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August 14, 2015 09:12
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Block principal pivoting algorithm for the L1-regularized linear regression (R)
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# = = = = = include = = = = = # | |
library(MASS) | |
# = = = = = function = = = = = # | |
obj_func <- function(y, A, x, lambda){ | |
obj_value <- 0.5 * sum((y - A%*%x)^2) + lambda * sum(abs(x)) | |
} | |
bpp <- function(A, y, lambda, Gram, intercept=TRUE){ | |
# parameter | |
K_max <- 3 | |
if(intercept){ | |
intercept <- mean(y) | |
y <- y - intercept | |
} | |
Aty <- t(A) %*% y | |
if(missing(Gram)){ | |
AtA <- t(A) %*% A | |
} | |
## step1 - - - - - | |
p <- ncol(A) | |
H <- 1:p | |
F_p <- c() | |
F_m <- c() | |
beta <- rep(0,p) | |
d <- - Aty | |
k <- K_max | |
t <- p + 1 | |
## step2 (Block Principal Pivoting) - - - - - | |
while(1){ | |
F <- union(F_p, F_m) | |
if(length(F)>0){ | |
d[F_p] <- lambda | |
d[F_m] <- -lambda | |
beta[F] <- ginv( AtA[F,F] ) %*% ( Aty[F] - d[F] ) | |
} | |
d[H] <- Aty[H] - AtA[H,F] %*% beta[F] | |
beta[H] <- 0 | |
J1 <- H[ d[H] > lambda ] | |
J2 <- H[ d[H] < -lambda ] | |
J3 <- F_p[ beta[F_p] < 0] | |
J4 <- F_m[ beta[F_m] > 0] | |
G <- c(J1,J2,J3,J4) | |
if(length(G)==0){ | |
break | |
}else if(length(G) < t){ | |
t <- length(G) | |
k <- K_max | |
G_hat <- G | |
}else{ | |
if(k >= 1){ | |
k <- k-1 | |
G_hat <- G | |
}else{ | |
k <- 0 | |
G_hat <- G[length(G)] | |
} | |
} | |
J1_hat <- intersect(G_hat, J1) | |
J2_hat <- intersect(G_hat, J2) | |
J3_hat <- intersect(G_hat, J3) | |
J4_hat <- intersect(G_hat, J4) | |
H <- union(setdiff(H,union(J1_hat,J2_hat)), union(J3_hat,J4_hat)) | |
F_p <- union(setdiff(F_p,J3_hat), J1_hat) | |
F_m <- union(setdiff(F_m,J4_hat), J2_hat) | |
} | |
return(beta) | |
} | |
## <<References>> | |
## [1] Fast Active-set-type Algorithms for L1-regularized Linear Regression | |
## Jingu Kim, Haesun Park | |
## http://jmlr.csail.mit.edu/proceedings/papers/v9/kim10a/kim10a.pdf | |
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