OGA {Ohit}

Orthogonal greedy algorithm

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)