Collaborative Research: Sufficient Dimension Reduction for High Dimensional Data with Applications in Bioinformatics

Abstract

proposals: 0405360 and 0405681

PIs: Cook & Li

COLLABORATIVE RESEARCH: Dimension Reduction with application to

bioinformatics

As represented in the existing literature, sufficient dimension reduction (SDR)

encompasses model-free methods for linearly reducing the dimension of the

predictor vector in regression and classification problems without loss of

information. SDR methodology has a brief but striking record of success,

although its inferential foundations are relatively narrow and the restriction

to linear reductions can be limiting in some applications. The investigators

and their co-authors expand the inferential foundations of SDR through the

development of optimal methods within the context of linear reduction and the

study of new nonlinear reduction methods. The new optimal reduction methods

permit the investigators to derive model-free tests of conditional independence,

which are roughly data-analytic equivalents of t-tests on coefficients in model-

based linear regression. They emphasize bioinformatics applications in general

and the analysis of data from high-throughput genomic technologies in

particular.

The computer revolution has produced an unprecedented capacity for data

generation, processing and storage, with the consequence that data reduction is

paramount in many research areas and business applications. For instance,

genomic technology can produce measurements for thousands of genes across

multiple tissue samples, and WalMart makes over 20 million transactions daily.

The development of diagnostics for breast cancer based on fine needle aspiration

can involve the study of numerous measurements on extracted cells across

hundreds of patients. In response to this proliferation of information, the

investigators and their colleagues study methods for reducing data to

an essential core. Their approach is unique because their overarching goal

is reduction without loss of information on the issues under consideration.

In the development of diagnostics for breast cancer, this goal translates

into reducing numerous cell measurements to an index that can be used to

classify a breast mass as malignant or benign without loss of information,

allowing the physician to present a more informed recommendation to the patient.