-
1
-
-
0036495139
-
Strong converse for identification via quantum channels.IEEE Trans
-
MR1889969
-
AHLSWEDE, R. andWINTER, A. (2002). Strong converse for identification via quantum channels.IEEE Trans. Inform. Theory 48 569-579. MR1889969.
-
(2002)
Inform. Theory
, vol.48
, pp. 569-579
-
-
Ahlswede, R.1
Winter, A.2
-
2
-
-
0003362033
-
Matrix Analysis.
-
Springer, New York.MR1477662
-
BHATIA, R. (1997). Matrix Analysis. Graduate Texts in Mathematics 169. Springer, New York.MR1477662
-
(1997)
Graduate Texts in Mathematics
, vol.169
-
-
Bhatia, R.1
-
3
-
-
0035607466
-
Operator Khintchine inequality in noncommutative probability
-
MR1812816
-
BUCHHOLZ, A. (2001). Operator Khintchine inequality in noncommutative probability. Math.319 1-16. MR1812816
-
(2001)
Math.Ann.
, vol.319
, pp. 1-16
-
-
Buchholz, A.1
-
4
-
-
0002455942
-
Distribution function inequalities for martingales
-
MR0365692
-
BURKHOLDER, D. L. (1973). Distribution function inequalities for martingales. Ann. Probab.1 19-42. MR0365692
-
(1973)
Ann. Probab.
, vol.1
, pp. 19-42
-
-
Burkholder, D.L.1
-
5
-
-
79955368914
-
Trace inequalities and quantum entropy: An introductory course.
-
Amer. Math. Soc., Providence, RI.MR2681769
-
CARLEN, E. (2010). Trace inequalities quantum entropy: An introductory course. In Entropy and the Quantum. Contemp. Math. 529 73-140. Amer. Math. Soc., Providence, RI.MR2681769
-
(2010)
In Entropy and the Quantum. Contemp. Math.
, vol.529
, pp. 73-140
-
-
Carlen, E.1
-
6
-
-
33847617461
-
Stein's method for concentration inequalities
-
MR2288072
-
CHATTERJEE, S. (2007). Stein's method for concentration inequalities. Probab. Theory Related Fields 138 305-321. MR2288072
-
(2007)
Probab. Theory Related Fields
, vol.138
, pp. 305-321
-
-
Chatterjee, S.1
-
8
-
-
84890096199
-
The masked sample covariance estimator:An analysis using matrix concentration inequalities
-
CHEN, R. Y., GITTENS, A. and TROPP, J. A. (2012). The masked sample covariance estimator: An analysis using matrix concentration inequalities. Information and Inference 12-20.
-
(2012)
Information and Inference
, pp. 12-20
-
-
Chen, R.Y.1
Gittens, A.2
Tropp, J.A.3
-
11
-
-
84861408239
-
Matrix probing and its conditioning
-
MR2888309
-
CHIU, J. andDEMANET, L. (2012).Matrix probing and its conditioning. SIAM J. Numer. Anal. 50 171-193. MR2888309
-
(2012)
SIAM J. Numer. Anal.
, vol.50
, pp. 171-193
-
-
Chiu, J.1
Demanet, L.2
-
13
-
-
84893503709
-
Concentration-based guarantees for low-rank matrix reconstruction
-
FOYGEL, R. and SREBRO, N. (2011). Concentration-based guarantees for low-rank matrix reconstruction. J. Mach. Learn. Res.,19:315-340
-
(2011)
J. Mach. Learn. Res.
, vol.19
, pp. 315-340
-
-
Foygel, R.1
Srebro, N.2
-
16
-
-
79951886985
-
Recovering low-rank matrices from few coefficients in any basis.
-
MR2815834
-
GROSS, D. (2011). Recovering low-rank matrices from few coefficients in any basis. IEEE Trans. Inform. Theory 57 1548-1566. MR2815834
-
(2011)
IEEE Trans. Inform. Theory
, vol.57
, pp. 1548-1566
-
-
Gross, D.1
-
17
-
-
69949191032
-
Functions of Matrices
-
Theory and Computation. SIAM, Philadelphia, PA. MR2396439
-
HIGHAM, N. J. (2008). Functions of Matrices: Theory and Computation. SIAM, Philadelphia, PA. MR2396439
-
(2008)
-
-
Higham, N.J.1
-
18
-
-
0000680233
-
A combinatorial central limit theorem
-
MR0044058
-
HOEFFDING, W. (1951). A combinatorial central limit theorem. Ann. Math. Statistics 22 558- 566. MR0044058
-
(1951)
Ann. Math. Statistics
, vol.22
, pp. 558-566
-
-
Hoeffding, W.1
-
19
-
-
84947403595
-
Probability inequalities for sums of bounded random variables
-
MR0144363
-
HOEFFDING, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 13-30. MR0144363
-
(1963)
J. Amer. Statist. Assoc.
, vol.58
, pp. 13-30
-
-
Hoeffding, W.1
-
20
-
-
84859392380
-
Tail inequalities for sums of random matrices that depend on the intrinsic dimension
-
MR2900355
-
HSU, D., KAKADE, S. M. and ZHANG, T. (2012). Tail inequalities for sums of random matrices that depend on the intrinsic dimension. Electron. Commun. Probab. 17 13. MR2900355
-
(2012)
Electron. Commun. Probab.
, vol.17
, pp. 13
-
-
Hsu, D.1
Kakade, S.M.2
Zhang, T.3
-
21
-
-
0038674589
-
Noncommutative Burkholder/Rosenthal inequalities
-
MR1964955
-
JUNGE, M. and XU, Q. (2003). Noncommutative Burkholder/Rosenthal inequalities. Ann. Probab. 31 948-995. MR1964955
-
(2003)
Ann. Probab.
, vol.31
, pp. 948-995
-
-
Junge, M.1
Xu, Q.2
-
22
-
-
57849107738
-
Noncommutative Burkholder/Rosenthal inequalities. II. Applications
-
MR2448025
-
JUNGE, M. and XU, Q. (2008). Noncommutative Burkholder/Rosenthal inequalities. II. Applications. Israel J. Math. 167 227-282. MR2448025
-
(2008)
Israel J. Math.
, vol.167
, pp. 227-282
-
-
Junge, M.1
Xu, Q.2
-
25
-
-
0012942540
-
The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs
-
RI. MR1849347
-
LEDOUX, M. (2001). The Concentration of Measure Phenomenon. Mathematical Surveys and Monographs 89. Amer. Math. Soc., Providence, RI. MR1849347
-
(2001)
Amer. Math. Soc., Providence
, vol.89
-
-
Ledoux, M.1
-
26
-
-
36649022319
-
Convex trace functions and the Wigner-Yanase-Dyson conjecture
-
MR0332080
-
LIEB, E. H. (1973). Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math. 11 267-288. MR0332080
-
(1973)
Adv. Math.
, vol.11
, pp. 267-288
-
-
Lieb, E.H.1
-
29
-
-
0000426206
-
Noncommutative Khintchine and Paley inequalities
-
MR1150376
-
LUST-PIQUARD, F. and PISIER, G. (1991). Noncommutative Khintchine and Paley inequalities. Ark. Mat. 29 241-260. MR1150376
-
(1991)
Ark. Mat.
, vol.29
, pp. 241-260
-
-
Lust-piquard, F.1
Pisier, G.2
-
30
-
-
84856484853
-
-
In Advances in Neural Information Processing Systems (J. Shawe-Taylor, R. S. Zemel, P. L. Bartlett, F. C. N. Pereira and K. Q. Weinberger, eds.)
-
MACKEY, L., TALWALKAR, A. and JORDAN, M. I. (2011). Divide-and-conquer matrix factorization. In Advances in Neural Information Processing Systems 24 (J. Shawe-Taylor, R. S. Zemel, P. L. Bartlett, F. C. N. Pereira and K. Q. Weinberger, eds.) 1134-1142.
-
(2011)
Divide-and-conquer matrix factorization.
, vol.24
, pp. 1134-1142
-
-
Mackey, L.1
Talwalkar, A.2
Jordan, M.I.3
-
31
-
-
0001035413
-
On the method of bounded differences.
-
London Mathematical Society Lecture Note Series Cambridge Univ. Press, Cambridge. MR1036755
-
MC DIARMID, C. (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. MR1036755
-
(1989)
In Surveys in Combinatorics, 1989 (Norwich, 1989).
, vol.141
, pp. 148-188
-
-
Mc Diarmid, C.1
-
33
-
-
0000143520
-
Some inequalities for the distributions of sums of independent random variables
-
NAGAEV, S. V. and PINELIS, I. F. (1977). Some inequalities for the distributions of sums of independent random variables. Theory Probab. Appl. 22 248-256.
-
(1977)
Theory Probab. Appl.
, vol.22
, pp. 248-256
-
-
Nagaev, S.V.1
Pinelis, I.F.2
-
34
-
-
84862020232
-
Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
-
MR2930649
-
NEGAHBAN, S. and WAINWRIGHT, M. J. (2012). Restricted strong convexity and weighted matrix completion: Optimal bounds with noise. J. Mach. Learn. Res. 13 1665-1697. MR2930649
-
(2012)
J. Mach. Learn. Res.
, vol.13
, pp. 1665-1697
-
-
Negahban, S.1
Wainwright, M.J.2
-
36
-
-
77955434395
-
Sums of random Hermitian matrices and an inequality by Rudelson
-
MR2653725
-
OLIVEIRA, R. I. (2010). Sums of random Hermitian matrices and an inequality by Rudelson. Electron. Commun. Probab. 15 203-212. MR2653725
-
(2010)
Electron. Commun. Probab.
, vol.15
, pp. 203-212
-
-
Oliveira, R.I.1
-
37
-
-
0242554667
-
-
Cambridge Studies in Advanced Mathematics Cambridge Univ. Press, Cambridge,MR1976867
-
PAULSEN, V. (2002). Completely Bounded Maps and Operator Algebras. Cambridge Studies in Advanced Mathematics Cambridge Univ. Press, Cambridge.177. MR1976867
-
(2002)
Completely Bounded Maps and Operator Algebras
, vol.177
-
-
Paulsen, V.1
-
38
-
-
0012475858
-
A survey of certain trace inequalities. In Functional Analysis and Operator Theory (Warsaw, 1992)
-
Polish Acad. Sci., Warsaw. MR1285615
-
PETZ, D. (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. MR1285615
-
(1994)
Banach Center Publ.
, vol.30
, pp. 287-298
-
-
Petz, D.1
-
39
-
-
0001638327
-
Optimum bounds for the distributions of martingales in Banach spaces
-
MR1331198
-
PINELIS, I. (1994). Optimum bounds for the distributions of martingales in Banach spaces. Ann. Probab. 22 1679-1706. MR1331198
-
(1994)
Ann. Probab.
, vol.22
, pp. 1679-1706
-
-
Pinelis, I.1
-
40
-
-
0031549892
-
Noncommutative martingale inequalities
-
MR1482934
-
PISIER, G. and XU, Q. (1997). Noncommutative martingale inequalities. Comm. Math. Phys. 189 667-698. MR1482934
-
(1997)
Comm. Math. Phys.
, vol.189
, pp. 667-698
-
-
Pisier, G.1
Xu, Q.2
-
41
-
-
78349246612
-
Compressive sensing and structured random matrices. In Theoretical Foundations and Numerical Methods for Sparse Recovery.
-
de Gruyter, Berlin. MR2731597
-
RAUHUT, H. (2010). Compressive sensing and structured random matrices. In Theoretical Foundations and Numerical Methods for Sparse Recovery. Radon Ser. Comput. Appl. Math. 9 1-92. de Gruyter, Berlin. MR2731597
-
(2010)
Radon Ser. Comput. Appl. Math.
, vol.9
, pp. 1-92
-
-
Rauhut, H.1
-
42
-
-
84856009825
-
A simpler approach to matrix completion
-
MR2877360
-
RECHT, B. (2011). A simpler approach to matrix completion. J. Mach. Learn. Res. 12 3413-3430. MR2877360
-
(2011)
J. Mach. Learn. Res.
, vol.12
, pp. 3413-3430
-
-
Recht, B.1
-
43
-
-
51249187914
-
On the subspaces of Lp (p > 2) spanned by sequences of independent random variables
-
MR0271721
-
ROSENTHAL, H. P. (1970). On the subspaces of Lp (p > 2) spanned by sequences of independent random variables. Israel J. Math. 8 273-303. MR0271721
-
(1970)
Israel J. Math.
, vol.8
, pp. 273-303
-
-
Rosenthal, H.P.1
-
44
-
-
0033541884
-
Random vectors in the isotropic position
-
MR1694526
-
RUDELSON, M. (1999). Random vectors in the isotropic position. J. Funct. Anal. 164 60-72. MR1694526
-
(1999)
J. Funct. Anal.
, vol.164
, pp. 60-72
-
-
Rudelson, M.1
-
45
-
-
34547728320
-
Sampling from large matrices: An approach through geometric functional analysis
-
(electronic). MR2351844
-
RUDELSON, M. and VERSHYNIN, R. (2007). Sampling from large matrices: An approach through geometric functional analysis. J. ACM 54 Art. 21, 19 pp. (electronic). MR2351844
-
(2007)
J. ACM 54 Art.
, vol.21
, pp. 19
-
-
Rudelson, M.1
Vershynin, R.2
-
46
-
-
81255179658
-
Moment inequalities for sums of random matrices and their applications in optimization
-
MR2853163
-
SO, A. M.-C. (2011). Moment inequalities for sums of random matrices and their applications in optimization. Math. Program. 130 125-151. MR2853163
-
(2011)
Math. Program.
, vol.130
, pp. 125-151
-
-
So, A.M.-C.1
-
47
-
-
0000457248
-
A bound for the error in the normal approximation to the distribution of a sum of dependent random variables.
-
(Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, CA. MR0402873
-
STEIN, C. (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. MR0402873
-
(1972)
In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability Probability Theory
, vol.2
, pp. 583-602
-
-
Stein, C.1
-
48
-
-
84859402279
-
Freedman's inequality for matrix martingales. Electron
-
MR2802042
-
TROPP, J. A. (2011). Freedman's inequality for matrix martingales. Electron. Commun. Probab. 16 262-270. MR2802042
-
(2011)
Commun. Probab.
, vol.16
, pp. 262-270
-
-
Tropp, J.A.1
-
49
-
-
84864315555
-
User-friendly tail bounds for sums of random matrices
-
MR2946459
-
TROPP, J. A. (2012). User-friendly tail bounds for sums of random matrices. Found. Comput. Math. 12 389-434. MR2946459
-
(2012)
Found. Comput. Math.
, vol.12
, pp. 389-434
-
-
Tropp, J.A.1
-
50
-
-
77951670104
-
Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications
-
MR2403380
-
WIGDERSON, A. and XIAO, D. (2008). Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications. Theory Comput. 4 53-76. MR2403380
-
(2008)
Theory Comput
, vol.4
, pp. 53-76
-
-
Wigderson, A.1
Xiao, D.2
|