 1–16
2001
Earlier work this paper cites.
Ledoux, MichelM. (2001). The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs 89. Amer. Math. Soc., Providence, RI
2001
Earlier work this paper cites.
Ahlswede, RudolfR. andWinter, AndreasA. (2002). Strong converse for identification via quantum channels. IEEE Trans. Inform. Theory 48 569–579
2002
Cited alongside, same era.
Paulsen, VernV. (2002). Completely Bounded Maps and Operator Algebras. Cambridge Studies in Advanced Mathematics 78. Cambridge Univ. Press, Cambridge
2002
Cited alongside, same era.
Junge, MariusM. andXu, QuanhuaQ. (2003). Noncommutative Burkholder/Rosenthal inequalities. Ann. Probab. 31 948–995
2003
Cited alongside, same era.
Chatterjee, SouravS. (2007). Stein’s method for concentration inequalities. Probab. Theory Related Fields 138 305–321
2007
Cited alongside, same era.
Rudelson, MarkM. andVershynin, RomanR. (2007). Sampling from large matrices: An approach through geometric functional analysis. J. ACM 54 Art. 21, 19 pp. (electronic)
2007
Cited alongside, same era.
Foygel, R.R. andSrebro, N.N. (2011). Concentration-based guarantees for low-rank matrix reconstruction. J. Mach. Learn. Res. 19 315–340
2011
Later among the works it cites.
Gittens, A.A. (2011). The spectral norm error of the naïve Nyström extension. Available at \arxivurl
2011
Later among the works it cites.
2011
Later among the works it cites.
Gross, DavidD. (2011). Recovering low-rank matrices from few coefficients in any basis. IEEE Trans. Inform. Theory 57 1548–1566
2011
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Chatterjee, S.S. (2008). Concentration inequalities with exchangeable pairs. Ph.D. thesis, Stanford Univ., Palo Alto
2008
Cited alongside, same era.
Higham, Nicholas J.N. J. (2008). Functions of Matrices: Theory and Computation. SIAM, Philadelphia, PA
2008
Cited alongside, same era.
Junge, MariusM. andXu, QuanhuaQ. (2008). Noncommutative Burkholder/Rosenthal inequalities. II. Applications. Israel J. Math. 167 227–282
2008
Cited alongside, same era.
Wigderson, AviA. andXiao, DavidD. (2008). Derandomizing the Ahlswede–Winter matrix-valued Chernoff bound using pessimistic estimators, and applications. Theory Comput. 4 53–76
2008
Cited alongside, same era.
Lugosi, G.G. (2009). Concentration-of-measure inequalities. Available at http://www.econ.upf.edu/~lugosi/anu.pdf
2009
Cited alongside, same era.
2009
Cited alongside, same era.
Carlen, EricE. (2010). Trace inequalities and quantum entropy: An introductory course. In Entropy and the Quantum. Contemp. Math. 529 73–140. Amer. Math. Soc., Providence, RI
2010
Cited alongside, same era.
2011
Later among the works it cites.
Mackey, L.L., Talwalkar, A.A. andJordan, M. I.M. I. (2011). Divide-and-conquer matrix factorization. In Advances in Neural Information Processing Systems 24 (J.J. Shawe-Taylor, R. S.R. S. Zemel, P. L.P. L. Bartlett, F. C. N.F. C. N. Pereira andK. Q.K. Q. Weinberger, eds.) 1134–1142
2011
Later among the works it cites.
2011
Later among the works it cites.
Recht, BenjaminB. (2011). A simpler approach to matrix completion. J. Mach. Learn. Res. 12 3413–3430
2011
Later among the works it cites.
So, Anthony Man-ChoA. M.-C. (2011). Moment inequalities for sums of random matrices and their applications in optimization. Math. Program. 130 125–151
2011
Later among the works it cites.
Tropp, Joel A.J. A. (2011). Freedman’s inequality for matrix martingales. Electron. Commun. Probab. 16 262–270
2011
Later among the works it cites.
Chen, R. Y.R. Y., Gittens, A.A. andTropp, J. A.J. A. (2012). The masked sample covariance estimator: An analysis using matrix concentration inequalities. Information and Inference 1 2–20
2012
Closest in time.
Chiu, JiaweiJ. andDemanet, LaurentL. (2012). Matrix probing and its conditioning. SIAM J. Numer. Anal. 50 171–193
2012
Closest in time.
Hsu, DanielD., Kakade, Sham M.S. M. andZhang, TongT. (2012). Tail inequalities for sums of random matrices that depend on the intrinsic dimension. Electron. Commun. Probab. 17 13
2012
Closest in time.
Negahban, SahandS. andWainwright, Martin J.M. J. (2012). Restricted strong convexity and weighted matrix completion: Optimal bounds with noise. J. Mach. Learn. Res. 13 1665–1697
2012
Closest in time.
Tropp, J. A.J. A. (2012). User-friendly tail bounds for sums of random matrices. Found. Comput. Math. 12 389–434
2012
Closest in time.
Koltchinskii, VladimirV. (2011). Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems. Lecture Notes in Math. 2033. Springer, Heidelberg
2033
Closest in time.