Topics

• Use of banding as a form of regularization
• Identification and estimation of graphical structures
• Penalized likelihood approach : choice of penalty; optimization method
• Models for correlation matrices in finance and estimation techniques

Suggested reading materials

• P. Bickel and E. Levina (2006): Regularized estimation of large covariance matrices
• N. Meinshausen and P. Buhlman (2006) : High dimensional graphs and variable selection with the lasso
• T. Guhr and B. Kaelber (2003): A new method to estimate the noise in a financial correlation matrix

Topics

• Tutorial by Eitan Greenshtein : [Handout]
• Concept of persistence in high dimensional problems
• Regularization for optimizing a quadratic form involving covariance matrix

Suggested reading materials

• E. Greenshtein and Y. Ritov (2004) : Persistence in high dimensional linear predictor-selection and the virtue of over-parametrization
• E. Greenshtein (2006) : Best subset selection, persistence in high dimensional statistical learning, and l_1 optimization

• Jack Silverstein's talk in the Berkeley node seminar : On eigenvalues of large dimensional sample covariance matrices

Topics

• Tutorial by Debashis Paul : Functional linear regression, factor models and estimation of eigenvalues and eigenvectors : [Outline], [ Board slides ]

Suggested reading materials

• P. Hall and J. Horowitz (2004) : Methodology and convergence rates for functional linear regression
• T. Tony Cai and P. Hall (2005) : Prediction in functional linear regression

• Supersymmetry in random matrix theory
• Reduction of a certain noise component in financial correlation matrices

Topics

• Identifying the structure of population covariance matrix from a sample for large dimensional data [ Board slides ]
• Summary of discussion

• Peter Bickel's talk in Berkeley node seminar : Regularized covariance matrix estimation [Abstract], [Talk slides]
• Ofer Zeitouni's talk : Some results on the limiting empirical spectral distributions when observations are non-i.i.d.

Topics

• Penalized likelihood for Gaussian graphical models with L_1 penalty
• Optimization problems - Maxdet algorithm
• Tapering and its effect on covariance matrices for stationary processes

Suggested reading materials

• M.Yuan and Y.Lin (2005) : Model selection and estimation in Gaussian graphical model

• Cari Kaufman's talk : Covariance tapering for likelihood based estimation in large spatial datasets
• Ming Yuan's talk : Model selection for Gaussian graphical models
• Sandrine Peche's talk in Berkeley node seminar : Universality results for the largest eigenvalue of deformed Wigner matrices

Topics

• Summary of discussions

• Jinchi Lv's talk : High dimensional covariance matrix estimation using a factor model
• Eitan Greenshtein's talk in Berkeley node seminar : Estimation of a high dimensional vector of means : A non-Bayesian empirical Bayes approach

Suggested reading materials

• Bai, P., Shen, H. and Truong, Y. (2006) : Robust independent component analysis for fMRI

• Young Truong's talk in Berkeley node seminar : Spatio-temporal modeling for fMRI data

Topics

• Issue of stability in model selection for high dimensional problems

Suggested reading materials

• Breiman, L. (1996) : Heuristics of instability and stabilization in model selection, Annals of Statistics 24 , 2350-2383.

• Greg Rempala's talk : Symmetric functionals on random matrices and matchings in bipartite random graphs [Abstract] , [Slides]

• Alexander Soshnikov's talk in the Berkeley node seminar : On the largest eigenvalue of random matrices
• Amir Dembo's talk in the Berkeley node seminar : Two results about large random matrices

Topics

• Regularization and stability of estimates

Suggested reading materials

• Bickel, P. and Li, B. (2006) : Regularization in statistics, Test 15 , 271-344.

Suggested reading materials

• Wainwright, M. (2006) : Sharp thresholds for high-dimensional and noisy recovery of sparsity

• Martin Wainwright's talk in the Berkeley node seminar : Sharp thresholds for sparsity recovery in the high-dimensional and noisy setting using l_1 relaxations
• Donald Richards' talk in the Berkeley node seminar : Models for real-world Investors, and the abyss between financial engineering and value investing

• Summary of discussions

• Leonard Choup's talk in the Berkeley node seminar : Finite N largest eigenvalue distribution