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Data processing inequalities for $f$-divergences can be sharpened using constants called "contraction coefficients" to produce strong data processing inequalities.
H. O. Hirschfeld, “A connection between correlation and contingency,” Mathematical Proceedings of the Cambridge Philosophical Society , vol. 31, no. 4, pp. 520–524, October 1935
1935
Earlier work this paper cites.
H. Gebelein, “Das statistische problem der korrelation als variations- und eigenwertproblem und sein zusammenhang mit der ausgleichsrechnung,” Zeitschrift für Angewandte Mathematik und Mechanik , vol. 21, no. 6, pp. 364–379, December 1941
1941
Earlier work this paper cites.
R. L. Dobrushin, “Central limit theorem for nonstationary Markov chains. I,” Theory of Probability and Its Applications , vol. 1, no. 1, pp. 65–80, 1956
1956
Earlier work this paper cites.
C. E. Shannon, “The zero error capacity of a noisy channel,” IRE Transactions on Information Theory , vol. 2, no. 3, pp. 706–715, September 1956
1956
Earlier work this paper cites.
O. V. Sarmanov, “Maximal correlation coefficient (non-symmetric case),” Doklady Akademii Nauk SSSR , vol. 121, no. 1, pp. 52–55, 1958, in Russian
1958
Earlier work this paper cites.
H. O. Lancaster, “The structure of bivariate distributions,” The Annals of Mathematical Statistics , vol. 29, no. 3, pp. 719–736, 1958
1958
Earlier work this paper cites.
A. Rényi, “On measures of dependence,” Acta Mathematica Academiae Scientiarum Hungarica , vol. 10, no. 3-4, pp. 441–451, 1959
1959
Earlier work this paper cites.
I. Csiszár, “Eine informationstheoretische ungleichung und ihre anwendung auf den beweis der ergodizität von Markoffschen ketten,” Publications of the Mathematical Institute of the Hungarian Academy of Sciences, ser. A , vol. 8, pp. 85–108, January 1963
1963
Earlier work this paper cites.
R. B. Ash, Information Theory , ser. Interscience Tracts in Pure and Applied Mathematics. New York: John Wiley & Sons, Inc., 1965, no. 19
1965
Earlier work this paper cites.
S. M. Ali and S. D. Silvey, “A general class of coefficients of divergence of one distribution from another,” Journal of the Royal Statistical Society, Series B (Methodological) , vol. 28, no. 1, pp. 131–142, 1966
1966
Earlier work this paper cites.
——, “Information-type measures of difference of probability distributions and indirect observations,” Studia Scientiarum Mathematicarum Hungarica , vol. 2, pp. 299–318, January 1967
1967
Earlier work this paper cites.
——, The Chi-Squared Distribution . New York: John Wiley & Sons Inc., 1969
1969
Earlier work this paper cites.
I. Csiszár, “A class of measures of informativity of observation channels,” Periodica Mathematica Hungaria , vol. 2, no. 1-4, pp. 191–213, March 1972
1972
Earlier work this paper cites.
J. Ziv and M. Zakai, “On functionals satisfying a data-processing theorem,” IEEE Transactions on Information Theory , vol. IT-19, no. 3, pp. 275–283, May 1973
1973
Earlier work this paper cites.
M. Zakai and J. Ziv, “A generalization of the rate-distortion theory and applications,” in Information Theory New Trends and Open Problems , ser. CISM International Centre for Mechanical Sciences (Courses and Lectures), G. Longo, Ed. Vienna: Springer, 1975, vol. 219, pp. 87–123
1975
Earlier work this paper cites.
H. S. Witsenhausen, “On sequences of pairs of dependent random variables,” SIAM Journal on Applied Mathematics , vol. 28, no. 1, pp. 100–113, January 1975
1975
Earlier work this paper cites.
R. Ahlswede and P. Gács, “Spreading of sets in product spaces and hypercontraction of the Markov operator,” The Annals of Probability , vol. 4, no. 6, pp. 925–939, December 1976
1976
Earlier work this paper cites.
J. Körner and K. Marton, “Comparison of two noisy channels,” in Topics in Information Theory (Second Colloq., Keszthely, 1975) , Amsterdam: North-Holland, 1977, p. 411�423
1977
Earlier work this paper cites.
E. Seneta, “Coefficients of ergodicity: Structure and applications,” Advances in Applied Probability , vol. 11, no. 3, pp. 576–590, September 1979
1979
Earlier work this paper cites.
I. Vincze, “On the concept and measure of information contained in an observation,” in Contributions to Probability: A Collection of Papers Dedicated to Eugene Lukacs , J. Gani and V. K. Rohatgi, Eds. New York: Academic Press, 1981, pp. 207–214
1981
Earlier work this paper cites.
——, Non-negative Matrices and Markov Chains , 2nd ed., ser. Springer Series in Statistics. New York: Springer, 1981
1981
Earlier work this paper cites.
M. J. Greenacre, Theory and Applications of Correspondence Analysis. San Diego, CA, USA: Academic Press, March 1984
1984
Earlier work this paper cites.
L. Breiman and J. H. Friedman, “Estimating optimal transformations for multiple regression and correlation,” Journal of the American Statistical Association , vol. 80, no. 391, pp. 580–598, September 1985
1985
Earlier work this paper cites.
L. Le Cam, Asymptotic Methods in Statistical Decision Theory , ser. Springer Series in Statistics. New York: Springer-Verlag, 1986
1986
Earlier work this paper cites.
F. Liese and I. Vajda, Convex Statistical Distances , ser. Teubner-Texte Zur Mathematik. Leipzig, Germany: Teubner, 1987, vol. 95
1987
Earlier work this paper cites.
M. Greenacre and T. Hastie, “The geometric interpretation of correspondence analysis,” Journal of the American Statistical Association , vol. 82, no. 398, pp. 437–447, June 1987
1987
Earlier work this paper cites.
A. Dembo, T. M. Cover, and J. A. Thomas, “Information theoretic inequalities,” IEEE Transactions on Information Theory , vol. 37, no. 6, pp. 1501–1518, November 1991
1991
Earlier work this paper cites.
J. E. Cohen, Y. Iwasa, G. Rautu, M. B. Ruskai, E. Seneta, and G. Zbăganu, “Relative entropy under mappings by stochastic matrices,” Linear Algebra and its Applications, Elsevier , vol. 179, pp. 211–235, January 1993
1993
Earlier work this paper cites.
M.-D. Choi, M. B. Ruskai, and E. Seneta, “Equivalence of certain entropy contraction coefficients,” Linear Algebra and its Applications, Elsevier , vol. 208-209, pp. 29–36, September 1994
1994
Cited alongside, same era.
F. E. Su, “Methods for quantifying rates of convergence for random walks on groups,” PhD Thesis in Mathematics, Harvard University, Cambridge, Massachusetts, 1995
1995
Cited alongside, same era.
M. van Dijk, “On a special class of broadcast channels with confidential messages,” IEEE Transactions on Information Theory , vol. 43, no. 2, pp. 712–714, March 1997
1997
Cited alongside, same era.
R. Bhatia, Matrix Analysis , ser. Graduate Texts in Mathematics. New York: Springer, 1997, vol. 169
1997
Cited alongside, same era.
E. Erkip and T. M. Cover, “The efficiency of investment information,” IEEE Transactions on Information Theory , vol. 44, no. 3, pp. 1026–1040, May 1998
A. A. Gohari and V. Anantharam, “Evaluation of Marton’s inner bound for the general broadcast channel,” IEEE Transactions on Information Theory , vol. 58, no. 2, pp. 608–619, February 2012
2012
Later among the works it cites.
E. Abbe and L. Zheng, “A coordinate system for Gaussian networks,” IEEE Transactions on Information Theory , vol. 58, no. 2, pp. 721–733, February 2012
2012
Later among the works it cites.
A. Kontorovich, “Obtaining measure concentration from Markov contraction,” Markov Processes and Related Fields , vol. 18, no. 4, pp. 613–638, 2012
2012
Later among the works it cites.
2013
Later among the works it cites.
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1998
Cited alongside, same era.
J. E. Cohen, J. H. B. Kemperman, and G. Zbăganu, Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population Sciences . Ann Arbor: Birkhäuser, 1998
1998
Cited alongside, same era.
W. S. Evans and L. J. Schulman, “Signal propagation and noisy circuits,” IEEE Transactions on Information Theory , vol. 45, no. 7, pp. 2367–2373, November 1999
1999
Cited alongside, same era.
S. Amari and H. Nagaoka, Methods of Information Geometry , ser. Translations of Mathematical Monographs. New York: Oxford University Press, 2000, vol. 191
2000
Cited alongside, same era.
L. Györfi and I. Vajda, “A class of modified Pearson and Neyman statistics,” Statistics and Decisions , vol. 19, no. 3, pp. 239–251, January 2001
2001
Cited alongside, same era.
S. S. Dragomir and V. Glus̆c̆ević, “Some inequalities for the Kullback-Leibler and χ 2 \chi^{2} -distances in information theory and applications,” Tamsui Oxford Journal of Mathematical Sciences , vol. 17, no. 2, pp. 97–111, 2001
2001
Cited alongside, same era.
A. A. Fedotov, P. Harremoës, and F. Topsøe, “Refinements of Pinsker’s inequality,” IEEE Transactions on Information Theory , vol. 49, no. 6, pp. 1491–1498, June 2003
2003
Cited alongside, same era.
V. Rakočević and H. K. Wimmer, “A variational characterization of canonical angles between subspaces,” Journal of Geometry , vol. 78, no. 1, pp. 122–124, 2003
2003
Cited alongside, same era.
——, “On hypercontractivity and the mutual information between Boolean functions,” in Proceedings of the 51st Annual Allerton Conference on Communication, Control, and Computing , Allerton House, UIUC, Illinois, USA, October 2-4 2013, pp. 13–19
2013
Later among the works it cites.
R. A. Horn and C. R. Johnson, Matrix Analysis , 2nd ed. New York: Cambridge University Press, 2013
2013
Later among the works it cites.
Y.-C. Li and C.-C. Yeh, “Some equivalent forms of Bernoulli’s inequality: A survey,” Applied Mathematics , vol. 4, no. 7, pp. 1070–1093, 2013
2013
Later among the works it cites.
S.-L. Huang, A. Makur, F. Kozynski, and L. Zheng, “Efficient statistics: Extracting information from iid observations,” in Proceedings of the 52nd Annual Allerton Conference on Communication, Control, and Computing , Allerton House, UIUC, Illinois, USA, October 1-3 2014, pp. 699–706
2014
Later among the works it cites.
S. Verdú, “Total variation distance and the distribution of relative information,” in Proceedings of the Information Theory and Applications Workshop (ITA) , San Diego, CA, USA, February 9-14 2014, pp. 1–3
2014
Later among the works it cites.
C. Nair, “An extremal inequality related to hypercontractivity of Gaussian random variables,” in Proceedings of the Information Theory and Applications Workshop (ITA) , San Diego, CA, USA, February 9-14 2014, pp. 1–7
2014
Later among the works it cites.
I. Sason, “Bounds on f f -divergences and related distances,” Department of Electrical Engineering, Technion-Israel Institute of technology, Haifa, Israel, Irwin and Joan Jacobs Center for Communication and Information Technologies (CCIT) Report 859, May 2014
2014
Later among the works it cites.
A. Makur and L. Zheng, “Bounds between contraction coefficients,” in Proceedings of the 53rd Annual Allerton Conference on Communication, Control, and Computing , Allerton House, UIUC, Illinois, USA, September 29-October 2 2015, pp. 1422–1429
2015
Closest in time.
A. Makur, “A study of local approximations in information theory,” Masters Thesis in Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, June 2015
2015
Closest in time.
A. Makur, F. Kozynski, S.-L. Huang, and L. Zheng, “An efficient algorithm for information decomposition and extraction,” in Proceedings of the 53rd Annual Allerton Conference on Communication, Control, and Computing , Allerton House, UIUC, Illinois, USA, September 29-October 2 2015, pp. 972–979
2015
Closest in time.
I. Sason, “Tight bounds for symmetric divergence measures and a new inequality relating f f -divergences,” in Proceedings of the IEEE Information Theory Workshop (ITW) , Jerusalem, Israel, April 26-May 1 2015
2015
Closest in time.
Y. Polyanskiy and Y. Wu, “Dissipation of information in channels with input constraints,” IEEE Transactions on Information Theory , vol. 62, no. 1, pp. 35–55, January 2016
2016
Closest in time.
M. Raginsky, “Strong data processing inequalities and Φ \Phi -Sobolev inequalities for discrete channels,” IEEE Transactions on Information Theory , vol. 62, no. 6, pp. 3355–3389, June 2016
2016
Closest in time.
I. Sason and S. Verdú, “ f f -divergence inequalities,” IEEE Transactions on Information Theory , vol. 62, no. 11, pp. 5973–6006, November 2016
2016
Closest in time.
2016
Closest in time.
——, “Strong data-processing inequalities for channels and Bayesian networks,” in Convexity and Concentration , ser. The IMA Volumes in Mathematics and its Applications, E. Carlen, M. Madiman, and E. M. Werner, Eds., vol. 161. New York: Springer, 2017, pp. 211–249
2017
Closest in time.
Y. Polyanskiy and Y. Wu, “Lecture notes on information theory,” August 2017, Lecture Notes 6.441, Department of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts, USA
2017
Closest in time.
F. du Pin Calmon, A. Makhdoumi, M. Médard, M. Varia, M. Christiansen, and K. R. Duffy, “Principal inertia components and applications,” IEEE Transactions on Information Theory , vol. 63, no. 8, pp. 5011–5038, August 2017
2017
Closest in time.
A. Makur and L. Zheng, “Polynomial singular value decompositions of a family of source-channel models,” IEEE Transactions on Information Theory , vol. 63, no. 12, pp. 7716–7728, December 2017
2017
Closest in time.
S.-L. Huang, A. Makur, L. Zheng, and G. W. Wornell, “An information-theoretic approach to universal feature selection in high-dimensional inference,” in Proceedings of the IEEE International Symposium on Information Theory (ISIT) , Aachen, Germany, June 25-30 2017, pp. 1336–1340
2017
Closest in time.
H. Kim, W. Gao, S. Kannan, S. Oh, and P. Viswanath, “Discovering potential correlations via hypercontractivity,” Entropy , vol. 19, no. 11, pp. 1–32, November 2017
2017
Closest in time.
F. du Pin Calmon, Y. Polyanskiy, and Y. Wu, “Strong data processing inequalities for input constrained additive noise channels,” IEEE Transactions on Information Theory , vol. 64, no. 3, pp. 1879–1892, March 2018
2018
Closest in time.
A. Makur and Y. Polyanskiy, “Comparison of channels: Criteria for domination by a symmetric channel,” IEEE Transactions on Information Theory , vol. 64, no. 8, pp. 5704–5725, August 2018
2018
Closest in time.