Description Usage Arguments Details Value Author(s) References See Also Examples
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.
1 | ftf.ada(y, k = 1, tau = 1, s.max=20, eps=0.1)
|
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 |
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.
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 |
Canhong Wen, Xueqin Wang, Yanhe Shen, Aijun Zhang
Wen,C., Wang, X., Shen, Y., and Zhang, A. (2017). "L0 trend filtering", technical report.
ftf
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