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#' Orthogonalizing EM with precomputed XtX
#'
#' @param xtx input matrix equal to \code{crossprod(x) / nrow(x)}.
#' where \code{x} is the design matrix.
#' It is highly recommended to scale by the number of rows in \code{x}.
#' If \code{xtx} is scaled, \code{xty} must also be scaled or else results may be meaningless!
#' @param xty numeric vector of length \code{nvars}. Equal to \code{crosprod(x, y) / nobs}.
#' It is highly recommended to scale by the number of rows in \code{x}.
#' @param family \code{"gaussian"} for least squares problems, \code{"binomial"} for binary response.
#' (only \code{gaussian} implemented currently)
#' @param penalty Specification of penalty type. Choices include:
#' \itemize{
#' \item \code{"elastic.net"} - elastic net penalty, extra parameters: \code{"alpha"}
#' \item \code{"lasso"} - lasso penalty
#' \item \code{"ols"} - ordinary least squares
#' \item \code{"mcp"} - minimax concave penalty, extra parameters: \code{"gamma"}
#' \item \code{"scad"} - smoothly clipped absolute deviation, extra parameters: \code{"gamma"}
#' \item \code{"mcp.net"} - minimax concave penalty + l2 penalty, extra parameters:
#' \code{"gamma"}, \code{"alpha"}
#' \item \code{"scad.net"} - smoothly clipped absolute deviation + l2 penalty, extra parameters:
#' \code{"gamma"}, \code{"alpha"}
#' \item \code{"grp.lasso"} - group lasso penalty
#' \item \code{"grp.lasso.net"} - group lasso penalty + l2 penalty, extra parameters: \code{"alpha"}
#' \item \code{"grp.mcp"} - group minimax concave penalty, extra parameters: \code{"gamma"}
#' \item \code{"grp.scad"} - group smoothly clipped absolute deviation, extra parameters: \code{"gamma"}
#' \item \code{"grp.mcp.net"} - group minimax concave penalty + l2 penalty, extra parameters: \code{"gamma"}, \code{"alpha"}
#' \item \code{"grp.scad.net"} - group smoothly clipped absolute deviation + l2 penalty, extra parameters: \code{"gamma"}, \code{"alpha"}
#' \item \code{"sparse.grp.lasso"} - sparse group lasso penalty (group lasso + lasso), extra parameters: \code{"tau"}
#' }
#' Careful consideration is required for the group lasso, group MCP, and group SCAD penalties. Groups as specified by the \code{groups} argument
#' should be chosen in a sensible manner.
#' @param lambda A user supplied lambda sequence. By default, the program computes
#' its own lambda sequence based on \code{nlambda} and \code{lambda.min.ratio}. Supplying
#' a value of lambda overrides this.
#' @param nlambda The number of lambda values - default is 100.
#' @param lambda.min.ratio Smallest value for lambda, as a fraction of \code{lambda.max}, the (data derived) entry
#' value (i.e. the smallest value for which all coefficients are zero). The default
#' depends on the sample size nobs relative to the number of variables nvars. The default is 0.0001
#' @param alpha mixing value for \code{elastic.net}, \code{mcp.net}, \code{scad.net}, \code{grp.mcp.net}, \code{grp.scad.net}.
#' penalty applied is (1 - alpha) * (ridge penalty) + alpha * (lasso/mcp/mcp/grp.lasso penalty)
#' @param gamma tuning parameter for SCAD and MCP penalties. must be >= 1
#' @param tau mixing value for \code{sparse.grp.lasso}. penalty applied is (1 - tau) * (group lasso penalty) + tau * (lasso penalty)
#' @param groups A vector of describing the grouping of the coefficients. See the example below. All unpenalized variables
#' should be put in group 0
#' @param scale.factor of length \code{nvars === ncol(xtx) == length(xty)} for scaling columns of \code{x}. The standard deviation
#' for each column of \code{x} is a common choice for \code{scale.factor}. Coefficients will be returned on original scale. Default is
#' no scaling.
#' @param penalty.factor Separate penalty factors can be applied to each coefficient.
#' This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables,
#' which implies no shrinkage, and that variable is always included in the model. Default is 1 for all
#' variables.
#' @param group.weights penalty factors applied to each group for the group lasso. Similar to \code{penalty.factor},
#' this is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some groups,
#' which implies no shrinkage, and that group is always included in the model. Default is sqrt(group size) for all
#' groups.
#' @param maxit integer. Maximum number of OEM iterations
#' @param tol convergence tolerance for OEM iterations
#' @param irls.maxit integer. Maximum number of IRLS iterations
#' @param irls.tol convergence tolerance for IRLS iterations. Only used if \code{family != "gaussian"}
#' @return An object with S3 class \code{"oem"}
#' @import Rcpp
#' @import Matrix
#' @import foreach
#' @export
#' @references Huling. J.D. and Chien, P. (2022), Fast Penalized Regression and Cross Validation for Tall Data with the oem Package.
#' Journal of Statistical Software 104(6), 1-24. doi:10.18637/jss.v104.i06
#' @examples
#' set.seed(123)
#' n.obs <- 1e4
#' n.vars <- 100
#'
#' true.beta <- c(runif(15, -0.25, 0.25), rep(0, n.vars - 15))
#'
#' x <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
#' y <- rnorm(n.obs, sd = 3) + x %*% true.beta
#'
#' fit <- oem(x = x, y = y,
#' penalty = c("lasso", "elastic.net",
#' "ols",
#' "mcp", "scad",
#' "mcp.net", "scad.net",
#' "grp.lasso", "grp.lasso.net",
#' "grp.mcp", "grp.scad",
#' "sparse.grp.lasso"),
#' standardize = FALSE, intercept = FALSE,
#' groups = rep(1:20, each = 5))
#'
#' xtx <- crossprod(x) / n.obs
#' xty <- crossprod(x, y) / n.obs
#'
#' fit.xtx <- oem.xtx(xtx = xtx, xty = xty,
#' penalty = c("lasso", "elastic.net",
#' "ols",
#' "mcp", "scad",
#' "mcp.net", "scad.net",
#' "grp.lasso", "grp.lasso.net",
#' "grp.mcp", "grp.scad",
#' "sparse.grp.lasso"),
#' groups = rep(1:20, each = 5))
#'
#' max(abs(fit$beta[[1]][-1,] - fit.xtx$beta[[1]]))
#' max(abs(fit$beta[[2]][-1,] - fit.xtx$beta[[2]]))
#'
#' layout(matrix(1:2, ncol = 2))
#' plot(fit.xtx)
#' plot(fit.xtx, which.model = 2)
#'
oem.xtx <- function(xtx,
xty,
family = c("gaussian", "binomial"),
penalty = c("elastic.net",
"lasso",
"ols",
"mcp", "scad",
"mcp.net", "scad.net",
"grp.lasso", "grp.lasso.net",
"grp.mcp", "grp.scad",
"grp.mcp.net", "grp.scad.net",
"sparse.grp.lasso"),
lambda = numeric(0),
nlambda = 100L,
lambda.min.ratio = NULL,
alpha = 1,
gamma = 3,
tau = 0.5,
groups = numeric(0),
scale.factor = numeric(0),
penalty.factor = NULL,
group.weights = NULL,
maxit = 500L,
tol = 1e-7,
irls.maxit = 100L,
irls.tol = 1e-3)
{
this.call <- match.call()
family <- match.arg(family)
## don't default to fitting all penalties!
## only allow multiple penalties if the user
## explicitly chooses multiple penalties
if ("penalty" %in% names(this.call))
{
penalty <- match.arg(penalty, several.ok = TRUE)
} else
{
penalty <- match.arg(penalty, several.ok = FALSE)
}
dims <- dim(xtx)
if (is.null(dims))
{
stop("xtx must be a matrix")
}
if (dims[1] != dims[2]) stop("xtx must be a square matrix equal to X'X. do NOT provide design matrix")
p <- dims[2]
xty <- drop(xty)
if (p != NROW(xty)) stop("xty must have length equal to the number of columns and rows of xtx. do NOT provide response vector")
if(inherits(xtx, "sparseMatrix"))
{
stop("Sparse matrices not allowed")
}
if (p < 2)
{
stop("xtx must have at least two columns")
}
if (family == "binomial") stop("binomial not implemented yet")
if (is.null(penalty.factor)) {
penalty.factor <- rep(1, p)
}
varnames <- colnames(xtx)
if(is.null(varnames)) varnames = paste("V", seq(p), sep="")
if (length(penalty.factor) != p) {
stop("penalty.factor must have same length as number of columns in x")
}
penalty.factor <- drop(penalty.factor)
if (any(grep("grp", penalty) > 0)) {
if (length(groups) != p) {
stop("groups must have same length as number of columns in x")
}
unique.groups <- sort(unique(groups))
zero.idx <- unique.groups[which(unique.groups == 0)]
groups <- drop(groups)
if (!is.null(group.weights))
{
if (length(zero.idx) > 0)
{
# force group weight for 0 group to be zero
group.weights[zero.idx] <- 0
}
group.weights <- drop(group.weights)
if (length(group.weights) != length(unique.groups)) {
stop("group.weights must have same length as the number of groups")
}
group.weights <- as.numeric(group.weights)
} else {
# default to sqrt(group size) for each group weight
group.weights <- numeric(0)
}
} else {
unique.groups <- numeric(0)
group.weights <- numeric(0)
}
if (is.null(lambda.min.ratio)) {
lambda.min.ratio <- 0.0001
} else {
lambda.min.ratio <- as.numeric(lambda.min.ratio)
}
if(lambda.min.ratio >= 1 | lambda.min.ratio <= 0)
{
stop("lambda.min.ratio must be between 0 and 1")
}
if(nlambda[1] <= 0)
{
stop("nlambda must be a positive integer")
}
if (!is.list(lambda))
{
lambda <- sort(as.numeric(lambda), decreasing = TRUE)
## ensure is double type
if (length(lambda) > 0)
{
lambda <- as.double(lambda)
}
lambda <- rep(list(lambda), length(penalty))
} else
{
if (length(lambda) != length(penalty))
{
stop("If list of lambda vectors is provided, it must be
the same length as the number of penalties fit")
}
nlambda.tmp <- length(lambda[[1]])
for (l in 1:length(lambda))
{
## check to make sure all things in the list are actually vectors
if ( is.null(lambda[[l]]) || length(lambda[[l]]) < 1 )
{
stop("Provided lambda vector must have at least one value")
}
if (length(lambda[[l]]) != nlambda.tmp)
{
stop("All provided lambda vectors must have same length")
}
## ensure is double type
lambda[[l]] <- as.double(sort(as.numeric(lambda[[l]]), decreasing = TRUE))
}
}
## ensure types are correct
## before sending to c++
groups <- as.integer(groups)
unique.groups <- as.integer(unique.groups)
nlambda <- as.integer(nlambda)
alpha <- as.double(alpha)
gamma <- as.double(gamma)
tau <- as.double(tau)
tol <- as.double(tol)
irls.tol <- as.double(irls.tol)
irls.maxit <- as.integer(irls.maxit)
maxit <- as.integer(maxit)
if (length(scale.factor) > 0)
{
if (length(scale.factor) != p) stop("scale.factor must be same length as xty (nvars)")
scale.factor <- as.double(scale.factor)
}
if(maxit <= 0 | irls.maxit <= 0)
{
stop("maxit and irls.maxit should be positive")
}
if(tol < 0 | irls.tol < 0)
{
stop("tol and irls.tol should be nonnegative")
}
options <- list(maxit = maxit,
tol = tol,
irls_maxit = irls.maxit,
irls_tol = irls.tol)
res <- switch(family,
"gaussian" = oemfit.xtx.gaussian(xtx, xty,
family,
penalty,
groups,
unique.groups,
group.weights,
lambda,
nlambda,
lambda.min.ratio,
alpha,
gamma,
tau,
scale.factor,
penalty.factor,
options),
"binomial" = oemfit.xtx.binomial(xtx, xty,
family,
penalty,
groups,
unique.groups,
group.weights,
lambda,
nlambda,
lambda.min.ratio,
alpha,
gamma,
tau,
scale.factor,
penalty.factor,
options)
)
for (i in 1:length(penalty))
{
if (penalty[i] == "ols") res$beta[[i]] <- matrix(res$beta[[i]], ncol = 1)
rownames(res$beta[[i]]) <- varnames
}
names(res$beta) <- penalty
nz <- lapply(1:length(res$beta), function(m)
sapply(predict.oem(res, type = "nonzero", which.model = m), length)
)
res$nvars <- p
res$penalty <- penalty
res$family <- family
res$varnames <- varnames
res$nzero <- nz
class(res) <- c(class(res), "oem")
res
}
oemfit.xtx.gaussian <- function(xtx,
xty,
family,
penalty,
groups,
unique.groups,
group.weights,
lambda,
nlambda,
lambda.min.ratio,
alpha,
gamma,
tau,
scale.factor,
penalty.factor,
options)
{
ret <- .Call("oem_xtx",
xtx,
xty,
family,
penalty,
groups,
unique.groups,
group.weights,
lambda,
nlambda,
lambda.min.ratio,
alpha,
gamma,
tau,
scale.factor,
penalty.factor,
options,
PACKAGE = "oem")
class(ret) <- "oemfit_gaussian"
ret
}
oemfit.xtx.binomial <- function(xtx,
xty,
family,
penalty,
groups,
unique.groups,
group.weights,
lambda,
nlambda,
lambda.min.ratio,
alpha,
gamma,
tau,
scale.factor,
penalty.factor,
options)
{
ret <- .Call("oem_xtx_logistic",
xtx,
xty,
family,
penalty,
groups,
unique.groups,
group.weights,
lambda,
nlambda,
lambda.min.ratio,
alpha,
gamma,
tau,
scale.factor,
penalty.factor,
options,
PACKAGE = "oem")
class(ret) <- "oemfit_binomial"
ret
}
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