References
Textbooks and expository articles on minimax theory
- Tsybakov, A. (2008). Introduction to Nonparametric Estimation,
Springer.
- Yu. B. (1997) Assuad, Fano, and Le Cam, Festschrift for Lucien Le
Cam,
pdf.
- John Duchi's notes on minimaxity from his class Statistics
311/Electrical Engineering 377.
Lecture 1, Tue Oct 27
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Various minimax rates for sparse regression can be obtained
- G. Raskutti, M. Wainwright, and B. Yu. Minimax rates of estimation for high-dimensional linear regression over lq balls. IEEE Transactions on Information Theory archive
57(10), 6976-6994.
- Rigollet, P. and Tsybakov, A.B. (2012). Exponential screening and optimal
rates of sparse estimation. Annals of Statistics, 39, 731-771.
- E. J. Candès and M. A. Davenport. How well can we estimate a sparse vector? Applied and Computational Harmonic Analysis 34, 317--323.
Lecture 4, Tue Oct 27
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- Yang and Barron (1999). Information-theoretic determination of minimax
rates of convergence, Annals of Statistics, 27(5), 1564-1599.
Lecture 7, Tue Nov 12
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- Wasserman, L. (2005). All of Nonparametric Statistics, Springer.
Sections 7.8, 7.0, 7.10 and 7.11.
- Tony Cai, Mark G. Low (2006), Adaptive Confidence Balls, Annals of
Statistics, 34 (1), 202 - 228.
- Baraud. Y. (2004). Confidence balls in Gaussian regression
Ann. Statist. 32 (2004), no. 2, 528--551.
Lecture 8, Thu Nov 19
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- Ingster, I. and Suslina, I. A. (2003). Nonparametric Goodness-of-Fit Testing Under Gaussian Models
Authors: Yu. I. Ingster, Springer. Sections 2.1 - 2.6.
- Arias-Castro, E., Candès, E.J., and Plan, Y. (2011). Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism, Ann. Statistics, 39(5), 2533-2556.
- Addario-Berry, L., Broutin,N., Devroye, L., Lugosi, G (2010). On combinatorial testing problems, Annals of Statistics, 38(5),, 3063-3092.
- Krishnamurthy, A. (2015). Minimaxity in Structured Normal Means
Inference, arxiv: 1506.07902
Lecture 9, Tue Nov 24
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- Kim, J., Rinaldo, A. and Wasserman, L. (2015). Minimax rates for
estimating the dimension of a manifold. preprint.
- Castro, R. and Nowak, R. (2008). Minimax Bounds for Active Learning, IEEE,
54(5), 2339-2353.
Lecture 11, Tue Dec 1
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- Raskutti, G., Wainwright, M. and Yu, B. (2012). Minimax-Optimal Rates
For Sparse Additive Models Over Kernel Classes Via Convex Programming,
JMLR, 3(1), 389-427
- Kirthevasan Kandasamy, Yaoliang Yu, (2015). Additive Approximations in High Dimensional Nonparametric
Regression via the SALSA. df
Lecture 12, Thu Dec 3
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- Vu and Lei (2013). Minimax Rates of Estimation for Sparse PCA in High
Dimensions, 1202.0786, AISTATS 2013
- Vu and Lei (2013). Minimax sparse principal subspace estimation in
high dimensions, Annals of Statistics, 41(6), 2905-2947.
Lecture 12, Thu Dec 3
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- Vu and Lei (2013). Minimax Rates of Estimation for Sparse PCA in High
Dimensions, 1202.0786, AISTATS 2013
- Vu and Lei (2013). Minimax sparse principal subspace estimation in
high dimensions, Annals of Statistics, 41(6), 2905-2947.
Lecture 13, Tue Dec 8
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- Birnbaum, A., Johnstone, I.M., Nadler, B. and Debashis, P. (2013).
Minimax bounds for sparse PCA with noisy high-dimensional data, Annals
of Statistics, 41(3), 1055-1084.
- Yuchen Zhang, Martin J. Wainwright, Michael I. Jordan: Lower bounds on
the performance of polynomial-time algorithms for sparse linear
regression. COLT 2014: 921-948
Lecture 14, Thu Dec 10
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- Cai, T.T., Zhang, C-H., Zhou, H. H. (2010). Optimal rates of
convergence for covariance matrix estimationi, Annals of Statistics,
38(4), 2118-2144.
- Castro, E.A., Devenport, M. and Candes, E. (20113). On the Fundamental
Limits of Adaptive Sensing, IEEE TRANSACTIONS ON INFORMATION THEORY,
59(1).
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