1d:T774,# Adaptive Fast Structural Filtering 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. ```r 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. ## Returns - **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 ```r 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) ```

fsf.ada function