OGA: Orthogonal greedy algorithm

In Ohit: OGA+HDIC+Trim and High-Dimensional Linear Regression Models

Description

Select valuables via orthogonal greedy algorithm (OGA).

Usage

OGA(X, y, Kn = NULL, c1 = 5)

Arguments

X	Input matrix of n rows and p columns.
y	Response vector of length n.
Kn	The number of OGA iterations. Kn must be a positive integer between 1 and p. Default is Kn=max(1, min(floor(c1*sqrt(n/log(p))), p)), where c1 is a tuning parameter.
c1	The tuning parameter for the number of OGA iterations. Default is c1=5.

Value

n	The number of observations.
p	The number of input variables.
Kn	The number of OGA iterations.
J_OGA	The index set of Kn variables sequencially selected by OGA.

Author(s)

Hai-Tang Chiou, Ching-Kang Ing and Tze Leung Lai.

References

Ing, C.-K. and Lai, T. L. (2011). A stepwise regression method and consistent model selection for high-dimensional sparse linear models. Statistica Sinica, 21, 1473–1513.

Examples

# Example setup (Example 3 in Section 5 of Ing and Lai (2011))
n = 400
p = 4000
q = 10
beta_1q = c(3, 3.75, 4.5, 5.25, 6, 6.75, 7.5, 8.25, 9, 9.75)
b = sqrt(3/(4 * q))

x_relevant = matrix(rnorm(n * q), n, q)
d = matrix(rnorm(n * (p - q), 0, 0.5), n, p - q)
x_relevant_sum = apply(x_relevant, 1, sum)
x_irrelevant = apply(d, 2, function(a) a + b * x_relevant_sum)
X = cbind(x_relevant, x_irrelevant)
epsilon = rnorm(n)
y = as.vector((x_relevant %*% beta_1q) + epsilon)

# Select valuables via OGA
OGA(X, y)

Example output

$n
[1] 400

$p
[1] 4000

$Kn
[1] 34

$J_OGA
 [1] 2382  712   10    9    8    7    5    6    4    3    2    1 2331 2558 1226
[16] 2093 3448 3201 2345 2275 3101 2319  387 2471 2430 1623 1992 3756 2268  845
[31] 2463 1907 3444 3147

Ohit documentation built on May 1, 2019, 8:43 p.m.