fsf.ada: Adaptive Fast Structural Filtering

In FastSF: Fast Structural Filtering

Description

This is a function that solves the structural filtering problem with L0 penalty via the primal dual active set algorithm. It fits a non-parametric regression model by minimizing the number of nonzero values in D*beta with constraints on the least squares error.

Usage

 fsf.ada(y, D, tau=1, s.max=20,  eps=0.1, ddinv=NULL)

Arguments

y	Response sequence to be filtered.
D	Penalty matrix on coeffient beta.
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 penalized coefficient(breaks in D*beta, default is 20
eps	Early stop criterion. The algorithm stops when mean squared error is less than eps.
ddinv	The inverse matrix of D*t(D), could be NULL input.

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

plotl0.

Examples

require(limSolve)
n <- 1000
sigma <- 0.5
y0 <- rep(0,n)
y0[100:150] <- 2
y0[400:600] <- -1
y0[800:810] <- 4
y <- y0 + sigma*rnorm(n)
y[800:810] <- y0[800:810] + sigma*rnorm(11)
D0 <- matrix(0, n-1,n)
diag(D0) <- -1
for(i in 1:(n-1)) D0[i,i+1] <- 1
ddt <- D0%*%t(D0)
ddinv<- Solve.banded(ddt, 1,1, B = diag(1,dim(D0)[1]))

re <- fsf.ada(y, D0, tau = 1, s.max = 10, eps = 0.1, ddinv = ddinv)

FastSF documentation built on May 2, 2019, 8:27 a.m.