which.region: Determine the Feasibility Region

In HDDesign: Sample Size Calculation for High Dimensional Classification Study

Description

Given the design assumption, determine which feasiblity region the design problem belongs to. The feasibility region is constructed from the asymptotic properties of the rare-and-weak model (Donoho and Jin 2009). The two groups are assumed to be equally proportioned, i.e. p_+1=p_-1=0.5. If the the problem is feasible, then the probability of correct classification (PCC) of the HCT classifer will approach 1 when the number of features goes to infinity. If the the problem is unfeasible, then the probability of correct classification (PCC) of any linear classifer will approach 0.5 when the number of features goes to infinity.

Usage

which.region(mu0, p, m, n)

Arguments

mu0	The effect size of the important features.
p	The number of the features in total.
m	The number of the important features.
n	The total sample size for the two groups.

Value

0	The classification problem belongs to the unfeasible region.
1	The classification problem belongs to the feasible region.
2	The classification problem belongs to the feasible region.
3	The classification problem belongs to the feasible region.
4	The classification problem belongs to the feasible region.

Region 1-4 are all feasible regions. Their difference is discussed in more details in ().

Author(s)

Meihua Wu <[e-mail]> Brisa N. Sanchez <[e-mail]> Peter X.K. Song <[e-mail]> Raymond Luu <[e-mail]> Wen Wang <[e-mail]>

References

Donoho, David, and Jiashun Jin. 2009. "Feature Selection by Higher Criticism Thresholding Achieves the Optimal Phase Diagram." Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences 367 (1906) (November 13): 4449-4470.

Examples

	which.region(mu0=0.4, p=500, m=10, n=80) 
	#return: 4

HDDesign documentation built on May 2, 2019, 6:41 a.m.