主 题: Impact of dimensionality and correlation learning
报告人: Prof.Jian Qing Fan (Princeton University)
时 间: 2008-10-31 下午 2:30 - 3:30
地 点: 理科一号楼 1560
Model selection and classification using high-dimensional features arise
frequently in many contemporary statistical studies such as tumor
classification
using microarray or other high-throughput data. The impact of
dimensionality on
classifications is largely poorly understood. We first demonstrate that
even for the independence classification rule, classification using
all the features can be as bad as the random guessing due to noise
accumulation in estimating population centroids in high-dimensional
feature space. In fact, we demonstrate further that almost all
linear discriminants can perform as bad as the random guessing.
Thus, it is paramount important to select a subset of important
features for high-dimensional classification, resulting in Features
Annealed Independence Rules (FAIR). The connections with the sure
independent screeing
(SIS) and iterative SIS(ISIS) of Fan and Lv (2007) in model selection
will be elucidated and extended. Further extension of the correlation
learning results
in independence learning for feature selection in general loss functions.
The choice of the optimal number of
features, or equivalently, the threshold value of the test
statistics are proposed based on an upper bound of the
classification error. Simulation studies and real data analysis
support our theoretical results and demonstrate convincingly the
advantage of our new classification procedure.
