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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Research Unit 1735

Program

Schedule

  Sun, Mar 13 Mon, Mar 14 Tue, Mar 15 Wed, Mar 16 Thu, Mar 17 Fri, Mar 18
Breakfast
08:00-9:00
           

09:00-10:30

  Harrison Zhou
(Lecture 1)
Harrison Zhou
(Lecture 2)
Harrison Zhou
(Lecture 3)

Ramon van Handel

(Lecture 2)

Ramon van Handel

(Lecture 3)

Break            
11:00-12:30  

Alexandre Tsybakov

(Lecture 1)

Alexandre Tsybakov

(Lecture 2)

Ramon van Handel

(Lecture 1)

Alexandre Tsybakov

(Lecture 3)

Alexandre Tsybakov

(Lecture 4)

Lunch
12:30-13:00
          Departure

14:00-16:30

 

  Participants' Introduction Harrison Zhou
(Group Exercises)
Excursion

Ramon van Handel

(Group Exercises)

16:30-18:00 Arrival Research Unit Talks Harrison Zhou
(Discussion)

Ramon van Handel

(Discussion)

 
Dinner
18:00-19:00
         
    Poster Session      

 

Lecture Series

This year's lecture series will be given by

 

ramon2.jpg

 
Ramon van Handel

Structured random matrices

Princeton University, USA

 

   
Lecture notes:
Structured random matrices

 

Background material:

Terence Tao "Topics in random matrix theory"    

Roman Vershynin "Introduction to the non-asymptotic analysis of random matrices"

 

   
     
   

 

       

tsybakov.jpg

 
Alexandre Tsybakov

Aggregation of estimators

Crest & Université Paris 6, France

   
 

 

References:

  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.
  2. Rigollet, P., Tsybakov, A.B. (2012) Sparse estimation by exponential weighting. Statistical Science, v. 27, 558–575.
  3. Tsybakov, A.B. (2003) Optimal rates of aggregation. Proceedings of COLT-2003,  Lecture Notes in Artificial Intelligence, v.2777, 303-313 .
  4. Rigollet, P., Tsybakov, A.B. (2011) Exponential Screening and optimal rates of sparse estimation. Annals of Statistics, v.39, 731-771.
  5. Dalalyan, A., Tsybakov, A.B. (2008) Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity. Machine Learning, v.72, 39-61.
  6. Dai, D., Rigollet, P., and Zhang, T.  (2012) Deviation optimal learning using greedy Q-aggregation. Annals of Statistics, v. 40, 1878-1905.
  7. Bellec, P. C. (2014). Optimal bounds for aggregation of affine estimators.
 

 

Comments:

  Items 1 and 2 are survey papers close to the material of the lectures.
  Item 3 is a starting paper on optimal rates of aggregation.
  Items 4 and 5 are devoted to detailed study of exponentially weighted aggregation.
  Items 6 and 7 are devoted to detailed study of Q-aggregation.
 

 

 

 

 

zhou.jpg

   
Harrison Huibin Zhou

Network Analysis and Beyond

Yale University, USA

 
   
     
In this short course some statistical optimalities in network analysis such as graphon estimation and community detection will be discussed.    

 

Tentatively topics include:

   
1. Graphon estimation: Minimax Upper and Lower Bounds    
2. Structural Linear Models: Rate-optimal Bayesian Posterior Contraction    
3. Community Detection for (Degree Corrected) Stochastic Block Models: Minimax Upper and Lower Bounds    
4. Community Detection for (Degree Corrected) Stochastic Block Models: Computationally Feasible Algorithms    

 

References:

   
1. Rate-optimal Graphon Estimation (with C. Gao and Y. Lu), Ann. Stat., 2015.    
2. A General Framework for Bayes Structured Linear Models (with C. Gao and A. W. van der Vaart).    
3. Optimal Rates of Structured Matrix Estimation and Completion (with O. Klopp, Y. Lu, S. Negahban, S. Tsybakov), in preparation.    
4. Minimax Rates of Community Detection in Stochastic Block Models (with A. Zhang), Ann. Stat., to appear.    
5. Achieving Optimal Misclassication Proportion in Stochastic Block Model (with C. Gao, Z. Ma, and A. Zhang).    

 

Poster Session

All participants are encouraged to present their work in a poster session on Tuesday evening.

 

Participants Short Introduction

All participants briefly introduce themselves and their research interests within ca. 2 minutes on Monday afternoon, supported by one or at most two slides. Please send your slide(s) until March 10 as a single .pdf-file to for1735.math@lists.uni-hamburg.de.