ftf.ada {FastSF}

Adaptive Fast Trend Filtering

Description

This is a function that adaptively solves the trend filtering problem with L0 penalty via the primal dual active set algorithm. It fits a k-th order piecewise polynomial by minimizing the number of breaks in the (k + 1)-st discrete derivative with the constraints on the least squares error.

Usage

 ftf.ada(y, k = 1, tau = 1, s.max=20, eps=0.1)

Arguments

y

Numeric vector of inputs.

k

An integer specifying the desired order of the piecewise polyomial produced by the solution of the trend filtering problem. Must be non-negative, and the default to 1 (linear trend filtering).

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 polynomial(breaks in the (k+1)-st derivative), default is 20

eps

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

Details

The L0 trend filtering fits an adaptive piecewise polynomial to linearly ordered observations with contraints on the number of knots, for a chosen integer k >= 0. The knots or the breaks in their (k + 1)-st discrete derivative are chosen adaptively based on the observations.

Value

y

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

beta

Filtered value

v

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

beta.all

Solution path of filtered 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

ftf.

Examples

set.seed(1)

sigma <- 0.5
y0 <- c((10:30)/3, (40:10)/4, 2:8)
y <- y0 + sigma*rnorm(length(y0))
re <- ftf.ada(y, k = 1, s.max = 5)