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Structured random matrices
Princeton University, USA |
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Lecture notes: |
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Structured random matrices |
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Background material:
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Terence Tao "Topics in random matrix theory" |
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Roman Vershynin "Introduction to the non-asymptotic analysis of random matrices"
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Aggregation of estimators
Crest & Université Paris 6, France
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References:
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1. Tsybakov, A.B. (2014) Aggregation and minimax optimality in high-dimensional estimation. In: Proceedings of the International Congress of Mathematicians (Seoul, August 2014), v.3, 225-246. |
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2. Rigollet, P., Tsybakov, A.B. (2012) Sparse estimation by exponential weighting. Statistical Science, v. 27, 558–575. |
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3. Tsybakov, A.B. (2003) Optimal rates of aggregation. Proceedings of COLT-2003, Lecture Notes in Artificial Intelligence, v.2777, 303-313 . |
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4. Rigollet, P., Tsybakov, A.B. (2011) Exponential Screening and optimal rates of sparse estimation. Annals of Statistics, v.39, 731-771. |
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5. Dalalyan, A., Tsybakov, A.B. (2008) Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity. Machine Learning, v.72, 39-61. |
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6. Dai, D., Rigollet, P., and Zhang, T. (2012) Deviation optimal learning using greedy Q-aggregation. Annals of Statistics, v. 40, 1878-1905. |
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7. Bellec, P. C. (2014). Optimal bounds for aggregation of affine estimators. |
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Comments:
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Items 1 and 2 are survey papers close to the material of the lectures. |
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Item 3 is a starting paper on optimal rates of aggregation. |
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Items 4 and 5 are devoted to detailed study of exponentially weighted aggregation. |
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Items 6 and 7 are devoted to detailed study of Q-aggregation. |
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Network Analysis and Beyond
Yale University, USA
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In this short course some statistical optimalities in network analysis such as graphon estimation and community detection will be discussed. |
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Tentatively topics include:
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1. Graphon estimation: Minimax Upper and Lower Bounds |
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2. Structural Linear Models: Rate-optimal Bayesian Posterior Contraction |
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3. Community Detection for (Degree Corrected) Stochastic Block Models: Minimax Upper and Lower Bounds |
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4. Community Detection for (Degree Corrected) Stochastic Block Models: Computationally Feasible Algorithms |
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References:
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1. Rate-optimal Graphon Estimation (with C. Gao and Y. Lu), Ann. Stat., 2015. |
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2. A General Framework for Bayes Structured Linear Models (with C. Gao and A. W. van der Vaart). |
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3. Optimal Rates of Structured Matrix Estimation and Completion (with O. Klopp, Y. Lu, S. Negahban, S. Tsybakov), in preparation. |
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4. Minimax Rates of Community Detection in Stochastic Block Models (with A. Zhang), Ann. Stat., to appear. |
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5. Achieving Optimal Misclassication Proportion in Stochastic Block Model (with C. Gao, Z. Ma, and A. Zhang). |
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