fsfused.ada {FastSF}

Adaptive Fast Sparse Fused Regression

Description

This is a function that solves the L0 fused problem via the primal dual active set algorithm in sparse condition. It fits a piecewise constant regression model by minimizing the number of breaks in derivative with constraints on the least squares error.

Usage

 fsfused.ada(y, tau=1, s.max=20, T, eps=0.1)

Arguments

y

Numeric vector of inputs.

tau

Step length for searching the best model, i.e., in the t-th iteration, a model with tau*t knots will be fitted.

s.max

The maximum nubmer of knots in the piecewise constant(breaks in the (k+1)-st derivative), default is 20

T

Number of non-zero values in fitted coefficient.

eps

Early stop criterion. The algorithm stops when mean squared error is less than eps

Value

y

The observed response vector. Useful for plotting and other methods.

beta

Fitted value

v

Primal coefficient. The indexes of the nonzero values correspond to the locations of the breaks.

beta.all

Solution path of fitted value, beta, corresponding to different degrees of freedom.

df

A vector giving an unbiased estimate of the degrees of freedom of the fit, i.e., the number of nonzero values in v.

Author(s)

Canhong Wen, Xueqin Wang, Yanhe Shen, Aijun Zhang

References

Wen,C., Wang, X., Shen, Y., and Zhang, A. (2017). "L0 trend filtering", technical report.

See Also

fsfused.

Examples

n <- 1000
sigma <- 0.5
y0 <- rep(0,n)
y0[100:150] <- 2.5
y0[400:600] <- -2.4
y0[800:810] <- 4
y <- y0 + sigma*rnorm(n)

re = fsfused.ada(y, tau=1, s.max=10, T = 260, eps=1.2*sigma^2)