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In this technical note, we give two extensions of the classical Fano inequality in information theory.
Notes for Transmission of Information, MIT course 6.574
R. M. Fano · 1952
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A lower bound on the risks of nonparametric estimates of densities in the uniform metric
R. Z. Has’minskii · 1978
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Statistical Estimation: Asymptotic Theory
I. A. Ibragimov and R. Z. Has’minskii · 1981
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Approximation dans les espaces métriques et théorie de l’estimation
L. Birgé · 1983
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Entropy and Information Theory
R. M. Gray · 1990
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Minimax risk over ℓ p \ell_{p} -balls for ℓ q \ell_{q} -error
D. L. Donoho and I. M. Johnstone · 1994
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Assouad, Fano, and Le Cam
B. Yu · 1997
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Convergence of Probability Measures
P. Billingsley · 1999
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Information-theoretic determination of minimax rates of convergence
Y. Yang and A. Barron · 1999
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A new lower bound for multiple hypothesis testing
L. Birgé · 2005
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Elements of Information Theory, Second Edition
T. M. Cover and J. A. Thomas · 2006
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The Dantzig selector: statistical estimation when p p is much larger than n n
E. J. Candes and T. Tao · 2007
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Simultaneous analysis of Lasso and Dantzig selector
P. Bickel, Y. Ritov, and A. Tsybakov · 2009
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Information theoretic bounds for compressed sensing
S. Aeron, V. Saligrama, and M. Zhao · 2010
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The convex geometry of linear inverse problems
V. Chandrasekaran, B. Recht, P. Parrilo, and A. S. Willsky · 2012
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Information-theoretic limits of selecting binary graphical models in high dimensions
N. P. Santhanam and M. J. Wainwright · 2012
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How well can we estimate a sparse vector
E. J. Candès and M. A. Davenport · 2013
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Local privacy and statistical minimax rates
J. C. Duchi, M. I. Jordan, and M. J. Wainwright · 2013
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Volume ratio, sparsity, and minimaxity under unitarily invariant norms
Z. Ma and Y. Wu · 2013
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Sparse Recovery and Fourier Sampling
E. Price · 2013
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Minimax rates of estimation for high-dimensional linear regression over ℓ q \ell_{q} -balls
G. Raskutti, M. J. Wainwright, and B. Yu · 2011
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Information-theoretic lower bounds for distributed estimation with communication constraints
Y. Zhang, J. C. Duchi, M. I. Jordan, and M. J. Wainwright · 2013
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