Seminar 16th December 2010 4 p.m. University of Southampton, Building 2, Room 3041
Robust covariance estimation using mathematical programming
Dr Tri-Dung Nguyen
University of Southampton, School of Mathematics
- Web page
- http://www.cormsis.soton.ac.uk/seminars/default.php
- Categories
- Optimisation, Scientific Computing
- Submitter
- Petrina Butler
Abstract
The outlier detection problem and the robust covariance estimation problem are often interchangeable.
Without outliers, the classical method of Maximum Likelihood Estimation (MLE) can be used to estimate parameters of a known distribution from observational data.
When outliers are present, they dominate the log likelihood function causing the MLE estimators to be pulled toward them.
Many robust statistical methods have been developed to detect outliers and to produce estimators that are robust against deviation from model assumptions.
However, the existing methods suffer either from computational complexity when problem size increases or from giving up desirable properties, such as affine equivariance.
An alternative approach is to design a special mathematical programming model to find the optimal weights for all the observations, such that at the optimal solution, outliers are given with smaller weight and can be detected.
This method produces a covariance estimator that has the following properties:
- First, it is affine equivariant.
- Second, it is computationally efficient even for large problem sizes.
- Third, it easy to incorporate prior beliefs into the estimator by using semi-definite programming.
The accuracy of this method is tested for different contamination models, including the most recently proposed ones.
Speaker
A guest of Professor Lyn Thomas, Director of CORMSIS and Professor of Management Science.
Contact
Katarzyna (Kasia) Bijak
CORMSIS Facilitator
Centre for Operational Research, Management Science and Information Systems
School of Management/School of Mathematics
02380 598964