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search_forward <- function(p_ref, refmodel, nterms_max, verbose = TRUE, opt,
search_terms = NULL, ...) {
iq <- ceiling(quantile(seq_len(nterms_max), 1:10 / 10))
if (is.null(search_terms)) {
allterms <- split_formula(refmodel$formula, data = refmodel$fetch_data())
} else {
allterms <- search_terms
}
chosen <- character()
total_terms <- count_terms_chosen(allterms)
stop_search <- min(total_terms, nterms_max)
submodls <- c()
for (size in seq_len(stop_search)) {
cands <- select_possible_terms_size(chosen, allterms, size = size)
if (is.null(cands))
next
full_cands <- lapply(cands, function(cand) c(chosen, cand))
subL <- lapply(full_cands, project_submodel,
p_ref = p_ref, refmodel = refmodel, regul = opt$regul, ...)
## select best candidate
imin <- which.min(sapply(subL, "[[", "ce"))
chosen <- c(chosen, cands[imin])
## append `submodl`
submodls <- c(submodls, list(subL[[imin]]$submodl))
if (verbose && count_terms_chosen(chosen) %in% iq) {
print(paste0(names(iq)[max(which(count_terms_chosen(chosen) == iq))],
" of terms selected."))
}
}
# For `solution_terms`, `reduce_models(chosen)` used to be used instead of
# `chosen`. However, `reduce_models(chosen)` and `chosen` should be identical
# at this place because select_possible_terms_size() already avoids redundant
# models. Thus, use `chosen` here because it matches `submodls` (this
# matching is necessary because later in .get_submodels()'s `!refit_prj` case,
# `submodls` is indexed with integers which are based on `solution_terms`):
return(nlist(solution_terms = setdiff(chosen, "1"), submodls))
}
search_L1_surrogate <- function(p_ref, d_train, family, intercept, nterms_max,
penalty, opt) {
## predictive mean and variance of the reference model (with parameters
## integrated out)
mu <- p_ref$mu
v <- p_ref$var
if (NCOL(mu) > 1 || NCOL(v) > 1) {
stop("Internal error: search_L1 received multiple draws. ",
"Please report to the developers.")
}
## L1-penalized projection (projection path).
## (Notice: here we use pmax = nterms_max+1 so that the computation gets
## carried until all the way down to the least regularization also for model
## size nterms_max)
search <- glm_elnet(d_train$x, mu, family,
lambda_min_ratio = opt$lambda_min_ratio,
nlambda = opt$nlambda,
pmax = nterms_max + 1, pmax_strict = FALSE,
weights = d_train$weights,
intercept = intercept, obsvar = v, penalty = penalty,
thresh = opt$thresh)
## sort the variables according to the order in which they enter the model in
## the L1-path
entering_indices <- apply(search$beta != 0, 1, function(num) {
which(num)[1] # na for those that did not enter
})
## variables that entered at some point
entered_variables <- c(seq_len(NCOL(d_train$x)))[!is.na(entering_indices)]
## variables that did not enter at any point
notentered_variables <- c(seq_len(NCOL(d_train$x)))[is.na(entering_indices)]
order_of_entered <- sort(entering_indices, index.return = TRUE)$ix
order <- c(entered_variables[order_of_entered], notentered_variables)
## fetch the coefficients corresponding to those points at the search_path
## where new variable enters
nvar <- length(order)
n <- nrow(p_ref$mu)
out <- list(
alpha = rep(NA, nterms_max + 1),
beta = matrix(0, nrow = nterms_max, ncol = nterms_max + 1),
lambda = rep(NA, nterms_max + 1),
w = matrix(NA, nrow = n, ncol = nterms_max + 1)
)
for (k in 0:nterms_max) {
if (k == 0) {
out$alpha[1] <- search$beta0[1]
out$lambda[1] <- search$lambda[1]
out$w[, 1] <- search$w[, 1]
} else {
## find those points in the L1-path where only the k most relevant
## features can have nonzero coefficient, and then fetch their
## coefficients with least regularization
ivar <- utils::tail(order, nvar - k)
steps_k_var <- which(colSums(search$beta[ivar, , drop = FALSE] != 0) == 0)
if (length(steps_k_var) > 0) {
j <- utils::tail(steps_k_var, 1)
} else {
## no steps where all the variables in set ivar would have zero
## coefficient (could be due to one or more of these variables having
## penalty = 0 so they are always in the model) so set the coefficients
## to be equal to the starting value
j <- 1
}
out$alpha[k + 1] <- search$beta0[j]
out$beta[1:k, k + 1] <- search$beta[order[1:k], j]
out$lambda[k + 1] <- search$lambda[j]
out$w[, k + 1] <- search$w[, j]
}
}
out$solution_terms <- order[1:nterms_max]
if (any(is.na(out$solution_terms)) &&
length(entered_variables) < nterms_max) {
if (length(setdiff(notentered_variables,
which(penalty == Inf))) > 0) {
warning("Less than nterms_max variables entered L1-path. ",
"Try reducing lambda_min_ratio. ")
}
}
return(out)
}
search_L1 <- function(p_ref, refmodel, nterms_max, penalty, opt) {
if (nterms_max == 0) {
stop("L1 search cannot be used for an empty (i.e. intercept-only) ",
"reference model.")
}
# TODO: In the following model.matrix() call, allow user-specified contrasts
# to be passed to argument `contrasts.arg`. The `contrasts.arg` default
# (`NULL`) uses `options("contrasts")` internally, but it might be more
# convenient to let users specify contrasts directly. At that occasion,
# contrasts should also be tested thoroughly (not done until now).
x <- model.matrix(refmodel$formula, data = refmodel$fetch_data())
x <- x[, colnames(x) != "(Intercept)", drop = FALSE]
## it's important to keep the original order because that's the order
## in which lasso will estimate the parameters
tt <- terms(refmodel$formula)
terms_ <- attr(tt, "term.labels")
search_path <- search_L1_surrogate(
p_ref, nlist(x, weights = refmodel$wobs), refmodel$family,
refmodel$intercept, ncol(x), penalty, opt
)
solution_terms <- collapse_contrasts_solution_path(
refmodel$formula, colnames(x)[search_path$solution_terms],
refmodel$fetch_data()
)
submodls <- lapply(0:length(solution_terms), function(nterms) {
if (nterms == 0) {
formula <- make_formula(c("1"))
beta <- NULL
x <- x[, numeric(), drop = FALSE]
} else {
formula <- make_formula(solution_terms[seq_len(nterms)])
variables <- unlist(lapply(
solution_terms[seq_len(nterms)],
function(term) {
# TODO: In the following model.matrix() call, allow user-specified
# contrasts to be passed to argument `contrasts.arg`. The
# `contrasts.arg` default (`NULL`) uses `options("contrasts")`
# internally, but it might be more convenient to let users specify
# contrasts directly. At that occasion, contrasts should also be
# tested thoroughly (not done until now).
mm <- model.matrix(as.formula(paste("~ 1 +", term)),
data = refmodel$fetch_data())
return(setdiff(colnames(mm), "(Intercept)"))
}
))
indices <- match(variables, colnames(x)[search_path$solution_terms])
indices <- indices[!is.na(indices)]
beta <- search_path$beta[indices, max(indices) + 1, drop = FALSE]
# Also reduce `x` (important for coef.subfit(), for example); note that
# `x <- x[, variables, drop = FALSE]` should also be possible, but the
# re-use of `colnames(x)` should provide another sanity check:
x <- x[, colnames(x)[search_path$solution_terms[indices]], drop = FALSE]
}
sub <- nlist(alpha = search_path$alpha[nterms + 1],
beta,
w = search_path$w[, nterms + 1],
formula,
x)
class(sub) <- "subfit"
return(list(sub))
})
return(list(solution_terms = solution_terms[seq_len(nterms_max)],
submodls = submodls[seq_len(nterms_max + 1)]))
}
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