English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For high-dimensional classification, it is well known that naively performingthe Fisher discriminant rule leads to poor results due to diverging spectra andnoise accumulation. Therefore, researchers proposed independence rules tocircumvent the diverse spectra, and sparse independence rules to mitigate theissue of noise accumulation. However, in biological applications, there areoften a group of correlated genes responsible for clinical outcomes, and theuse of the covariance information can significantly reduce misclassificationrates. The extent of such error rate reductions is unveiled by comparing themisclassification rates of the Fisher discriminant rule and the independencerule. To materialize the gain based on finite samples, a Regularized OptimalAffine Discriminant (ROAD) is proposed based on a covariance penalty. ROADselects an increasing number of features as the penalization relaxes. Furtherbenefits can be achieved when a screening method is employed to narrow thefeature pool before hitting the ROAD. An efficient Constrained CoordinateDescent algorithm (CCD) is also developed to solve the associated optimizationproblems. Sampling properties of oracle type are established. Simulationstudies and real data analysis support our theoretical results and demonstratethe advantages of the new classification procedure under a variety ofcorrelation structures. A delicate result on continuous piecewise linearsolution path for the ROAD optimization problem at the population leveljustifies the linear interpolation of the CCD algorithm.

A ROAD to Classification in High Dimensional Space