Extremely Efficient Procedures for Composite L0 Penalized Estimation(1d).
AMIAS(y, D_type="fused.1d", composite=FALSE, W_type="identity", k1=NULL,
k2=1, D=NULL, W=NULL, T1=NULL, T2=min(10,nmw[1]-1), rho1=n^2, rho2=n^2, h=5,
tao=1, outer_itermax=20, select_max=min(20,nm[1]-1), eps=0.1, iter_max=10,
smooth=TRUE, ...)Observe sequence, with length n.
Specifcation of \(D\), either one of "fused.1d" or "fused.tfk". when \(D\) is set, it would be "user".
Whether to use composite L0 penalty.
Specifcation of \(W\), either one of "identity", "fused.1d" or "fused.tfk". when \(W\) is set, it would be "user".
Integer: used to generate \(D\) for polynomial trend filtering of order k(see genDtf1d for Details).
Integer: used to generate \(W\) for polynomial trend filtering of order k(see genDtf1d for Details).
Matrix in the penalty item(see Details).
Matrix in the penalty item for composite L0 panalty(see Details).
The number of change point to detect in \(D\beta\) penalty,default is NULL and it would be selected adatively.
The number of change point to detect in \(W\beta\) penalty,default is 10.
The lagrange operator of the argumented lagrange form for split item in \(D\beta\).
The lagrange operator of the argumented lagrange form for split item in \(W\beta\).
Arguments for my.rollmean.
Number: increment of the T1 sequence in adative function algorithm.
The maximum iterations to select T1 adatively.
The maximum number of change point to detect.
The threshold to stop the adative AMIAS algorithm, when \(MSE\) is smaller than \(eps\).
The maximum iterations to setect change point for given T1.
Whether to smooth the data, if TRUE, it smooth the input data.
Other arguments.
A list with class attribute 'AMIAS.1d' and named components:
The call that produced this object.
Observe sequence, if smooth, the smooth y would be return.
The fitting coefficients in the noparameter model.
Whether to use composite L0 penalty.
Integer: used to generate D for polynomial trend filtering of order k(see Details).
Integer: used to generate W for polynomial trend filtering of order k(see Details).
The split variable of the argumented lagrange form in \(D\beta\)
The lagrange operator of the argumented lagrange form in \(D\beta\) for linear item.
The split variable of the argumented lagrange form in \(W\beta\)
The lagrange operator of the argumented lagrange form in \(W\beta\) for linear item.
Degree of freedom of the seleted model.
The number of change point to detect in \(W\beta\) penalty.
Specifcation of \(D\), default is "fused.1d". when D is set, it would be "user".
Specifcation of \(D\), default is "identity". when W is set, it would be "user".
The lagrange operator of the argumented lagrange form in \(D\beta\) for split item.
The lagrange operator of the argumented lagrange form in \(W\beta\) for split item.
Number: increment of the T1 sequence in adative function algorithm.
The threshold to stop the adative AMIAS algorithm, when MSE is smaller than eps.
The iterations to setect change point for given T1
The maximum iterations to setect change point for given T1
Whether to smooth the data.
The maximum iterations to select T1 adatively.
The maximum number of change point to detect.
The Parameter of models implied by T1 and T2 is fit by primal dual active set
and this is the number of change point to detect in AMIAS. Note that the
model to fit is $$ \beta_i + \sigma_i,$$ and the objective function
is $$1/2*RSS + \lambda_1*penalty_1 + \lambda_2*penalty_2(\lambda_2 = 0 for
non-composite type),$$ where $$panalty_1 = |D\beta|_0 , panalty_2 = |W\beta|_0.$$
If the parameter T1 is not set, a sequence of T1 would be fitted
by increment tao adatively. For details, see the AMIAS paper.
Wen, C., Zhu, J., Wang, X., and Zhang, A. (2017) L0 trend filtering for piecewise smooth modeling, technique report.
# NOT RUN {
library(AMIAS)
set.seed(12580)
n <- 100
sigma <- 0.3
y0 <- rep(0,n)
y0[10:15] <- 2
y0[40:60] <- -1
y0[80:82] <- 4
y <- y0 + sigma*rnorm(n)
y[80:82] <- y0[80:82] + sigma*rnorm(3)
AMIAS(y, h=1, outer_itermax=5)
# }
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