T. Tony Cai

Department of Statistics

The Wharton School

University of Pennsylvania

http://stat.wharton.upenn.edu/~tcai

Half-day Short Course

The analysis of high-dimensional data now commonly arising in scientific investigations poses many statistical challenges not present in smaller scale studies. In these lectures I will discuss high-dimensional linear regression with large p and small n. This problem has attracted much recent interest in a number of fields including applied mathematics, electrical engineering, and statistics.

To provide a proper background and foundation for the main topics, we shall begin with discussions on the high-dimensional Gaussian sequence model. We then consider the linear regression y = Xβ + z, where the dimension of the signal β is much larger than the number of observations. It is now well understood that ℓ1 minimization methods provide effective ways for high dimensional sparse regression. I will present an elementary and unified analysis of the ℓ1 minimization methods including Lasso and the Dantzig Selector in three settings: noiseless, bounded error and Gaussian noise. Time  permitting, I will also discuss ℓ1 minimization approaches to sparse covariance matrix estimation.

References

[1] Cai, T., Wang, L. and Xu, G. (2009). Stable recovery of sparse signals and an oracle inequality. Technical Report.

[2] Cai, T., Wang, L. and Xu, G. (2010). Shifting inequality and recovery of sparse signals. IEEE Transactions on Signal Processing 58, 1300-1308.

[3] Candes, E. and Tao, T. (2007). The Dantzig selector: statistical estimation when p is much larger than n. Ann. Statist. 35, 2313-2351.                                                  

[4] Donoho, D. L. and Johnstone, I. M. (1994). Ideal spatial adaptation via wavelet shrinkage. Biometrika 81, 425-455.

Registration:

By Credit Card on this site or to register by check, include the check made payable to BCASA, your name, affiliation, and mail by April 9 to:

Huichao Chen, PhD
Department of Biostatistics/CBAR
Harvard University
651 Huntington Ave, FXB 607
Boston, MA 02115

Directions:

Website

Harvard/Longwood Campus Map(PDF)

Mass Transit:

The school is directly across from the Brigham Circle Green Line (E) stop on the MBTA.

By Car:

From North or South of Boston

·         Take I-93 North/South to Exit 26 (Storrow Drive).

·         Follow Storrow Drive approximately 2.5 miles to Kenmore Square/Fenway exit (on left).

·         The exit ramp forks, stay to your right.

·         Take right at first light into Kenmore Square.

·         Take leftmost fork at second light onto Brookline Avenue.

·         Follow Brookline Avenue approximately 1 mile and through a major intersection

      (Beth Israel Hospital will be on the left).

     Watch for blue and white Longwood Medical area signs.

·         Take left on Longwood Avenue.

·         Take a right on Huntington Avenue.

                                                                                  
From West of Boston

·         Take I-90 to exit 18. Follow Storrow Drive eastbound to Kenmore Square/Fenway exit.

·         Follow directions above.

or

·         Route 95 to Route 9 east.

·         Turn left on Brookline Avenue after Brookline Village intersection.

·         Turn right onto Longwood Avenue.

·         At the end of Longwood, turn right onto Huntington Avenue.  

Parking:

There are a very limited number of metered parking spaces available on Huntington Avenue in front of the HSPH.  Children's Parking Garage Open 24 hours a day, and is located across the street from the hospital's Main Entrance. It is at the corner of Blackfan Circle and Longwood Avenue.

The garage operates under the Central Paystation system in order to make exiting the garage more efficient for parkers. Parkers will need to take their tickets with them when they leave their cars. Before returning to their cars, parkers must take their tickets to the new paystation located in the garage lobby. The cashiers will process the ticket and hand it back to the parker. The parker can simply place the processed ticket in the exit gate of the garage to leave.

Other Parking Options:

You may also want to consider using the 375 Longwood Parking Lot located three blocks from the hospital at Longwood Avenue and Plymouth Street, behind Brueggers' Bagels.