From e7f62fb21a9796b8729c53e9b9a55122059594e8 Mon Sep 17 00:00:00 2001 From: Julien Chiquet Date: Sat, 23 May 2026 08:23:34 +0200 Subject: [PATCH 1/4] added observation weights for sparse and group-sparse variants. --- R/group_sparse_lm.R | 64 +++++++++++---------- R/group_sparse_lm_aliases.R | 60 +++++++++++-------- R/sparse_lm.R | 87 +++++++++++++++------------- R/sparse_lm_aliases.R | 30 ++++++---- man/bounded_reg.Rd | 3 +- man/fused_lasso.Rd | 3 +- man/group_lava.Rd | 3 +- man/group_sparse_lm.Rd | 22 +++++-- man/lava.Rd | 3 +- man/ridge.Rd | 3 +- man/sparse_lm.Rd | 13 ++++- src/Quadrupen/ActiveSet.h | 11 ++-- src/Quadrupen/BaseLava.h | 2 +- src/Quadrupen/RegressionData.h | 50 +++++++++------- src/wrapper_SparseRegression.cpp | 16 +++--- tests/testthat/test-obs-weights.R | 95 +++++++++++++++++++++++++++++++ 16 files changed, 308 insertions(+), 157 deletions(-) create mode 100644 tests/testthat/test-obs-weights.R diff --git a/R/group_sparse_lm.R b/R/group_sparse_lm.R index 5cbcc37..f4391c5 100644 --- a/R/group_sparse_lm.R +++ b/R/group_sparse_lm.R @@ -1,36 +1,36 @@ #' Fit a linear model with (sparse) group regularisation #' #' Adjust a linear model with (sparse) group regularization, that is, a -#' mixture of an element-wise \eqn{\ell_1}{l1} norm and a group-wise mixed-norm -#' (either \eqn{\ell_1/\ell_2}{l1/l2}, \eqn{\ell_1/\ell_\infty}{l1/linf} or -#' cooperative). We also add a (possibly structured) \eqn{\ell_2}{l2}-norm (ridge-like). -#' The solution path is computed on an automatically tuned grid of values for +#' mixture of an element-wise \eqn{\ell_1}{l1} norm and a group-wise mixed-norm +#' (either \eqn{\ell_1/\ell_2}{l1/l2}, \eqn{\ell_1/\ell_\infty}{l1/linf} or +#' cooperative). We also add a (possibly structured) \eqn{\ell_2}{l2}-norm (ridge-like). +#' The solution path is computed on an automatically tuned grid of values for #' the sparse group penalty. The mixture coefficient and the amount of ridge-like #' regularization are fixed by the user. See details for the criterion optimized. -#' +#' #' @inheritParams sparse_lm -#' -#' @param alpha real scalar in (0,1); tunes mixture between \eqn{\ell_1}{l1} +#' +#' @param alpha real scalar in (0,1); tunes mixture between \eqn{\ell_1}{l1} #' group penalties. Default is 0.0 (standard group-lasso). #' #' @param group vector of integers indicating group belonging. Must #' match the number of column in \code{x}. Must be SORTED integers #' starting from 1. #' -#' @param type string indicating the sparse-group variant to be fitted. +#' @param type string indicating the sparse-group variant to be fitted. #' Could be "l2", "coop", or "linf". Default is "l2" (regular Group-Lasso) #' #' @return an object with class [SparseGroupFit], inheriting from [QuadrupenFit]. #' #' @seealso See also [QuadrupenFit] -#' +#' #' @keywords models, regression #' #' @examples #' ## Simulating multivariate Gaussian with blockwise correlation #' ## and piecewise constant vector of parameters #' beta <- rep(c(0,1,0,-1,0), c(25,10,25,10,25)) -#' grp <- rep(1:5, c(25,10,25,10,25)) +#' grp <- rep(1:5, c(25,10,25,10,25)) #' cor <- 0.75 #' Soo <- toeplitz(cor^(0:(25-1))) ## Toeplitz correlation for irrelevant variables #' Sww <- matrix(cor,10,10) ## bloc correlation between active variables @@ -44,56 +44,56 @@ #' ## and with structuring prior #' labels <- rep("irrelevant", length(beta)) #' labels[beta != 0] <- "relevant" -#' +#' #' ## Group-Lasso #' plot(group_lasso(x, y, grp), label=labels) -#' +#' #' ## Sparse Group-Lasso #' plot(sparse_group_lasso(x, y, grp, alpha = 0.75), label=labels) -#' +#' #' \dontrun{ #' ## Sparse Group-Lasso + L2 regularization #' plot(group_sparse_lm(x, y, grp, type = "l2", alpha = .75, lambda2=.5), #' label=labels) #' plot(group_sparse_lm(x, y, grp, type = "l2", alpha = .75, lambda2=10), #' label=labels) -#' plot(group_sparse_lm(x, y, grp, type = "l2", alpha = .75, lambda2=10, +#' plot(group_sparse_lm(x, y, grp, type = "l2", alpha = .75, lambda2=10, #' struct=solve(Sigma)), label=labels) #' } -#' +#' #' ## Group-Lasso L1/LINF #' plot(group_l1linf(x, y, grp), label=labels) -#' +#' #' ## Sparse Group-Lasso L1/LINF #' plot(sparse_group_l1linf(x, y, grp, alpha = 0.75), label=labels) -#' +#' #' \dontrun{ #' ## Sparse L1/LINF Group-Lasso + L2 regularization #' plot(group_sparse_lm(x, y, grp, type = "linf", alpha = .75, lambda2=.5), #' label=labels) #' plot(group_sparse_lm(x, y, grp, type = "linf", alpha = .75, lambda2=10), #' label=labels) -#' plot(group_sparse_lm(x, y, grp, type = "linf", alpha = .75, lambda2=10, +#' plot(group_sparse_lm(x, y, grp, type = "linf", alpha = .75, lambda2=10, #' struct=solve(Sigma)), label=labels) #' } -#' +#' #' ## Cooperative-Lasso #' plot(coop_lasso(x, y, grp), label=labels) -#' +#' #' ## Sparse Cooperative-Lasso #' plot(sparse_coop_lasso(x, y, grp, alpha = 0.75), label=labels) -#' +#' #' \dontrun{ #' ## Sparse Cooperative-Lasso + L2 regularization #' plot(group_sparse_lm(x, y, grp, type = "coop", alpha = .75, lambda2=.5), #' label=labels) #' plot(group_sparse_lm(x, y, grp, type = "coop", alpha = .75, lambda2=10), #' label=labels) -#' plot(group_sparse_lm(x, y, grp, type = "coop", alpha = .75, lambda2=10, +#' plot(group_sparse_lm(x, y, grp, type = "coop", alpha = .75, lambda2=10, #' struct=solve(Sigma)), label=labels) #' } #' @export -group_sparse_lm <- +group_sparse_lm <- function(x, y, group, @@ -101,6 +101,7 @@ group_sparse_lm <- lambda1 = NULL, lambda2 = 0.01, alpha = 0.0, + weights = rep(1,nrow(x)), penscale = sqrt(tabulate(group)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -111,11 +112,11 @@ group_sparse_lm <- maxfeat = ifelse(lambda2 < 1e-2, min(2*nrow(x),ncol(x)), min(4*nrow(x),ncol(x))), beta0 = numeric(ncol(x)), control = list()) { - + stopifnot(alpha < 1 && alpha >= 0) stopifnot(!is.unsorted(group)) type <- match.arg(type) - + ## ============================================ ## RECOVER LOW LEVEL CONFIGURATION ## @@ -127,16 +128,17 @@ group_sparse_lm <- ctrl$normalize <- normalize ctrl$beta0 <- beta0 ctrl$maxfeat <- maxfeat - + ## ============================================ ## INSTANTIATE THE DATA MODEL ## myData <- DataModel$new( covariates = x, outcome = y, - cov_struct = struct + cov_struct = struct, + obs_weights = weights ) - + ## ============================================ ## INSTANTIATE THE PENALIZED MODEL ## @@ -145,10 +147,10 @@ group_sparse_lm <- intercept = intercept, group = group, type = type, - regParam = list(lambda = lambda1, + regParam = list(lambda = lambda1, gamma = lambda2, alpha = alpha, - lambda_factor = penscale, + lambda_factor = penscale, min_ratio = minratio, n_lambda = nlambda1) ) @@ -157,7 +159,7 @@ group_sparse_lm <- ## if (ctrl$verbose > 0) cat("\nModel fitting and optimization") myModel$fit(ctrl) - + ## ============================================ ## POSTREATMENT + SEND BACK THE RESULTING MODEL ## diff --git a/R/group_sparse_lm_aliases.R b/R/group_sparse_lm_aliases.R index 2b7552b..f073138 100644 --- a/R/group_sparse_lm_aliases.R +++ b/R/group_sparse_lm_aliases.R @@ -1,11 +1,12 @@ #' @rdname group_sparse_lm #' @export -group_lasso <- +group_lasso <- function(x, y, group, lambda1 = NULL, lambda2 = 0.0, + weights = rep(1,nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -14,7 +15,7 @@ group_lasso <- maxfeat = ncol(x), beta0 = numeric(ncol(x)), control = list(method = "quadra")) { - + out <- group_sparse_lm( x, y, @@ -23,6 +24,7 @@ group_lasso <- lambda1 = lambda1, lambda2 = lambda2, alpha = 0.0, + weights = weights, penscale = penscale, struct = Matrix::Diagonal(ncol(x), 1), intercept = intercept, @@ -33,18 +35,19 @@ group_lasso <- maxfeat = maxfeat, beta0 = beta0, control = control) - - out + + out } #' @rdname group_sparse_lm #' @export -group_l1linf <- +group_l1linf <- function(x, y, group, lambda1 = NULL, lambda2 = 0.0, + weights = rep(1,nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -53,7 +56,7 @@ group_l1linf <- maxfeat = ncol(x), beta0 = numeric(ncol(x)), control = list()) { - + out <- group_sparse_lm( x, y, @@ -62,6 +65,7 @@ group_l1linf <- lambda1 = lambda1, lambda2 = lambda2, alpha = 0.0, + weights = weights, penscale = penscale, struct = Matrix::Diagonal(ncol(x), 1), intercept = intercept, @@ -72,18 +76,19 @@ group_l1linf <- maxfeat = maxfeat, beta0 = beta0, control = control) - - out + + out } #' @rdname group_sparse_lm #' @export -coop_lasso <- +coop_lasso <- function(x, y, group, lambda1 = NULL, lambda2 = 0.0, + weights = rep(1,nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -92,7 +97,7 @@ coop_lasso <- maxfeat = ncol(x), beta0 = numeric(ncol(x)), control = list()) { - + out <- group_sparse_lm( x, y, @@ -101,6 +106,7 @@ coop_lasso <- lambda1 = lambda1, lambda2 = lambda2, alpha = 0.0, + weights = weights, penscale = penscale, struct = Matrix::Diagonal(ncol(x), 1), intercept = intercept, @@ -111,19 +117,20 @@ coop_lasso <- maxfeat = maxfeat, beta0 = beta0, control = control) - - out + + out } #' @rdname group_sparse_lm #' @export -sparse_group_lasso <- +sparse_group_lasso <- function(x, y, group, lambda1 = NULL, lambda2 = 0.0, alpha = 0.5, + weights = rep(1,nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -132,7 +139,7 @@ sparse_group_lasso <- maxfeat = ncol(x), beta0 = numeric(ncol(x)), control = list()) { - + out <- group_sparse_lm( x, y, @@ -141,6 +148,7 @@ sparse_group_lasso <- lambda1 = lambda1, lambda2 = lambda2, alpha = alpha, + weights = weights, penscale = penscale, struct = Matrix::Diagonal(ncol(x), 1), intercept = intercept, @@ -151,19 +159,20 @@ sparse_group_lasso <- maxfeat = maxfeat, beta0 = beta0, control = control) - - out + + out } #' @rdname group_sparse_lm #' @export -sparse_group_l1linf <- +sparse_group_l1linf <- function(x, y, group, lambda1 = NULL, lambda2 = 0.0, alpha = 0.0, + weights = rep(1,nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -172,7 +181,7 @@ sparse_group_l1linf <- maxfeat = ncol(x), beta0 = numeric(ncol(x)), control = list()) { - + out <- group_sparse_lm( x, y, @@ -181,6 +190,7 @@ sparse_group_l1linf <- lambda1 = lambda1, lambda2 = lambda2, alpha = alpha, + weights = weights, penscale = penscale, struct = Matrix::Diagonal(ncol(x), 1), intercept = intercept, @@ -191,19 +201,20 @@ sparse_group_l1linf <- maxfeat = maxfeat, beta0 = beta0, control = control) - - out + + out } #' @rdname group_sparse_lm #' @export -sparse_coop_lasso <- +sparse_coop_lasso <- function(x, y, group, lambda1 = NULL, lambda2 = 0.0, alpha = 0.0, + weights = rep(1,nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -212,7 +223,7 @@ sparse_coop_lasso <- maxfeat = ncol(x), beta0 = numeric(ncol(x)), control = list()) { - + out <- group_sparse_lm( x, y, @@ -221,6 +232,7 @@ sparse_coop_lasso <- lambda1 = lambda1, lambda2 = lambda2, alpha = alpha, + weights = weights, penscale = penscale, struct = Matrix::Diagonal(ncol(x), 1), intercept = intercept, @@ -231,6 +243,6 @@ sparse_coop_lasso <- maxfeat = maxfeat, beta0 = beta0, control = control) - - out + + out } diff --git a/R/sparse_lm.R b/R/sparse_lm.R index 77bea4f..702d194 100644 --- a/R/sparse_lm.R +++ b/R/sparse_lm.R @@ -1,6 +1,6 @@ #' Fit a linear model with sparse regularization #' -#' Adjust a linear model with sparse regularization. +#' Adjust a linear model with sparse regularization. #' We also add a (possibly structured) \eqn{\ell_2}{l2}-norm #' (ridge-like). The solution path is computed at a grid of values for the #' \eqn{\ell_1}{l1}-penalty, fixing the amount of \eqn{\ell_2}{l2} @@ -22,9 +22,12 @@ #' @param lambda2 real scalar; tunes the \eqn{\ell_2}{l2} penalty in #' the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso. #' +#' @param weights vector with real positive values that weight the +#' observations (like in weighted least square). +#' Default sets all weights to 1. +#' #' @param penscale vector with real positive values that weight the -#' \eqn{\ell_1}{l1}-penalty of each feature. Default sets all weights -#' to 1. +#' penalty of each feature. Default sets all weights to 1. #' #' @param struct matrix structuring the coefficients, possibly #' sparsely encoded. Must be at least positive semidefinite (this is @@ -38,8 +41,8 @@ #' normalized to have unit L2 norm before fitting. Default is #' `TRUE`. #' -#' @param refit logical: indicates if the non null coefficients should be -#' refit to avoid excessive bias. Default is FALSE. Can be changed later +#' @param refit logical: indicates if the non null coefficients should be +#' refit to avoid excessive bias. Default is FALSE. Can be changed later #' (both raw and refit coefficients are stored). #' #' @param nlambda1 integer that indicates the number of values to put @@ -61,43 +64,43 @@ #' `min(nrow(x),ncol(x))` for small `lambda2` (<0.01) and #' `min(4*nrow(x),ncol(x))` otherwise. Use with care, as it #' considerably changes the computation time. -#' +#' #' @param beta0 a starting point for the vector of parameter. By default, -#' will initialized zero. May save time in some situation. +#' will initialized zero. May save time in some situation. #' #' @param control list of argument controlling low level options of #' the algorithm --use with care and at your own risk-- : -#' * `verbose`: integer; activate verbose mode --this one is not -#' too risky!-- set to `0` for no output; `1` for warnings only, -#' and `2` for tracing the whole progression. Default is `1`. -#' Automatically set to `0` when the method is embedded within +#' * `verbose`: integer; activate verbose mode --this one is not +#' too risky!-- set to `0` for no output; `1` for warnings only, +#' and `2` for tracing the whole progression. Default is `1`. +#' Automatically set to `0` when the method is embedded within #' cross-validation or stability selection. #' * `timer`: logical; use to record the timing of the #' algorithm. Default is `FALSE`. #' * `maxiter` the maximal number of iteration used in the active set algorithm #' to solve the problem for a given value of lambda1 . Default is 50. -#' * `method` a string for the underlying solver used. Either -#' `"quadra"`, `"fista"` or `"pgd"`. Default is `"quadra"`. +#' * `method` a string for the underlying solver used. Either +#' `"quadra"`, `"fista"` or `"pgd"`. Default is `"quadra"`. #' * `factmat` Boolean indicating if matrix factorization should be used to -#' solve the sub-system. If `TRUE` (the default), a Cholesky decomposition is -#' maintained along the path. If `FALSE`, the sub-system are solved with +#' solve the sub-system. If `TRUE` (the default), a Cholesky decomposition is +#' maintained along the path. If `FALSE`, the sub-system are solved with #' a conjugate gradient algorithm. -#' * `threshold` a threshold for convergence. The algorithm stops +#' * `threshold` a threshold for convergence. The algorithm stops #' when the optimality conditions are fulfill up to this threshold. #' Default is `1e-6`. -#' * `monitor` indicates if a monitoring of the convergence should be -#' recorded, by computing a lower bound between the current solution and -#' the optimum: when `'0'` (the default), no monitoring is provided; -#' when `'1'`, the bound derived in Grandvalet et al. is computed; when +#' * `monitor` indicates if a monitoring of the convergence should be +#' recorded, by computing a lower bound between the current solution and +#' the optimum: when `'0'` (the default), no monitoring is provided; +#' when `'1'`, the bound derived in Grandvalet et al. is computed; when #' `'>1'`, the Fenchel duality gap is computed along the algorithm. -#' -#' @param type string indicating the sparse variant to be fitted. -#' Could be "l1", "mcp" or "scad". Default is "l1". +#' +#' @param type string indicating the sparse variant to be fitted. +#' Could be "l1", "mcp" or "scad". Default is "l1". #' be careful as scad and mcp are still experimental and have not been fully tested yet -#' -#' @param eta real positive scalar for tuning SCAD or MCP penalties. +#' +#' @param eta real positive scalar for tuning SCAD or MCP penalties. #' Default is 3.7. Ignored when type == "l1". -#' +#' #' @details The optimized criterion is the following: \if{latex}{\deqn{% #' \hat{\beta}_{\lambda_1,\lambda_2} = \arg \min_{\beta} \frac{1}{2} #' (y - X \beta)^T (y - X \beta) + \lambda_1 pen_{\eta}(D \beta) + @@ -114,11 +117,11 @@ #' structuring matrix \eqn{S}{S} is provided via the `struct` #' argument, a positive semidefinite matrix (possibly of class #' `Matrix`). -#' +#' #' @return an object with class [SparseFit], inheriting from [QuadrupenFit]. #' #' @seealso See also [SparseFit] -#' +#' #' @keywords models, regression #' #' @examples @@ -138,16 +141,16 @@ #' #' ## Lasso #' plot(lasso(x, y), label=labels) -#' +#' #' ## SCAD #' plot(scad(x, y), label=labels) -#' +#' #' ## MCP #' plot(mcp(x, y), label=labels) -#' +#' #' ## Elastic-net #' plot(elastic_net(x,y,lambda2=1), label=labels) -#' +#' #' ## Structured Elastic-net (l2-structuring prior) #' plot(elastic_net(x,y,lambda2=3,struct=solve(Sigma)), label=labels) #' @@ -156,7 +159,7 @@ #' #' ## MCP + L2 #' plot(mcp(x, y, eta = 3, lambda2=1), label=labels) -#' +#' #' @export sparse_lm <- function(x, y, @@ -164,6 +167,7 @@ sparse_lm <- function(x, lambda1 = NULL, lambda2 = 0.01, eta = 3.7, + weights = rep(1,nrow(x)), penscale = rep(1,ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -179,7 +183,7 @@ sparse_lm <- function(x, if (type == "mcp") stopifnot(eta > 1) if (type == "scad") stopifnot(eta > 2) if (type != "l1") warning("SCAD and MCP are still highly experimental and in development") - + ## ============================================ ## RECOVER LOW LEVEL CONFIGURATION ## @@ -190,16 +194,17 @@ sparse_lm <- function(x, ctrl$factmat <- ctrl$method == "QUADRA" ctrl$normalize <- normalize ctrl$beta0 <- beta0 - + ## ============================================ ## INSTANTIATE THE DATA MODEL ## myData <- DataModel$new( covariates = x, outcome = y, - cov_struct = struct + cov_struct = struct, + obs_weights = weights ) - + ## ============================================ ## INSTANTIATE THE PENALIZED MODEL ## @@ -207,19 +212,19 @@ sparse_lm <- function(x, data = myData, intercept = intercept, type = type, - regParam = list(lambda = lambda1, + regParam = list(lambda = lambda1, gamma = lambda2, eta = eta, - lambda_factor = penscale, + lambda_factor = penscale, min_ratio = minratio, n_lambda = nlambda1) ) - + ## ============================================ ## FIT THE MODEL WITH ACTIVE SET ALGORITHM ## if (ctrl$verbose > 0) cat("\nModel fitting and optimization") myModel$fit(ctrl) - + ## ============================================ ## POSTREATMENT + SEND BACK THE RESULTING MODEL ## diff --git a/R/sparse_lm_aliases.R b/R/sparse_lm_aliases.R index 9353e03..a602393 100644 --- a/R/sparse_lm_aliases.R +++ b/R/sparse_lm_aliases.R @@ -5,6 +5,7 @@ elastic.net <- function(x, y, lambda1 = NULL, lambda2 = 0.5, + weights = rep(1,nrow(x)), penscale = rep(1,ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -15,15 +16,16 @@ elastic.net <- function(x, maxfeat = ifelse(lambda2 < 1e-2, min(nrow(x),ncol(x)), min(4*nrow(x),ncol(x))), beta0 = numeric(ncol(x)), control = list(method = "quadra")) { - + lifecycle::deprecate_warn("1.1.0", "elastic.net()", "elastic_net()") - + out <- sparse_lm(x, y, type = "l1", lambda1 = lambda1, lambda2 = lambda2, eta = 0, + weights = weights, penscale = penscale, struct = struct, intercept = intercept, @@ -34,7 +36,7 @@ elastic.net <- function(x, maxfeat = maxfeat, beta0 = beta0, control = control) - out + out } #' @rdname sparse_lm @@ -43,6 +45,7 @@ elastic_net <- function(x, y, lambda1 = NULL, lambda2 = 0.5, + weights = rep(1,nrow(x)), penscale = rep(1,ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -53,13 +56,14 @@ elastic_net <- function(x, maxfeat = ifelse(lambda2 < 1e-2, min(nrow(x),ncol(x)), min(4*nrow(x),ncol(x))), beta0 = numeric(ncol(x)), control = list(method = "quadra")) { - + out <- sparse_lm(x, y, type = "l1", lambda1 = lambda1, lambda2 = lambda2, eta = 0, + weights = weights, penscale = penscale, struct = struct, intercept = intercept, @@ -70,7 +74,7 @@ elastic_net <- function(x, maxfeat = maxfeat, beta0 = beta0, control = control) - out + out } #' @rdname sparse_lm @@ -78,6 +82,7 @@ elastic_net <- function(x, lasso <- function(x, y, lambda1 = NULL, + weights = rep(1,nrow(x)), penscale = rep(1,ncol(x)), intercept = TRUE, normalize = TRUE, @@ -87,13 +92,14 @@ lasso <- function(x, maxfeat = min(nrow(x),ncol(x)), beta0 = numeric(ncol(x)), control = list(method = "quadra")) { - + out <- sparse_lm(x, y, type = "l1", lambda1 = lambda1, lambda2 = 0, eta = 0, + weights = weights, penscale = penscale, intercept = intercept, normalize = normalize, @@ -113,6 +119,7 @@ mcp <- function(x, lambda1 = NULL, lambda2 = 0.0, eta = 3, + weights = rep(1,nrow(x)), penscale = rep(1,ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -123,13 +130,14 @@ mcp <- function(x, maxfeat = ifelse(lambda2 < 1e-2, min(nrow(x),ncol(x)), min(4*nrow(x),ncol(x))), beta0 = numeric(ncol(x)), control = list(method = "quadra")) { - + out <- sparse_lm(x, y, type = "mcp", lambda1 = lambda1, lambda2 = lambda2, eta = eta, + weights = weights, penscale = penscale, struct = struct, intercept = intercept, @@ -140,7 +148,7 @@ mcp <- function(x, maxfeat = maxfeat, beta0 = beta0, control = control) - out + out } #' @rdname sparse_lm @@ -150,6 +158,7 @@ scad <- function(x, lambda1 = NULL, lambda2 = 0.0, eta = 3.7, + weights = rep(1,nrow(x)), penscale = rep(1,ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -160,13 +169,14 @@ scad <- function(x, maxfeat = ifelse(lambda2 < 1e-2, min(nrow(x),ncol(x)), min(4*nrow(x),ncol(x))), beta0 = numeric(ncol(x)), control = list(method = "quadra")) { - + out <- sparse_lm(x, y, type = "scad", lambda1 = lambda1, lambda2 = lambda2, eta = eta, + weights = weights, penscale = penscale, struct = struct, intercept = intercept, @@ -177,5 +187,5 @@ scad <- function(x, maxfeat = maxfeat, beta0 = beta0, control = control) - out + out } diff --git a/man/bounded_reg.Rd b/man/bounded_reg.Rd index 9e6ed58..cca2de8 100644 --- a/man/bounded_reg.Rd +++ b/man/bounded_reg.Rd @@ -53,8 +53,7 @@ shrunken to \code{minratio*lambda1.max}.} the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso.} \item{penscale}{vector with real positive values that weight the -\eqn{\ell_1}{l1}-penalty of each feature. Default sets all weights -to 1.} +penalty of each feature. Default sets all weights to 1.} \item{struct}{matrix structuring the coefficients, possibly sparsely encoded. Must be at least positive semidefinite (this is diff --git a/man/fused_lasso.Rd b/man/fused_lasso.Rd index 7de4c38..0d773b1 100644 --- a/man/fused_lasso.Rd +++ b/man/fused_lasso.Rd @@ -41,8 +41,7 @@ the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso.} \item{pen_fused}{penalty used for fusing the variables (either L1, L2 or Huber). Default is L1} \item{penscale}{vector with real positive values that weight the -\eqn{\ell_1}{l1}-penalty of each feature. Default sets all weights -to 1.} +penalty of each feature. Default sets all weights to 1.} \item{struct}{Description of the graph that corresponds to the \code{lambda2} penalty structure. If \code{NULL} (the default) a chain graph is assumed, like in the standard fused-lasso. diff --git a/man/group_lava.Rd b/man/group_lava.Rd index ecf6b30..70c5ae5 100644 --- a/man/group_lava.Rd +++ b/man/group_lava.Rd @@ -49,8 +49,7 @@ shrunken to \code{minratio*lambda1.max}.} the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso.} \item{penscale}{vector with real positive values that weight the -\eqn{\ell_1}{l1}-penalty of each feature. Default sets all weights -to 1.} +penalty of each feature. Default sets all weights to 1.} \item{struct}{matrix structuring the coefficients, possibly sparsely encoded. Must be at least positive semidefinite (this is diff --git a/man/group_sparse_lm.Rd b/man/group_sparse_lm.Rd index f094da7..f86c6c1 100644 --- a/man/group_sparse_lm.Rd +++ b/man/group_sparse_lm.Rd @@ -18,6 +18,7 @@ group_sparse_lm( lambda1 = NULL, lambda2 = 0.01, alpha = 0, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -36,6 +37,7 @@ group_lasso( group, lambda1 = NULL, lambda2 = 0, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -52,6 +54,7 @@ group_l1linf( group, lambda1 = NULL, lambda2 = 0, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -68,6 +71,7 @@ coop_lasso( group, lambda1 = NULL, lambda2 = 0, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -85,6 +89,7 @@ sparse_group_lasso( lambda1 = NULL, lambda2 = 0, alpha = 0.5, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -102,6 +107,7 @@ sparse_group_l1linf( lambda1 = NULL, lambda2 = 0, alpha = 0, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -119,6 +125,7 @@ sparse_coop_lasso( lambda1 = NULL, lambda2 = 0, alpha = 0, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), intercept = TRUE, normalize = TRUE, @@ -156,9 +163,12 @@ the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso.} \item{alpha}{real scalar in (0,1); tunes mixture between \eqn{\ell_1}{l1} group penalties. Default is 0.0 (standard group-lasso).} +\item{weights}{vector with real positive values that weight the +observations (like in weighted least square). +Default sets all weights to 1.} + \item{penscale}{vector with real positive values that weight the -\eqn{\ell_1}{l1}-penalty of each feature. Default sets all weights -to 1.} +penalty of each feature. Default sets all weights to 1.} \item{struct}{matrix structuring the coefficients, possibly sparsely encoded. Must be at least positive semidefinite (this is @@ -243,7 +253,7 @@ regularization are fixed by the user. See details for the criterion optimized. ## Simulating multivariate Gaussian with blockwise correlation ## and piecewise constant vector of parameters beta <- rep(c(0,1,0,-1,0), c(25,10,25,10,25)) -grp <- rep(1:5, c(25,10,25,10,25)) +grp <- rep(1:5, c(25,10,25,10,25)) cor <- 0.75 Soo <- toeplitz(cor^(0:(25-1))) ## Toeplitz correlation for irrelevant variables Sww <- matrix(cor,10,10) ## bloc correlation between active variables @@ -270,7 +280,7 @@ plot(group_sparse_lm(x, y, grp, type = "l2", alpha = .75, lambda2=.5), label=labels) plot(group_sparse_lm(x, y, grp, type = "l2", alpha = .75, lambda2=10), label=labels) -plot(group_sparse_lm(x, y, grp, type = "l2", alpha = .75, lambda2=10, +plot(group_sparse_lm(x, y, grp, type = "l2", alpha = .75, lambda2=10, struct=solve(Sigma)), label=labels) } @@ -286,7 +296,7 @@ plot(group_sparse_lm(x, y, grp, type = "linf", alpha = .75, lambda2=.5), label=labels) plot(group_sparse_lm(x, y, grp, type = "linf", alpha = .75, lambda2=10), label=labels) -plot(group_sparse_lm(x, y, grp, type = "linf", alpha = .75, lambda2=10, +plot(group_sparse_lm(x, y, grp, type = "linf", alpha = .75, lambda2=10, struct=solve(Sigma)), label=labels) } @@ -302,7 +312,7 @@ plot(group_sparse_lm(x, y, grp, type = "coop", alpha = .75, lambda2=.5), label=labels) plot(group_sparse_lm(x, y, grp, type = "coop", alpha = .75, lambda2=10), label=labels) -plot(group_sparse_lm(x, y, grp, type = "coop", alpha = .75, lambda2=10, +plot(group_sparse_lm(x, y, grp, type = "coop", alpha = .75, lambda2=10, struct=solve(Sigma)), label=labels) } } diff --git a/man/lava.Rd b/man/lava.Rd index ed7dcaa..c948dc1 100644 --- a/man/lava.Rd +++ b/man/lava.Rd @@ -39,8 +39,7 @@ shrunken to \code{minratio*lambda1.max}.} the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso.} \item{penscale}{vector with real positive values that weight the -\eqn{\ell_1}{l1}-penalty of each feature. Default sets all weights -to 1.} +penalty of each feature. Default sets all weights to 1.} \item{struct}{matrix structuring the coefficients, possibly sparsely encoded. Must be at least positive semidefinite (this is diff --git a/man/ridge.Rd b/man/ridge.Rd index cd97445..2c5a190 100644 --- a/man/ridge.Rd +++ b/man/ridge.Rd @@ -38,8 +38,7 @@ checked internally). If \code{NULL} (the default), the identity matrix is used. See details below.} \item{penscale}{vector with real positive values that weight the -\eqn{\ell_1}{l1}-penalty of each feature. Default sets all weights -to 1.} +penalty of each feature. Default sets all weights to 1.} \item{intercept}{logical; indicates if an intercept should be included in the model. Default is \code{TRUE}.} diff --git a/man/sparse_lm.Rd b/man/sparse_lm.Rd index 526ab91..5c22b89 100644 --- a/man/sparse_lm.Rd +++ b/man/sparse_lm.Rd @@ -16,6 +16,7 @@ sparse_lm( lambda1 = NULL, lambda2 = 0.01, eta = 3.7, + weights = rep(1, nrow(x)), penscale = rep(1, ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -33,6 +34,7 @@ elastic.net( y, lambda1 = NULL, lambda2 = 0.5, + weights = rep(1, nrow(x)), penscale = rep(1, ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -50,6 +52,7 @@ elastic_net( y, lambda1 = NULL, lambda2 = 0.5, + weights = rep(1, nrow(x)), penscale = rep(1, ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -66,6 +69,7 @@ lasso( x, y, lambda1 = NULL, + weights = rep(1, nrow(x)), penscale = rep(1, ncol(x)), intercept = TRUE, normalize = TRUE, @@ -83,6 +87,7 @@ mcp( lambda1 = NULL, lambda2 = 0, eta = 3, + weights = rep(1, nrow(x)), penscale = rep(1, ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -101,6 +106,7 @@ scad( lambda1 = NULL, lambda2 = 0, eta = 3.7, + weights = rep(1, nrow(x)), penscale = rep(1, ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -137,9 +143,12 @@ the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso.} \item{eta}{real positive scalar for tuning SCAD or MCP penalties. Default is 3.7. Ignored when type == "l1".} +\item{weights}{vector with real positive values that weight the +observations (like in weighted least square). +Default sets all weights to 1.} + \item{penscale}{vector with real positive values that weight the -\eqn{\ell_1}{l1}-penalty of each feature. Default sets all weights -to 1.} +penalty of each feature. Default sets all weights to 1.} \item{struct}{matrix structuring the coefficients, possibly sparsely encoded. Must be at least positive semidefinite (this is diff --git a/src/Quadrupen/ActiveSet.h b/src/Quadrupen/ActiveSet.h index bb0f233..4062046 100644 --- a/src/Quadrupen/ActiveSet.h +++ b/src/Quadrupen/ActiveSet.h @@ -80,8 +80,9 @@ void ActiveSet::add_var(uword var_in, const RegressionData& data A_(k) = var_in ; is_in_[var_in] = 1 ; - vec new_col = data.X_.t() * data.X_.col(var_in) - - data.n_ * data.X_bar_ * arma::as_scalar(data.X_bar_[var_in]) + data.S_.col(var_in) ; + vec wcol = data.weights_ % vec(data.X_.col(var_in)) ; + vec new_col = data.X_.t() * wcol - + data.n_w_ * data.X_bar_ * arma::as_scalar(data.X_bar_[var_in]) + data.S_.col(var_in) ; // Single allocation for XTXA_: copy old columns then set new one mat new_XTXA_(data.p_, k + 1, arma::fill::none) ; @@ -115,8 +116,10 @@ void ActiveSet::add_vars(uvec vars, const RegressionData& data) A_.resize(p_total) ; A_.tail(n_new) = vars ; - mat new_cols = data.X_.t() * data.X_.cols(vars) - - data.n_ * data.X_bar_ * data.X_bar_.rows(vars).t() + + mat WXvars(data.X_.cols(vars)) ; + WXvars.each_col() %= data.weights_ ; + mat new_cols = data.X_.t() * WXvars - + data.n_w_ * data.X_bar_ * data.X_bar_.rows(vars).t() + data.S_.cols(vars) ; // Single allocation for XTXA_ diff --git a/src/Quadrupen/BaseLava.h b/src/Quadrupen/BaseLava.h index b7fc1a7..6c1fd40 100644 --- a/src/Quadrupen/BaseLava.h +++ b/src/Quadrupen/BaseLava.h @@ -48,7 +48,7 @@ class BaseLava : public ConcreteBase { mat B_proj = C_inv * V * diagmat(D / (D2 + 1)) * U.t() ; return { RegressionData(K12 * Xc, K12 * (orig.y_ - orig.y_bar_), - sp_mat(orig.p_, orig.p_), ones(orig.p_), false, false), + sp_mat(orig.p_, orig.p_), ones(orig.n_), false, false), std::move(Proj), std::move(B_proj) } ; diff --git a/src/Quadrupen/RegressionData.h b/src/Quadrupen/RegressionData.h index 4b37a8f..08f3d65 100644 --- a/src/Quadrupen/RegressionData.h +++ b/src/Quadrupen/RegressionData.h @@ -38,14 +38,15 @@ class RegressionData { vec y_ ; // vector of response sp_mat S_ ; // Structuring matrix vec weights_ ; // observation weights + double n_w_ = 0.0; // sum of weights (= n_ when weights are uniform) bool centered_ ; // should intercept be considered? bool scaled_ ; // should predictors be standardized? mat XTX_ ; // Gram matrix vec XTy_ ; // responses to predictors vector - vec X_bar_ ; // mean of the predictors - vec norm_X_ ; // norm of the predictors - double y_bar_ ; // mean of the response - double norm_y_ ; // norm of the response + vec X_bar_ ; // weighted mean of the predictors + vec norm_X_ ; // weighted L2 norm of the predictors (centered) + double y_bar_ ; // weighted mean of the response + double norm_y_ ; // weighted L2 norm of the response RegressionData() ; RegressionData(const Environment& dataModel, const bool& center, const bool& scale); @@ -57,10 +58,9 @@ class RegressionData { void precompute_XTX() ; - void scale_regressors(vec weights) ; - }; + template RegressionData::RegressionData( const Environment& dataModel, @@ -100,31 +100,35 @@ void RegressionData::scale_struct(const double gamma) { template void RegressionData::precompute_XTX() { - XTX_ = X_.t() * X_ - n_ * X_bar_ * X_bar_.t() + S_; + mat WX = X_ ; + WX.each_col() %= weights_ ; + XTX_ = X_.t() * WX - n_w_ * X_bar_ * X_bar_.t() + S_ ; }; template void RegressionData::standardize() { + n_w_ = sum(weights_) ; + if (centered_) { - X_bar_ = mean(X_, 0).t(); - y_bar_ = mean(y_) ; + X_bar_ = X_.t() * weights_ / n_w_ ; + y_bar_ = dot(weights_, y_) / n_w_ ; } else { X_bar_ = zeros(p_) ; - y_bar_ = 0; + y_bar_ = 0 ; } if (scaled_) { - norm_X_ = sqrt(trans(sum(square(X_))) - n_ * square(X_bar_)); - norm_X_.replace(0.0, 1.0); // constant columns: leave unchanged (avoid div by zero) + norm_X_ = sqrt((weights_.t() * (X_ % X_)).t() - n_w_ * square(X_bar_)) ; + norm_X_.replace(0.0, 1.0) ; X_.each_row() /= norm_X_.t() ; X_bar_ /= norm_X_ ; } else { - norm_X_ = ones(p_); + norm_X_ = ones(p_) ; } - norm_y_ = sqrt(sum(square(y_))) ; + norm_y_ = sqrt(dot(weights_, square(y_))) ; - XTy_ = X_.t() * (y_-y_bar_) - sum(y_-y_bar_) * X_bar_ ; + XTy_ = X_.t() * (weights_ % (y_ - y_bar_)) ; } // Specialization for sp_mat: column scaling via non-zero iterator — O(nnz) instead @@ -133,16 +137,22 @@ void RegressionData::standardize() { template <> inline void RegressionData::standardize() { + n_w_ = sum(weights_) ; + if (centered_) { - X_bar_ = mean(X_, 0).t() ; - y_bar_ = mean(y_) ; + X_bar_ = X_.t() * weights_ / n_w_ ; + y_bar_ = dot(weights_, y_) / n_w_ ; } else { X_bar_ = zeros(p_) ; y_bar_ = 0 ; } if (scaled_) { - norm_X_ = sqrt(trans(sum(square(X_))) - n_ * square(X_bar_)) ; + // weighted column squared norms via non-zero iterator — O(nnz) + vec col_sq_wt = zeros(p_) ; + for (auto it = X_.begin() ; it != X_.end() ; ++it) + col_sq_wt[it.col()] += weights_[it.row()] * (*it) * (*it) ; + norm_X_ = sqrt(col_sq_wt - n_w_ * square(X_bar_)) ; norm_X_.replace(0.0, 1.0) ; for (auto it = X_.begin() ; it != X_.end() ; ++it) *it /= norm_X_[it.col()] ; @@ -150,7 +160,7 @@ inline void RegressionData::standardize() { } else { norm_X_ = ones(p_) ; } - norm_y_ = sqrt(sum(square(y_))) ; + norm_y_ = sqrt(dot(weights_, square(y_))) ; - XTy_ = X_.t() * (y_ - y_bar_) - sum(y_ - y_bar_) * X_bar_ ; + XTy_ = X_.t() * (weights_ % (y_ - y_bar_)) ; } diff --git a/src/wrapper_SparseRegression.cpp b/src/wrapper_SparseRegression.cpp index 5f01c1c..27ac82d 100644 --- a/src/wrapper_SparseRegression.cpp +++ b/src/wrapper_SparseRegression.cpp @@ -40,8 +40,8 @@ List mcp_dense_cpp( const List &control ) { RegressionData data(dataModel, intercept, as(control["normalize"])) ; - SparseRegularizer enet(std::move(data), regParam, control) ; - return enet.to_list(enet.solution_path(control)) ; + SparseRegularizer mcp(std::move(data), regParam, control) ; + return mcp.to_list(mcp.solution_path(control)) ; } // [[Rcpp::export]] @@ -52,8 +52,8 @@ List mcp_sparse_cpp( const List &control ) { RegressionData data(dataModel, intercept, as(control["normalize"])) ; - SparseRegularizer enet(std::move(data), regParam, control) ; - return enet.to_list(enet.solution_path(control)) ; + SparseRegularizer mcp(std::move(data), regParam, control) ; + return mcp.to_list(mcp.solution_path(control)) ; } // [[Rcpp::export]] @@ -64,8 +64,8 @@ List scad_dense_cpp( const List &control ) { RegressionData data(dataModel, intercept, as(control["normalize"])) ; - SparseRegularizer enet(std::move(data), regParam, control) ; - return enet.to_list(enet.solution_path(control)) ; + SparseRegularizer scad(std::move(data), regParam, control) ; + return scad.to_list(scad.solution_path(control)) ; } // [[Rcpp::export]] @@ -76,6 +76,6 @@ List scad_sparse_cpp( const List &control ) { RegressionData data(dataModel, intercept, as(control["normalize"])) ; - SparseRegularizer enet(std::move(data), regParam, control) ; - return enet.to_list(enet.solution_path(control)) ; + SparseRegularizer scad(std::move(data), regParam, control) ; + return scad.to_list(scad.solution_path(control)) ; } diff --git a/tests/testthat/test-obs-weights.R b/tests/testthat/test-obs-weights.R new file mode 100644 index 0000000..6d60fd2 --- /dev/null +++ b/tests/testthat/test-obs-weights.R @@ -0,0 +1,95 @@ +context("Observation weights: consistency between quadrupen and glmnet") + +tol <- 1e-2 + +## Shared data generated once for all tests +set.seed(2025) +n <- 100L +p <- 50L +x <- matrix(rnorm(n * p), n, p) +y <- rnorm(n) + +## Exponential weights (sum != n, values vary widely) +w <- rexp(n, rate = 1) + +test_that("unit weights give the same result as no weights", { + + fit_default <- lasso(x, y) + fit_unit_w <- lasso(x, y, weights = rep(1, n)) + + expect_equal(as.matrix(fit_default$coefficients), + as.matrix(fit_unit_w$coefficients), + check.attributes = FALSE, tolerance = tol) + + expect_equal(fit_default$intercept, + fit_unit_w$intercept, + check.attributes = FALSE, tolerance = tol) +}) + +test_that("weighted lasso matches glmnet (intercept, normalized)", { + + require(glmnet) + + ## lambda1_quad = lambda_glmnet * sqrt(sum(w)): + ## quadrupen scales by L2 norm of each column (= sqrt(n_w) * glmnet sd_w), + ## while glmnet normalizes to unit weighted variance. The ratio gives sqrt(n_w). + n_w <- sum(w) + fit_glmn <- glmnet(x, y, weights = w, lambda.min.ratio = 1e-2) + fit_quad <- lasso(x, y, weights = w, lambda1 = fit_glmn$lambda * sqrt(n_w)) + + expect_equal(as.matrix(fit_quad$coefficients), + as.matrix(fit_glmn$beta), + check.attributes = FALSE, tolerance = tol) + + expect_equal(fit_quad$intercept, + fit_glmn$a0, + check.attributes = FALSE, tolerance = tol) + + expect_equal(as.matrix(fit_quad$fitted), + predict(fit_glmn, x), + check.attributes = FALSE, tolerance = tol) +}) + +test_that("weighted lasso matches glmnet (no intercept, normalized)", { + + require(glmnet) + + n_w <- sum(w) + fit_glmn <- glmnet(x, y, weights = w, intercept = FALSE, lambda.min.ratio = 1e-2) + fit_quad <- lasso(x, y, weights = w, intercept = FALSE, lambda1 = fit_glmn$lambda * sqrt(n_w)) + + expect_equal(as.matrix(fit_quad$coefficients), + as.matrix(fit_glmn$beta), + check.attributes = FALSE, tolerance = tol) + + expect_equal(as.matrix(fit_quad$fitted), + predict(fit_glmn, x), + check.attributes = FALSE, tolerance = tol) +}) + +test_that("upweighted observations are equivalent to replicated observations", { + + ## Conceptual WLS check: upweighting observation i by integer k is exactly + ## equivalent to having k copies of that row in the data (unit weights). + ## Both objectives are identical term-by-term, so solutions must match + ## at the same lambda1 values. + + upweight_idx <- 1:10 + k <- 3L + + w_up <- rep(1L, n) + w_up[upweight_idx] <- k + + x_rep <- rbind(x, x[rep(upweight_idx, k - 1L), ]) + y_rep <- c(y, y[rep(upweight_idx, k - 1L)]) + + ## Use normalize=FALSE so that column norms are the same for both fits + ## (the replicated dataset has a different n, hence different norms otherwise). + fit_rep <- lasso(x_rep, y_rep, normalize = FALSE, intercept = FALSE) + fit_w <- lasso(x, y, weights = w_up, normalize = FALSE, intercept = FALSE, + lambda1 = fit_rep$major_tuning) + + expect_equal(as.matrix(fit_w$coefficients), + as.matrix(fit_rep$coefficients), + check.attributes = FALSE, tolerance = tol) +}) From 2263b5327c425e9a2916cf5092a4e26b78ee38aa Mon Sep 17 00:00:00 2001 From: Julien Chiquet Date: Sat, 23 May 2026 08:54:00 +0200 Subject: [PATCH 2/4] added observation weights for SVD based methods (ridge, lava, grp lava). --- R/group-lava.R | 9 +- R/lava.R | 4 +- R/ridge.R | 4 +- README.qmd | 79 ++++++------- man/group_lava.Rd | 5 + man/lava.Rd | 5 + man/ridge.Rd | 5 + src/Quadrupen/BaseLava.h | 35 ++++-- src/Quadrupen/RidgeRegression.cpp | 17 +-- tests/testthat/test-obs-weights-svd.R | 152 ++++++++++++++++++++++++++ tests/testthat/test-ridge.R | 22 ++-- 11 files changed, 260 insertions(+), 77 deletions(-) create mode 100644 tests/testthat/test-obs-weights-svd.R diff --git a/R/group-lava.R b/R/group-lava.R index 9ea518a..3c1eba0 100644 --- a/R/group-lava.R +++ b/R/group-lava.R @@ -82,6 +82,7 @@ group_lava <- function(x, type = c("l2", "coop", "linf"), lambda1 = NULL, lambda2 = 1, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -111,7 +112,8 @@ group_lava <- function(x, myData <- DataModel$new( covariates = x, outcome = y, - cov_struct = struct + cov_struct = struct, + obs_weights = weights ) ## ============================================ @@ -122,10 +124,11 @@ group_lava <- function(x, intercept = intercept, group = group, type = match.arg(type), - regParam = list(lambda = lambda1, + regParam = list(lambda = lambda1, gamma = lambda2, + alpha = 0, eta = 1, - lambda_factor = penscale, + lambda_factor = penscale, min_ratio = minratio, n_lambda = nlambda1) ) diff --git a/R/lava.R b/R/lava.R index 1054b0f..f148f5e 100644 --- a/R/lava.R +++ b/R/lava.R @@ -54,6 +54,7 @@ lava <- function(x, y, lambda1 = NULL, lambda2 = 1, + weights = rep(1, nrow(x)), penscale = rep(1,ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -82,7 +83,8 @@ lava <- function(x, myData <- DataModel$new( covariates = x, outcome = y, - cov_struct = struct + cov_struct = struct, + obs_weights = weights ) ## ============================================ diff --git a/R/ridge.R b/R/ridge.R index d9a6630..7f7a733 100644 --- a/R/ridge.R +++ b/R/ridge.R @@ -58,6 +58,7 @@ ridge <- function(x, y, lambda = NULL, + weights = rep(1, nrow(x)), struct = Matrix::Diagonal(ncol(x),1), penscale = rep(1,ncol(x)), intercept = TRUE, @@ -81,7 +82,8 @@ ridge <- function(x, myData <- DataModel$new( covariates = as.matrix(x), outcome = y, - cov_struct = struct + cov_struct = struct, + obs_weights = weights ) myData$CholStruct() diff --git a/README.qmd b/README.qmd index 76aa086..f478b78 100644 --- a/README.qmd +++ b/README.qmd @@ -14,29 +14,31 @@ knitr::opts_chunk$set(echo = TRUE, fig.path = "man/figures/") ## Description -Fits the solution paths of classical sparse regression models with efficient -active set algorithms by solving small sub-problems. Depending on the penalty, -the sub-problems can be solved exactly (*i.e.* for the LASSO) or with generic -solvers. The available optimizer includes quadratic solvers, Newton-based -approaches and generic FISTA or PGD algorithms. Also provides a few methods for +Fits the solution paths of classical sparse regression models with efficient +active set algorithms by solving small sub-problems. Depending on the penalty, +the sub-problems can be solved exactly (*i.e.* for the LASSO) or with generic +solvers. The available optimizer includes quadratic solvers, Newton-based +approaches and generic FISTA or PGD algorithms. Also provides a few methods for model selection purpose (information criteria, cross-validation, stability selection). **Quadrupen** covers the following regularizers - LASSO^[1] (Least Absolute Shrinkage and Selection Operator) - - +- SCAD^[2] (Smoothly Clip Absolute Deviation) - _preliminary version_ +- MCP^[3] (Minimax Concave Penalty) - _preliminary version_ - Group-LASSO^[4] ($\ell_1/\ell_2$ or $\ell_1/\ell_\infty$) - Cooperative-LASSO^[5] - Sparse Group-LASSO^[6] and Sparse Cooperative-LASSO - Bounded Regression ($\ell_\infty$-norm). +- LAVA^[10] and the group-LAVA variants for the all the group-sparse methods +- Ridge Regression^[11] -For all these regularizers, **Quadrupen** offers the possibility to add an +For all these regularizers, **Quadrupen** offers the possibility to add an $\ell_2$/ridge-like "structured" penalty to embed some external knowledge about the statistical dependence between the features. This is sometimes referred to as the -"Structured Elastic-Net"^[7]. +"Structured Elastic-Net"^[7]. -We also provide in the package the implementation of the Generalized Fused-LASSO^[8] originally +We also provide in the package the implementation of the Generalized Fused-LASSO^[8] originally proposed by Holger Höfling now archived from CRAN ([original repo here](https://github.com/cran/FusedLasso)). The original version of **Quadrupen** only includes Lasso, Elastic-Net and Bounded regression. It was used as an illustration for our paper *"Sparsity by worst-case penalties"*^[9]. I eventually used it to include my personal implementation of sparse methods for linear regression. @@ -49,11 +51,11 @@ While likely not as fast as highly specialized packages like *glmnet*, the use o devtools::install_github("jchiquet/quadrupen") ``` -Many examples and demos can be found in the `inst` directory. Here is a more illustrative one: +Many examples and demos can be found in the `inst` directory. Here is a more illustrative one: ## Example: structured penalized regression -This example is extracted form chapter 1 of my [habilitation](https://tel.archives-ouvertes.fr/tel-01288976/). You can get more insight by reading pages 65-66, 70-71. +This example is extracted form chapter 1 of my [habilitation](https://tel.archives-ouvertes.fr/tel-01288976/). You can get more insight by reading pages 65-66, 70-71. First, load the package @@ -101,7 +103,7 @@ rPred.block <- function(n, p, sizes=rmultinom(1,p,rep(p/K,K)), rho=rep(0.75,4)) K <- length(rho) stopifnot(sum(sizes) == p | length(rho) != length(sizes)) Cs <- lapply(1:K, function(k) chol.uniform(sizes[k],rho[k])) - + rmv <- function() { return( unlist(lapply(1:K, function(k) { @@ -156,17 +158,17 @@ plot(ridge(x,y, intercept=FALSE), labels=labels) plot(lasso(x,y, intercept=FALSE), labels=labels) ``` - +#### MCP (Minimax Concave Penalty) - - - +```{r mcp_nostruct} +plot(mcp(x,y, intercept=FALSE), labels=labels) +``` - +#### SCAD (Smoothly Clipped Absolute Deviation) - - - +```{r scad_nostruct} +plot(scad(x,y, intercept=FALSE), labels=labels) +``` #### Elastic-net ($\ell_1+\ell_2$ penalty) @@ -288,29 +290,19 @@ We let the possibility to add structured-$\ell_2$ penalty to this mixed-group pe plot(group_sparse_lm(x, y, group, type = "l2", alpha = 0.5, lambda2 = 2, struct = L, intercept=FALSE), labels=labels) ``` -#### Sparse Group-Lasso LInf + Structured ElasticNet (group sparse L1/LInf + structured L2) - -```{r sparse-grpenet-l1linf} -plot(group_sparse_lm(x, y, group, type = "linf", alpha = 0.5, lambda2 = 2, struct = L, intercept=FALSE), labels=labels) -``` - -#### Sparse Cooperative-Lasso + Structured ElasticNet (sign-coherent group lasso + structured L2) - -```{r sparse-coopenet} -plot(group_sparse_lm(x, y, group, type = "coop", alpha = 0.5, lambda2 = 2, struct = L, intercept=FALSE), labels=labels) -``` - ## References -^[1]: Tibshirani, Robert. "Regression shrinkage and selection via the lasso." Journal of the Royal Statistical Society Series B: Statistical Methodology 58.1 (1996): 267-288. - - -^[4]: Yuan, Ming, and Yi Lin. "Model selection and estimation in regression with grouped variables." Journal of the Royal Statistical Society Series B: Statistical Methodology 68.1 (2006): 49-67. -^[5]: Chiquet, Julien, Yves Grandvalet, and Camille Charbonnier. "Sparsity with sign-coherent groups of variables via the cooperative-lasso." (2012): 795-830. -^[6]: Simon, Noah, et al. "A sparse-group lasso." Journal of computational and graphical statistics 22.2 (2013): 231-245. -^[7]: Slawski, Martin. "The structured elastic net for quantile regression and support vector classification." Statistics and Computing 22.1 (2012): 153-168. -^[8]: Hoefling, Holger. "A path algorithm for the fused lasso signal approximator." Journal of Computational and Graphical Statistics 19.4 (2010): 984-1006. -^[9]: Grandvalet, Yves, Julien Chiquet, and Christophe Ambroise. "Sparsity by worst-case penalties." arXiv preprint arXiv:1210.2077 (2012). +[^1]: Tibshirani, Robert. "Regression shrinkage and selection via the lasso." Journal of the Royal Statistical Society Series B: Statistical Methodology 58.1 (1996): 267-288. +[^2]: Fan, Jianqing, and Runze Li. "Variable selection via nonconcave penalized likelihood and its oracle properties." Journal of the American statistical Association 96.456 (2001): 1348-1360. +[^3]: Zhang, C. H. Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38(2), (2010): 894-942. +[^4]: Yuan, Ming, and Yi Lin. "Model selection and estimation in regression with grouped variables." Journal of the Royal Statistical Society Series B: Statistical Methodology 68.1 (2006): 49-67. +[^5]: Chiquet, Julien, Yves Grandvalet, and Camille Charbonnier. "Sparsity with sign-coherent groups of variables via the cooperative-lasso." (2012): 795-830. +[^6]: Simon, Noah, et al. "A sparse-group lasso." Journal of computational and graphical statistics 22.2 (2013): 231-245. +[^7]: Slawski, Martin. "The structured elastic net for quantile regression and support vector classification." Statistics and Computing 22.1 (2012): 153-168. +[^8]: Hoefling, Holger. "A path algorithm for the fused lasso signal approximator." Journal of Computational and Graphical Statistics 19.4 (2010): 984-1006. +[^9]: Grandvalet, Yves, Julien Chiquet, and Christophe Ambroise. "Sparsity by worst-case penalties." arXiv preprint arXiv:1210.2077 (2012). +[^10]: Chernozhukov, Victor, Christian Hansen, and Yuan Liao. "A lava attack on the recovery of sums of dense and sparse signals." The Annals of Statistics (2017): 39-76. +[^11]: Hoerl, Arthur E., and Robert W. Kennard. "Ridge regression: Biased estimation for nonorthogonal problems." Technometrics 12.1 (1970): 55-67. ## Appendix: functions for data generation @@ -350,7 +342,7 @@ rPred.block <- function(n, p, sizes=rmultinom(1,p,rep(p/K,K)), rho=rep(0.75,4)) K <- length(rho) stopifnot(sum(sizes) == p | length(rho) != length(sizes)) Cs <- lapply(1:K, function(k) chol.uniform(sizes[k],rho[k])) - + rmv <- function() { return( unlist(lapply(1:K, function(k) { @@ -362,4 +354,3 @@ rPred.block <- function(n, p, sizes=rmultinom(1,p,rep(p/K,K)), rho=rep(0.75,4)) return(t(replicate(n, rmv(), simplify=TRUE))) } ``` - diff --git a/man/group_lava.Rd b/man/group_lava.Rd index 70c5ae5..7fb13b6 100644 --- a/man/group_lava.Rd +++ b/man/group_lava.Rd @@ -11,6 +11,7 @@ group_lava( type = c("l2", "coop", "linf"), lambda1 = NULL, lambda2 = 1, + weights = rep(1, nrow(x)), penscale = sqrt(tabulate(group)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -48,6 +49,10 @@ shrunken to \code{minratio*lambda1.max}.} \item{lambda2}{real scalar; tunes the \eqn{\ell_2}{l2} penalty in the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso.} +\item{weights}{vector with real positive values that weight the +observations (like in weighted least square). +Default sets all weights to 1.} + \item{penscale}{vector with real positive values that weight the penalty of each feature. Default sets all weights to 1.} diff --git a/man/lava.Rd b/man/lava.Rd index c948dc1..cc619d2 100644 --- a/man/lava.Rd +++ b/man/lava.Rd @@ -9,6 +9,7 @@ lava( y, lambda1 = NULL, lambda2 = 1, + weights = rep(1, nrow(x)), penscale = rep(1, ncol(x)), struct = Matrix::Diagonal(ncol(x), 1), intercept = TRUE, @@ -38,6 +39,10 @@ shrunken to \code{minratio*lambda1.max}.} \item{lambda2}{real scalar; tunes the \eqn{\ell_2}{l2} penalty in the Elastic-net. Default is 0.01. Set to 0 to recover the Lasso.} +\item{weights}{vector with real positive values that weight the +observations (like in weighted least square). +Default sets all weights to 1.} + \item{penscale}{vector with real positive values that weight the penalty of each feature. Default sets all weights to 1.} diff --git a/man/ridge.Rd b/man/ridge.Rd index 2c5a190..af814f9 100644 --- a/man/ridge.Rd +++ b/man/ridge.Rd @@ -8,6 +8,7 @@ ridge( x, y, lambda = NULL, + weights = rep(1, nrow(x)), struct = Matrix::Diagonal(ncol(x), 1), penscale = rep(1, ncol(x)), intercept = TRUE, @@ -32,6 +33,10 @@ levels. If \code{NULL} (the default), a vector is generated with \code{lambda_max} where only the intercept is included, then shrunken to \code{minratio*lambda_max}.} +\item{weights}{vector with real positive values that weight the +observations (like in weighted least square). +Default sets all weights to 1.} + \item{struct}{matrix structuring the coefficients, possibly sparsely encoded. Must be at least positive semidefinite (this is checked internally). If \code{NULL} (the default), the identity matrix is diff --git a/src/Quadrupen/BaseLava.h b/src/Quadrupen/BaseLava.h index 6c1fd40..36b9ab3 100644 --- a/src/Quadrupen/BaseLava.h +++ b/src/Quadrupen/BaseLava.h @@ -38,17 +38,31 @@ class BaseLava : public ConcreteBase { static LavaData lava_preprocess(RegressionData orig, double gamma) { orig.scale_struct(gamma) ; - mat Xc = orig.X_ ; Xc.each_row() -= orig.X_bar_.t() ; + mat Xc = orig.X_ ; Xc.each_row() -= orig.X_bar_.t() ; + // Weighted: diag(sqrtW) * Xc for SVD; sqrtW is baked into B_proj and transformed data + vec sqrtW = sqrt(orig.weights_) ; + mat Xwc = Xc ; Xwc.each_col() %= sqrtW ; + mat C_inv = solve(trimatu(chol(orig.S_.as_dense())), eye(orig.p_, orig.p_)) ; mat U, V ; vec D ; - svd_econ(U, D, V, Xc * C_inv) ; + svd_econ(U, D, V, Xwc * C_inv) ; vec D2 = square(D) ; - mat Proj = U * diagmat(D2 / (D2 + 1)) * U.t() ; - mat K12 = U * diagmat(1 / sqrt(D2 + 1)) * U.t() ; - mat B_proj = C_inv * V * diagmat(D / (D2 + 1)) * U.t() ; + vec kcoeff = 1 / sqrt(D2 + 1) - 1 ; // K12_w applied as: Xwc + U * (kcoeff .* U^T Xwc) + + mat Proj = U * diagmat(D2 / (D2 + 1)) * U.t() ; + // B_proj_w = C_inv * V * diag(D/(D2+1)) * (diag(sqrtW) * U)^T + mat WU = U ; WU.each_col() %= sqrtW ; + mat B_proj = C_inv * V * diagmat(D / (D2 + 1)) * WU.t() ; + + // X_new = K12_w * Xwc (efficient: Xwc + U * diag(kcoeff) * U^T Xwc) + mat UtXwc = U.t() * Xwc ; UtXwc.each_col() %= kcoeff ; + mat X_new = Xwc + U * UtXwc ; + // y_new = K12_w * (sqrtW % y_c) + vec y_wc = sqrtW % (orig.y_ - orig.y_bar_) ; + vec y_new = y_wc + U * (kcoeff % (U.t() * y_wc)) ; + return { - RegressionData(K12 * Xc, K12 * (orig.y_ - orig.y_bar_), - sp_mat(orig.p_, orig.p_), ones(orig.n_), false, false), + RegressionData(X_new, y_new, sp_mat(orig.p_, orig.p_), ones(orig.n_), false, false), std::move(Proj), std::move(B_proj) } ; @@ -121,11 +135,12 @@ class BaseLava : public ConcreteBase { this->intercept_.push_back(orig_data_.y_bar_ - dot(beta.col(i) + b_.col(i), orig_data_.X_bar_)) ; uvec A = this->active_[i] ; mat XsA = Xs.cols(A) ; mat XsAT = XsA.t() ; - vec w = (orig_data_.y_ - this->data_.y_bar_) - Xs * b_.col(i) ; - vec beta_debiased = solve(XsAT * XsA, XsAT * w) ; + vec w = (orig_data_.y_ - orig_data_.y_bar_) - Xs * b_.col(i) ; + mat WXsA = XsA ; WXsA.each_col() %= orig_data_.weights_ ; + vec beta_debiased = solve(XsAT * WXsA, XsAT * (orig_data_.weights_ % w)) ; this->debiased_.insert(this->debiased_.end(), beta_debiased.begin(), beta_debiased.end()) ; this->intercept_debiased_.push_back( - this->data_.y_bar_ - dot(beta_debiased, this->data_.X_bar_(A)) - dot(b_.col(i), this->data_.X_bar_)) ; + orig_data_.y_bar_ - dot(beta_debiased, orig_data_.X_bar_(A)) - dot(b_.col(i), orig_data_.X_bar_)) ; beta.col(i) /= orig_data_.norm_X_ ; } sparse_coef_ = beta ; diff --git a/src/Quadrupen/RidgeRegression.cpp b/src/Quadrupen/RidgeRegression.cpp index c3765c9..bf3edcc 100644 --- a/src/Quadrupen/RidgeRegression.cpp +++ b/src/Quadrupen/RidgeRegression.cpp @@ -32,14 +32,17 @@ List RidgeRegression::to_list(const List& monitoring) { List RidgeRegression::solution_path(const mat& C_inv) { - // SVD DECOMPOSITION OF ( X * C^-1) - vec eta ; // eigen value of X cinv - mat U ; // left singular vectors of X - mat V ; // right singular vectors of X - svd_econ(U, eta, V, (data_.X_.each_row() - data_.X_bar_.t())*C_inv) ; - + // Weighted SVD: diag(sqrtW) * Xc * C_inv + vec sqrtW = sqrt(data_.weights_) ; + mat Xwc = data_.X_ ; + Xwc.each_row() -= data_.X_bar_.t() ; + Xwc.each_col() %= sqrtW ; + + vec eta ; mat U, V ; + svd_econ(U, eta, V, Xwc * C_inv) ; + mat C_invV = C_inv * V ; - mat Uty = trans(U) * (data_.y_ - data_.y_bar_) ; + vec Uty = U.t() * (sqrtW % (data_.y_ - data_.y_bar_)) ; vector timing ; // successive timing for solving for each lambda value wall_clock timer ; timer.tic(); // clock diff --git a/tests/testthat/test-obs-weights-svd.R b/tests/testthat/test-obs-weights-svd.R new file mode 100644 index 0000000..bd9e805 --- /dev/null +++ b/tests/testthat/test-obs-weights-svd.R @@ -0,0 +1,152 @@ +context("Observation weights for SVD-based methods (Ridge, Lava, GroupLava)") + +tol_ridge <- 1e-3 +tol_lava <- 1e-2 + +set.seed(2025) +n <- 100L +p <- 50L +x <- matrix(rnorm(n * p), n, p) +y <- rnorm(n) + +w <- rexp(n, rate = 1) # general weights, sum != n + +## ── Ridge ───────────────────────────────────────────────────────────────────── + +test_that("weighted ridge: unit weights give the same result as no weights", { + + fit_default <- ridge(x, y) + fit_unit_w <- ridge(x, y, weights = rep(1, n)) + + expect_equal(as.matrix(fit_default$coefficients), + as.matrix(fit_unit_w$coefficients), + check.attributes = FALSE, tolerance = tol_ridge) + expect_equal(fit_default$intercept, + fit_unit_w$intercept, + check.attributes = FALSE, tolerance = tol_ridge) +}) + +test_that("weighted ridge matches direct WLS formula", { + + ## Direct WLS ridge closed form (no external package): + ## beta_hat(lambda) = (X_n^T W X_n + lambda I)^{-1} X_n^T W y_c / norm_X + ## where X_n is column-standardized with weighted norms, y_c is weighted-mean centred. + ## MASS::lm.ridge does NOT implement standard WLS ridge, so we avoid it. + + lam <- 10^seq(1, -1, length.out = 20) + n_w <- sum(w) + x_bar <- as.numeric(t(x) %*% w / n_w) + y_bar <- sum(w * y) / n_w + xc <- sweep(x, 2, x_bar) + normx <- sqrt(as.numeric(t(w) %*% (xc^2))) + xn <- sweep(xc, 2, normx, "/") + yc <- y - y_bar + XtWX <- crossprod(xn, w * xn) + XtWy <- as.numeric(crossprod(xn, w * yc)) + + direct <- sapply(lam, function(l) { + b_norm <- solve(XtWX + l * diag(p), XtWy) + b_norm / normx + }) + mu_direct <- y_bar - as.numeric(t(x_bar) %*% direct) + + fit_quad <- ridge(x, y, weights = w, lambda = lam, intercept = TRUE, normalize = TRUE) + + expect_equal(as.matrix(fit_quad$coefficients), direct, + check.attributes = FALSE, tolerance = tol_ridge) + expect_equal(fit_quad$intercept, mu_direct, + check.attributes = FALSE, tolerance = tol_ridge) +}) + +test_that("weighted ridge: upweighted observations equivalent to replicated observations", { + + upweight_idx <- 1:10 + k <- 3L + + w_up <- rep(1L, n) ; w_up[upweight_idx] <- k + x_rep <- rbind(x, x[rep(upweight_idx, k - 1L), ]) + y_rep <- c(y, y[rep(upweight_idx, k - 1L)]) + + lam <- 10^seq(1, -1, length.out = 20) + fit_w <- ridge(x, y, weights = w_up, lambda = lam, normalize = FALSE) + fit_rep <- ridge(x_rep, y_rep, lambda = lam, normalize = FALSE) + + expect_equal(as.matrix(fit_w$coefficients), + as.matrix(fit_rep$coefficients), + check.attributes = FALSE, tolerance = tol_ridge) +}) + +## ── Lava ────────────────────────────────────────────────────────────────────── + +test_that("weighted lava: unit weights give the same result as no weights", { + + fit_default <- lava(x, y) + fit_unit_w <- lava(x, y, weights = rep(1, n)) + + expect_equal(fit_default$coefficients, + fit_unit_w$coefficients, + check.attributes = FALSE, tolerance = tol_lava) +}) + +test_that("weighted lava as weighted lasso (lambda2 -> infty)", { + + ## When the dense penalty dominates, the dense component vanishes + ## and Lava reduces to Lasso — regardless of observation weights. + lasso_out <- lasso(x, y, weights = w) + lava_out <- lava(x, y, weights = w, + lambda1 = lasso_out$major_tuning, lambda2 = 1e5) + + expect_equal(lava_out$coefficients, + as.matrix(lasso_out$coefficients), + check.attributes = FALSE, tolerance = tol_lava) + expect_equal(lava_out$intercept, + lasso_out$intercept, + check.attributes = FALSE, tolerance = tol_lava) +}) + +test_that("weighted lava as weighted ridge (lambda1 -> infty)", { + + ## When the sparse penalty dominates, the sparse component vanishes + ## and Lava reduces to Ridge — the most important consistency check + ## for the weighted SVD preprocessing. + lambda2_val <- 0.75 + ridge_out <- ridge(x, y, weights = w, lambda = lambda2_val) + lava_out <- lava(x, y, weights = w, lambda1 = 1e8, lambda2 = lambda2_val) + + expect_equal(lava_out$coefficients, + as.matrix(ridge_out$coefficients), + check.attributes = FALSE, tolerance = tol_lava) + expect_equal(lava_out$intercept, + ridge_out$intercept, + check.attributes = FALSE, tolerance = tol_lava) +}) + +## ── GroupLava ───────────────────────────────────────────────────────────────── + +test_that("weighted group_lava: unit weights give the same result as no weights", { + + grp <- rep(1:(p / 5), each = 5) + + fit_default <- group_lava(x, y, group = grp) + fit_unit_w <- group_lava(x, y, group = grp, weights = rep(1, n)) + + expect_equal(fit_default$coefficients, + fit_unit_w$coefficients, + check.attributes = FALSE, tolerance = tol_lava) +}) + +test_that("weighted group_lava as weighted ridge (lambda1 -> infty)", { + + grp <- rep(1:(p / 5), each = 5) + lambda2_val <- 1.0 + ridge_out <- ridge(x, y, weights = w, lambda = lambda2_val) + glava_out <- group_lava(x, y, group = grp, weights = w, + lambda1 = 1e8, lambda2 = lambda2_val) + + expect_equal(glava_out$coefficients, + as.matrix(ridge_out$coefficients), + check.attributes = FALSE, tolerance = tol_lava) + expect_equal(glava_out$intercept, + ridge_out$intercept, + check.attributes = FALSE, tolerance = tol_lava) +}) diff --git a/tests/testthat/test-ridge.R b/tests/testthat/test-ridge.R index f9077d8..eaae3b7 100644 --- a/tests/testthat/test-ridge.R +++ b/tests/testthat/test-ridge.R @@ -1,4 +1,4 @@ -context("Consistency of the Lasso solution paths (package 'lars' and 'glmnet')") +context("Consistency of the Ridge solution path (package MASS)") testDataEnet <- readRDS("dataTest-Enet.rds") @@ -7,8 +7,8 @@ tol <- 1e-4 require(MASS) test_that("lasso_quad2lars", { - - + + get_ridge <- function(x,y,intercept) { lambda <- 10^seq(2,-2,len = 100) @@ -20,28 +20,28 @@ test_that("lasso_quad2lars", { ridge_mass <- MASS::lm.ridge(y ~ x + 0, lambda = lambda * nrow(x)) mass <- list(coef = t(coefficients(ridge_mass)), mu = rep(0,length(lambda))) - + } ridge_quad <- ridge(x, y, intercept=intercept, normalize=TRUE, lambda=lambda) quad <- list(coef = as.matrix(ridge_quad$coefficients), mu = ridge_quad$intercept) - - + + return(list(quad=quad,mass=mass)) } - + x <- testDataEnet$x_prostate y <- testDataEnet$y_prostate - + ## Run the tests... with.intercept <- get_ridge(x,y,TRUE) expect_equal(with.intercept$quad, with.intercept$mass, check.attributes = FALSE, tolerance = tol) - + without.intercept <- get_ridge(x,y,FALSE) expect_equal(without.intercept$quad, without.intercept$mass, check.attributes = FALSE, tolerance = tol) - + ## RANDOM DATA x <- testDataEnet$x_sim y <- testDataEnet$y_sim @@ -51,7 +51,7 @@ test_that("lasso_quad2lars", { with.intercept <- get_ridge(x,y,TRUE) expect_equal(with.intercept$quad, with.intercept$mass, check.attributes = FALSE, tolerance = tol) - + without.intercept <- get_ridge(x,y,FALSE) expect_equal(without.intercept$quad, without.intercept$mass, check.attributes = FALSE, tolerance = tol) From 05cad6a55eb28eab7869da16b7ce38a243d75322 Mon Sep 17 00:00:00 2001 From: Julien Chiquet Date: Sat, 23 May 2026 09:18:24 +0200 Subject: [PATCH 3/4] regenerating README --- README.md | 160 +++++++++++------------ README.qmd | 84 ++++++------ man/figures/breg-nostruct-1.png | Bin 0 -> 129777 bytes man/figures/breg_nostruct-1.png | Bin 98347 -> 139951 bytes man/figures/bregridge-nostruct-1.png | Bin 0 -> 127950 bytes man/figures/bregridge_nostruct-1.png | Bin 124335 -> 126564 bytes man/figures/bregridge_struct-1.png | Bin 34620 -> 37994 bytes man/figures/enet-nostruct-1.png | Bin 0 -> 194356 bytes man/figures/enet_nostruct-1.png | Bin 198791 -> 187698 bytes man/figures/enet_struct-1.png | Bin 63590 -> 66350 bytes man/figures/fused-lasso-1.png | Bin 0 -> 124166 bytes man/figures/grplasso-l1l2-1.png | Bin 128135 -> 126476 bytes man/figures/grplasso-l1linf-1.png | Bin 127458 -> 122389 bytes man/figures/img-cor-struct-1.png | Bin 0 -> 50648 bytes man/figures/lasso-nostruct-1.png | Bin 0 -> 148313 bytes man/figures/lasso_nostruct-1.png | Bin 101549 -> 154761 bytes man/figures/lava-nostruct-1.png | Bin 0 -> 152775 bytes man/figures/lava-nostruct-2.png | Bin 0 -> 112968 bytes man/figures/lava_nostruct-1.png | Bin 169653 -> 167485 bytes man/figures/lava_nostruct-2.png | Bin 114538 -> 110837 bytes man/figures/lava_struct-1.png | Bin 147868 -> 146758 bytes man/figures/lava_struct-2.png | Bin 47896 -> 48487 bytes man/figures/mcp-nostruct-1.png | Bin 0 -> 143624 bytes man/figures/mcp_nostruct-1.png | Bin 118690 -> 138621 bytes man/figures/ridge-nostruct-1.png | Bin 0 -> 71191 bytes man/figures/ridge_nostruct-1.png | Bin 65854 -> 64402 bytes man/figures/ridge_struct-1.png | Bin 72208 -> 67052 bytes man/figures/scad-nostruct-1.png | Bin 0 -> 150054 bytes man/figures/scad_nostruct-1.png | Bin 119234 -> 163006 bytes man/figures/sparse-cooplasso-1.png | Bin 127254 -> 122552 bytes man/figures/sparse-grpenet-l1l2-1.png | Bin 52792 -> 57357 bytes man/figures/sparse-grplasso-coop-1.png | Bin 141141 -> 136177 bytes man/figures/sparse-grplasso-l1l2-1.png | Bin 141626 -> 135642 bytes man/figures/sparse-grplasso-l1linf-1.png | Bin 149113 -> 121424 bytes man/figures/unnamed-chunk-3-1.png | Bin 49894 -> 50530 bytes 35 files changed, 119 insertions(+), 125 deletions(-) create mode 100644 man/figures/breg-nostruct-1.png create mode 100644 man/figures/bregridge-nostruct-1.png create mode 100644 man/figures/enet-nostruct-1.png create mode 100644 man/figures/fused-lasso-1.png create mode 100644 man/figures/img-cor-struct-1.png create mode 100644 man/figures/lasso-nostruct-1.png create mode 100644 man/figures/lava-nostruct-1.png create mode 100644 man/figures/lava-nostruct-2.png create mode 100644 man/figures/mcp-nostruct-1.png create mode 100644 man/figures/ridge-nostruct-1.png create mode 100644 man/figures/scad-nostruct-1.png diff --git a/README.md b/README.md index b84ac1b..8db85f7 100644 --- a/README.md +++ b/README.md @@ -19,25 +19,28 @@ algorithms. Also provides a few methods for model selection purpose **Quadrupen** covers the following regularizers - LASSO[^1] (Least Absolute Shrinkage and Selection Operator) - - -- Group-LASSO[^2] ($\ell_1/\ell_2$ or $\ell_1/\ell_\infty$) -- Cooperative-LASSO[^3] -- Sparse Group-LASSO[^4] and Sparse Cooperative-LASSO +- SCAD[^2] (Smoothly Clip Absolute Deviation) - *preliminary version* +- MCP[^3] (Minimax Concave Penalty) - *preliminary version* +- Group-LASSO[^4] ($\ell_1/\ell_2$ or $\ell_1/\ell_\infty$) +- Cooperative-LASSO[^5] +- Sparse Group-LASSO[^6] and Sparse Cooperative-LASSO - Bounded Regression ($\ell_\infty$-norm). +- LAVA[^7] and the group-LAVA variants for the all the group-sparse + methods +- Ridge Regression[^8] For all these regularizers, **Quadrupen** offers the possibility to add an $\ell_2$/ridge-like “structured” penalty to embed some external knowledge about the statistical dependence between the features. This is -sometimes referred to as the “Structured Elastic-Net”[^5]. +sometimes referred to as the “Structured Elastic-Net”[^9]. We also provide in the package the implementation of the Generalized -Fused-LASSO[^6] originally proposed by Holger Höfling now archived from +Fused-LASSO[^10] originally proposed by Holger Höfling now archived from CRAN ([original repo here](https://github.com/cran/FusedLasso)). The original version of **Quadrupen** only includes Lasso, Elastic-Net and Bounded regression. It was used as an illustration for our paper -*“Sparsity by worst-case penalties”*[^7]. I eventually used it to +*“Sparsity by worst-case penalties”*[^11]. I eventually used it to include my personal implementation of sparse methods for linear regression. @@ -67,12 +70,7 @@ First, load the package library(quadrupen) ``` - - ---------------------------------------------- - 'quadrupen' package version 0.3-9xxx - - Still under development... feedback welcome - ---------------------------------------------- + 'quadrupen' package version 1.0-0 ### A toy data set advocating for structured regularization @@ -100,7 +98,7 @@ x <- rPred.block(n, p, sizes = group, rho=c(0.25, 0.75, 0.25, 0.75, 0.25)) Indeed, the correlation structure between the regressors exhibits a strong pattern: -![](man/figures/unnamed-chunk-3-1.png) +![](man/figures/img-cor-struct-1.png) We draw the response variable by fixing the variance of the noise ratio to get an $R^2$ equal to $0.8$. @@ -122,7 +120,7 @@ fit the regularization path to this data set plot(ridge(x,y, intercept=FALSE), labels=labels) ``` -![](man/figures/ridge_nostruct-1.png) +![](man/figures/ridge-nostruct-1.png) #### Lasso ($\ell_1$ penalty) @@ -130,23 +128,37 @@ plot(ridge(x,y, intercept=FALSE), labels=labels) plot(lasso(x,y, intercept=FALSE), labels=labels) ``` -![](man/figures/lasso_nostruct-1.png) +![](man/figures/lasso-nostruct-1.png) + +#### MCP (Minimax Concave Penalty) + +``` r +plot(mcp(x,y, intercept=FALSE), labels=labels) +``` + + Warning in sparse_lm(x, y, type = "mcp", lambda1 = lambda1, lambda2 = lambda2, + : SCAD and MCP are still highly experimental and in development - +![](man/figures/mcp-nostruct-1.png) - +#### SCAD (Smoothly Clipped Absolute Deviation) - +``` r +plot(scad(x,y, intercept=FALSE), labels=labels) +``` - + Warning in sparse_lm(x, y, type = "scad", lambda1 = lambda1, lambda2 = lambda2, + : SCAD and MCP are still highly experimental and in development - +![](man/figures/scad-nostruct-1.png) - +#### SCAD (Smoothly Clipped Absolute Deviation) - +``` r +plot(fused_lasso(x,y, lambda2 = 5, intercept=FALSE), labels=labels) +``` - +![](man/figures/fused-lasso-1.png) #### Elastic-net ($\ell_1+\ell_2$ penalty) @@ -154,7 +166,7 @@ plot(lasso(x,y, intercept=FALSE), labels=labels) plot(elastic_net(x,y, lambda2=1, intercept=FALSE), labels=labels) ``` -![](man/figures/enet_nostruct-1.png) +![](man/figures/enet-nostruct-1.png) #### Bounded regression ($\ell_\infty$ penalty) @@ -162,7 +174,7 @@ plot(elastic_net(x,y, lambda2=1, intercept=FALSE), labels=labels) plot(bounded_reg(x,y, lambda2=0, intercept=FALSE), labels=labels) ``` -![](man/figures/breg_nostruct-1.png) +![](man/figures/breg-nostruct-1.png) #### Bounded regression + Ridge ($\ell_\infty+\ell_2$ penalty) @@ -170,7 +182,7 @@ plot(bounded_reg(x,y, lambda2=0, intercept=FALSE), labels=labels) plot(bounded_reg(x,y, lambda2=5, intercept=FALSE), labels=labels) ``` -![](man/figures/bregridge_nostruct-1.png) +![](man/figures/bregridge-nostruct-1.png) #### Lava (sparse + dense signal decomposition) @@ -179,13 +191,13 @@ out_lava <- lava(x,y, lambda2=1, intercept=FALSE) out_lava$plot_path(component = "sparse", labels=labels) ``` -![](man/figures/lava_nostruct-1.png) +![](man/figures/lava-nostruct-1.png) ``` r out_lava$plot_path(component = "dense", labels=labels) ``` -![](man/figures/lava_nostruct-2.png) +![](man/figures/lava-nostruct-2.png) ### Regularization with smooth prior knowledge @@ -324,44 +336,6 @@ plot(group_sparse_lm(x, y, group, type = "l2", alpha = 0.5, lambda2 = 2, struct ![](man/figures/sparse-grpenet-l1l2-1.png) -#### Sparse Group-Lasso LInf + Structured ElasticNet (group sparse L1/LInf + structured L2) - -``` r -plot(group_sparse_lm(x, y, group, type = "linf", alpha = 0.5, lambda2 = 2, struct = L, intercept=FALSE), labels=labels) -``` - -![](man/figures/sparse-grpenet-l1linf-1.png) - -#### Sparse Cooperative-Lasso + Structured ElasticNet (sign-coherent group lasso + structured L2) - -``` r -plot(group_sparse_lm(x, y, group, type = "coop", alpha = 0.5, lambda2 = 2, struct = L, intercept=FALSE), labels=labels) -``` - -![](man/figures/sparse-coopenet-1.png) - -## References - -[^8]: Tibshirani, Robert. “Regression shrinkage and selection via the -lasso.” Journal of the Royal Statistical Society Series B: Statistical -Methodology 58.1 (1996): 267-288. - - -[^9]: Yuan, Ming, and Yi Lin. “Model selection and estimation in -regression with grouped variables.” Journal of the Royal Statistical -Society Series B: Statistical Methodology 68.1 (2006): 49-67. [^10]: -Chiquet, Julien, Yves Grandvalet, and Camille Charbonnier. “Sparsity -with sign-coherent groups of variables via the cooperative-lasso.” -(2012): 795-830. [^11]: Simon, Noah, et al. “A sparse-group lasso.” -Journal of computational and graphical statistics 22.2 (2013): 231-245. -[^12]: Slawski, Martin. “The structured elastic net for quantile -regression and support vector classification.” Statistics and Computing -22.1 (2012): 153-168. [^13]: Hoefling, Holger. “A path algorithm for the -fused lasso signal approximator.” Journal of Computational and Graphical -Statistics 19.4 (2010): 984-1006. [^14]: Grandvalet, Yves, Julien -Chiquet, and Christophe Ambroise. “Sparsity by worst-case penalties.” -arXiv preprint arXiv:1210.2077 (2012). - ## Appendix: functions for data generation ``` r @@ -400,7 +374,7 @@ rPred.block <- function(n, p, sizes=rmultinom(1,p,rep(p/K,K)), rho=rep(0.75,4)) K <- length(rho) stopifnot(sum(sizes) == p | length(rho) != length(sizes)) Cs <- lapply(1:K, function(k) chol.uniform(sizes[k],rho[k])) - + rmv <- function() { return( unlist(lapply(1:K, function(k) { @@ -413,30 +387,46 @@ rPred.block <- function(n, p, sizes=rmultinom(1,p,rep(p/K,K)), rho=rep(0.75,4)) } ``` -[^1]: 1 - -[^2]: 4 - -[^3]: 5 +## References -[^4]: 6 +[^1]: Tibshirani, Robert. “Regression shrinkage and selection via the + lasso.” Journal of the Royal Statistical Society Series B: + Statistical Methodology 58.1 (1996): 267-288. -[^5]: 7 +[^2]: Fan, Jianqing, and Runze Li. “Variable selection via nonconcave + penalized likelihood and its oracle properties.” Journal of the + American statistical Association 96.456 (2001): 1348-1360. -[^6]: 8 +[^3]: Zhang, C. H. Nearly unbiased variable selection under minimax + concave penalty. The Annals of Statistics, 38(2), (2010): 894-942. -[^7]: 9 +[^4]: Yuan, Ming, and Yi Lin. “Model selection and estimation in + regression with grouped variables.” Journal of the Royal Statistical + Society Series B: Statistical Methodology 68.1 (2006): 49-67. -[^8]: 1 +[^5]: Chiquet, Julien, Yves Grandvalet, and Camille Charbonnier. + “Sparsity with sign-coherent groups of variables via the + cooperative-lasso.” (2012): 795-830. -[^9]: 4 +[^6]: Simon, Noah, et al. “A sparse-group lasso.” Journal of + computational and graphical statistics 22.2 (2013): 231-245. -[^10]: 5 +[^7]: Chernozhukov, Victor, Christian Hansen, and Yuan Liao. “A lava + attack on the recovery of sums of dense and sparse signals.” The + Annals of Statistics (2017): 39-76. -[^11]: 6 +[^8]: Hoerl, Arthur E., and Robert W. Kennard. “Ridge regression: Biased + estimation for nonorthogonal problems.” Technometrics 12.1 (1970): + 55-67. -[^12]: 7 +[^9]: Slawski, Martin. “The structured elastic net for quantile + regression and support vector classification.” Statistics and + Computing 22.1 (2012): 153-168. -[^13]: 8 +[^10]: Hoefling, Holger. “A path algorithm for the fused lasso signal + approximator.” Journal of Computational and Graphical Statistics + 19.4 (2010): 984-1006. -[^14]: 9 +[^11]: Grandvalet, Yves, Julien Chiquet, and Christophe Ambroise. + “Sparsity by worst-case penalties.” arXiv preprint arXiv:1210.2077 + (2012). diff --git a/README.qmd b/README.qmd index f478b78..28eb766 100644 --- a/README.qmd +++ b/README.qmd @@ -23,28 +23,38 @@ model selection purpose (information criteria, cross-validation, stability selec **Quadrupen** covers the following regularizers -- LASSO^[1] (Least Absolute Shrinkage and Selection Operator) -- SCAD^[2] (Smoothly Clip Absolute Deviation) - _preliminary version_ -- MCP^[3] (Minimax Concave Penalty) - _preliminary version_ -- Group-LASSO^[4] ($\ell_1/\ell_2$ or $\ell_1/\ell_\infty$) -- Cooperative-LASSO^[5] -- Sparse Group-LASSO^[6] and Sparse Cooperative-LASSO +- LASSO[^1] (Least Absolute Shrinkage and Selection Operator) +- SCAD[^2] (Smoothly Clip Absolute Deviation) - _preliminary version_ +- MCP[^3] (Minimax Concave Penalty) - _preliminary version_ +- Group-LASSO[^4] ($\ell_1/\ell_2$ or $\ell_1/\ell_\infty$) +- Cooperative-LASSO[^5] +- Sparse Group-LASSO[^6] and Sparse Cooperative-LASSO - Bounded Regression ($\ell_\infty$-norm). -- LAVA^[10] and the group-LAVA variants for the all the group-sparse methods -- Ridge Regression^[11] +- LAVA[^10] and the group-LAVA variants for the all the group-sparse methods +- Ridge Regression[^11] For all these regularizers, **Quadrupen** offers the possibility to add an $\ell_2$/ridge-like "structured" penalty to embed some external knowledge about -the statistical dependence between the features. This is sometimes referred to as the -"Structured Elastic-Net"^[7]. +the statistical dependence between the features. This is sometimes referred to as the "Structured Elastic-Net"[^7]. -We also provide in the package the implementation of the Generalized Fused-LASSO^[8] originally -proposed by Holger Höfling now archived from CRAN ([original repo here](https://github.com/cran/FusedLasso)). +We also provide in the package the implementation of the Generalized Fused-LASSO[^8] originally proposed by Holger Höfling now archived from CRAN ([original repo here](https://github.com/cran/FusedLasso)). -The original version of **Quadrupen** only includes Lasso, Elastic-Net and Bounded regression. It was used as an illustration for our paper *"Sparsity by worst-case penalties"*^[9]. I eventually used it to include my personal implementation of sparse methods for linear regression. +The original version of **Quadrupen** only includes Lasso, Elastic-Net and Bounded regression. It was used as an illustration for our paper *"Sparsity by worst-case penalties"*[^9]. I eventually used it to include my personal implementation of sparse methods for linear regression. While likely not as fast as highly specialized packages like *glmnet*, the use of a working set algorithm combined with efficient solvers, sparse matrix support when applicable, and templated C++ code makes it both competitive and versatile. +[^1]: Tibshirani, Robert. "Regression shrinkage and selection via the lasso." Journal of the Royal Statistical Society Series B: Statistical Methodology 58.1 (1996): 267-288. +[^2]: Fan, Jianqing, and Runze Li. "Variable selection via nonconcave penalized likelihood and its oracle properties." Journal of the American statistical Association 96.456 (2001): 1348-1360. +[^3]: Zhang, C. H. Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38(2), (2010): 894-942. +[^4]: Yuan, Ming, and Yi Lin. "Model selection and estimation in regression with grouped variables." Journal of the Royal Statistical Society Series B: Statistical Methodology 68.1 (2006): 49-67. +[^5]: Chiquet, Julien, Yves Grandvalet, and Camille Charbonnier. "Sparsity with sign-coherent groups of variables via the cooperative-lasso." (2012): 795-830. +[^6]: Simon, Noah, et al. "A sparse-group lasso." Journal of computational and graphical statistics 22.2 (2013): 231-245. +[^7]: Slawski, Martin. "The structured elastic net for quantile regression and support vector classification." Statistics and Computing 22.1 (2012): 153-168. +[^8]: Hoefling, Holger. "A path algorithm for the fused lasso signal approximator." Journal of Computational and Graphical Statistics 19.4 (2010): 984-1006. +[^9]: Grandvalet, Yves, Julien Chiquet, and Christophe Ambroise. "Sparsity by worst-case penalties." arXiv preprint arXiv:1210.2077 (2012). +[^10]: Chernozhukov, Victor, Christian Hansen, and Yuan Liao. "A lava attack on the recovery of sums of dense and sparse signals." The Annals of Statistics (2017): 39-76. +[^11]: Hoerl, Arthur E., and Robert W. Kennard. "Ridge regression: Biased estimation for nonorthogonal problems." Technometrics 12.1 (1970): 55-67. + ## Installation ```{r install, eval=FALSE} @@ -59,7 +69,7 @@ This example is extracted form chapter 1 of my [habilitation](https://tel.archiv First, load the package -```{r} +```{r load-quadrupen} library(quadrupen) ``` @@ -67,7 +77,7 @@ library(quadrupen) See pages 29--30 in my [habilitation](https://tel.archives-ouvertes.fr/tel-01288976/). Code for additional function is given by the end of the present document (Appendix). -```{r, echo=FALSE} +```{r chol-functions-internal, echo=FALSE} chol.uniform <- function(p,rho) { q <- 0 ## sum_k^(i-1) c.k^2 @@ -131,12 +141,12 @@ x <- rPred.block(n, p, sizes = group, rho=c(0.25, 0.75, 0.25, 0.75, 0.25)) ``` Indeed, the correlation structure between the regressors exhibits a strong pattern: -```{r echo=FALSE} +```{r img-cor-struct, echo=FALSE} Matrix::image(Matrix::Matrix(cor(x))) ``` We draw the response variable by fixing the variance of the noise ratio to get an $R^2$ equal to $0.8$. -```{r} +```{r draw-response} dat <- rlm(x,beta,mu,r2=0.8) y <- dat$y sigma <- dat$sigma @@ -148,49 +158,55 @@ Now we try the available penalized regression methods in `quadrupen` to fit the #### Ridge regression ($\ell_2$ penalty) -```{r ridge_nostruct} +```{r ridge-nostruct} plot(ridge(x,y, intercept=FALSE), labels=labels) ``` #### Lasso ($\ell_1$ penalty) -```{r lasso_nostruct} +```{r lasso-nostruct} plot(lasso(x,y, intercept=FALSE), labels=labels) ``` #### MCP (Minimax Concave Penalty) -```{r mcp_nostruct} +```{r mcp-nostruct} plot(mcp(x,y, intercept=FALSE), labels=labels) ``` #### SCAD (Smoothly Clipped Absolute Deviation) -```{r scad_nostruct} +```{r scad-nostruct} plot(scad(x,y, intercept=FALSE), labels=labels) ``` +#### SCAD (Smoothly Clipped Absolute Deviation) + +```{r fused-lasso} +plot(fused_lasso(x,y, lambda2 = 5, intercept=FALSE), labels=labels) +``` + #### Elastic-net ($\ell_1+\ell_2$ penalty) -```{r enet_nostruct} +```{r enet-nostruct} plot(elastic_net(x,y, lambda2=1, intercept=FALSE), labels=labels) ``` #### Bounded regression ($\ell_\infty$ penalty) -```{r breg_nostruct} +```{r breg-nostruct} plot(bounded_reg(x,y, lambda2=0, intercept=FALSE), labels=labels) ``` #### Bounded regression + Ridge ($\ell_\infty+\ell_2$ penalty) -```{r bregridge_nostruct} +```{r bregridge-nostruct} plot(bounded_reg(x,y, lambda2=5, intercept=FALSE), labels=labels) ``` #### Lava (sparse + dense signal decomposition) -```{r lava_nostruct} +```{r lava-nostruct} out_lava <- lava(x,y, lambda2=1, intercept=FALSE) out_lava$plot_path(component = "sparse", labels=labels) out_lava$plot_path(component = "dense", labels=labels) @@ -290,23 +306,9 @@ We let the possibility to add structured-$\ell_2$ penalty to this mixed-group pe plot(group_sparse_lm(x, y, group, type = "l2", alpha = 0.5, lambda2 = 2, struct = L, intercept=FALSE), labels=labels) ``` -## References - -[^1]: Tibshirani, Robert. "Regression shrinkage and selection via the lasso." Journal of the Royal Statistical Society Series B: Statistical Methodology 58.1 (1996): 267-288. -[^2]: Fan, Jianqing, and Runze Li. "Variable selection via nonconcave penalized likelihood and its oracle properties." Journal of the American statistical Association 96.456 (2001): 1348-1360. -[^3]: Zhang, C. H. Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38(2), (2010): 894-942. -[^4]: Yuan, Ming, and Yi Lin. "Model selection and estimation in regression with grouped variables." Journal of the Royal Statistical Society Series B: Statistical Methodology 68.1 (2006): 49-67. -[^5]: Chiquet, Julien, Yves Grandvalet, and Camille Charbonnier. "Sparsity with sign-coherent groups of variables via the cooperative-lasso." (2012): 795-830. -[^6]: Simon, Noah, et al. "A sparse-group lasso." Journal of computational and graphical statistics 22.2 (2013): 231-245. -[^7]: Slawski, Martin. "The structured elastic net for quantile regression and support vector classification." Statistics and Computing 22.1 (2012): 153-168. -[^8]: Hoefling, Holger. "A path algorithm for the fused lasso signal approximator." Journal of Computational and Graphical Statistics 19.4 (2010): 984-1006. -[^9]: Grandvalet, Yves, Julien Chiquet, and Christophe Ambroise. "Sparsity by worst-case penalties." arXiv preprint arXiv:1210.2077 (2012). -[^10]: Chernozhukov, Victor, Christian Hansen, and Yuan Liao. "A lava attack on the recovery of sums of dense and sparse signals." The Annals of Statistics (2017): 39-76. -[^11]: Hoerl, Arthur E., and Robert W. Kennard. "Ridge regression: Biased estimation for nonorthogonal problems." Technometrics 12.1 (1970): 55-67. - ## Appendix: functions for data generation -```{r appendix_func_data, eval=FALSE} +```{r appendix-func-data, eval=FALSE} chol.uniform <- function(p,rho) { q <- 0 ## sum_k^(i-1) c.k^2 @@ -354,3 +356,5 @@ rPred.block <- function(n, p, sizes=rmultinom(1,p,rep(p/K,K)), rho=rep(0.75,4)) return(t(replicate(n, rmv(), simplify=TRUE))) } ``` + +## References diff --git a/man/figures/breg-nostruct-1.png b/man/figures/breg-nostruct-1.png new file mode 100644 index 0000000000000000000000000000000000000000..608a4ff7288815c9a90b21875679b150e16c936e GIT binary patch literal 129777 zcmcG#WpG@v(l+RrV`gS%h?(OtGsMiy%PJtvdO{WDB@p58;K0DZ5TztVmBGNk|A2vg*@6WJJ-NS-GzJx49V9iK z!N8Du|6N}O?Tbyoz(~NPM1@s6GS1e`buiRdVYb+8Uu#BZyqSN2{~|N!N5eeBlapmH zd^CEAKa?|SIUYuzjpPVrt$t)82}8sbZn@J-)?MOdJAD6%#}R^~;kex)xQ88_>U<#p z|GK%%S6iI8)txW8KH>{r9{f`k{CJIf0z3Ddb`|N z-`qZc-W|gRt;_Pr2D6-7-E{*UB<4$T23QDRN@QrJve3Zc28%| zeZ^0WGj&`7YcY2lbF|@HD%a>8_laLujzb0aX2{svVGg= 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z=TSJ@x0-R?^}G^*jU5uBw3KNV&8{D&CF%NPp20r2q_q{o)?kmfvu1HeviAkmqFHXe zBDXI9p)(ha!~F+l($NqIGQ>XXruF+eh%_<2TYjQ9xN3oh)8LFFM&am)_5#1{LxNV+ zOw~^8ucnJ~#fF^doQuI4VwEjPvE615g$t)F)6?BV(0zBEu5jsy%iOOlJayP)x{;5V zMo7y01*B85-h{o#B7Ke{{R=UrKcw3=u(_-vcxIc+3~CFDjQ-M-y7pHd-Nft^3wBtG(=bE@E+;Y3b3h zSaS{lK-E-wE2HC%_Ldc2>bFL0$)wr0nXMoNIDx}!!#>~e3Wsi(e!b$&m(DET-0O(C=kd*JuwGqkD! zRha%IHFYftdu4J5>y95HMBkdK$bEwPP1K01(h56@{O(pXe Date: Sat, 23 May 2026 09:29:00 +0200 Subject: [PATCH 4/4] fix lasso test --- tests/testthat/test-lasso.R | 38 ++++++++++++++++++------------------- 1 file changed, 18 insertions(+), 20 deletions(-) diff --git a/tests/testthat/test-lasso.R b/tests/testthat/test-lasso.R index b2582f5..845e3ef 100644 --- a/tests/testthat/test-lasso.R +++ b/tests/testthat/test-lasso.R @@ -16,79 +16,77 @@ test_that("lasso_quad2lars", { lambda1=lambda1, lambda2=0, control=list(method="quadra")) quad <- list(coef = as.matrix(lasso.quadru$coefficients), rss = deviance(lasso.quadru)) - + lars <- list(coef = t(lasso.larsen$beta[-iols, ]), rss = lasso.larsen$RSS[-iols]) - + return(list(quad=quad,lars=lars)) } - + ## PROSTATE DATA SET x <- testDataEnet$x_prostate y <- testDataEnet$y_prostate - + ## Run the tests... with.intercept <- get.lars(x,y,TRUE,TRUE) expect_equal(with.intercept$quad, with.intercept$lars, check.attributes = FALSE, tolerance = tol) - + with.intercept.unnormalized <-get.lars(x,y,TRUE,FALSE) expect_equal(with.intercept.unnormalized$quad, with.intercept.unnormalized$lars, check.attributes = FALSE, tolerance = tol) - + without.intercept <- get.lars(x,y,FALSE,TRUE) expect_equal(without.intercept$quad, without.intercept$lars, check.attributes = FALSE, tolerance = tol) - + without.intercept.unnormalized <- get.lars(x,y,FALSE,FALSE) expect_equal(without.intercept.unnormalized$quad, without.intercept.unnormalized$lars, check.attributes = FALSE, tolerance = tol) - + ## RANDOM DATA x <- testDataEnet$x_sim y <- testDataEnet$y_sim - + ## Run the tests... with.intercept <-get.lars(x,y,TRUE,TRUE) expect_equal(with.intercept$coef.quad, with.intercept$coef.lars, check.attributes = FALSE, tolerance = tol) - + with.intercept.unnormalized <-get.lars(x,y,TRUE,FALSE) expect_equal(with.intercept.unnormalized$coef.quad, with.intercept.unnormalized$coef.lars, check.attributes = FALSE, tolerance = tol) - + without.intercept <-get.lars(x,y,FALSE,TRUE) expect_equal(without.intercept$coef.quad, without.intercept$coef.lars, check.attributes = FALSE, tolerance = tol) - + without.intercept.unnormalized <-get.lars(x,y,FALSE,FALSE) expect_equal(without.intercept.unnormalized$coef.quad, without.intercept.unnormalized$coef.lars, check.attributes = FALSE, tolerance = tol) - + }) test_that("lasso_quad2glmnet", { - + require(glmnet) - + ## SECOND CHECK: compare to glmnet with prescaling of x x <- matrix(rnorm(100*50),100,50) y <- rnorm(100) y <- y - mean(y) n <- nrow(x) p <- ncol(x) - + ## If thresh is set to the default, the test won't pass!!! ## This is because coordinate descent is fast yet not extremely accurate lasso.glmn <- glmnet(x,y, lambda.min.ratio=1e-2)#, thresh=1e-20) lasso.quad <- elastic_net(x,y, lambda1=lasso.glmn$lambda*sqrt(n), lambda2=0) - + quad <- list(coef = as.matrix(lasso.quad$coefficients), - mu = lasso.quad$intercept, fitted = as.matrix(lasso.quad$fitted)) - + glmn <- list(coef = as.matrix(lasso.glmn$beta), - mu = lasso.glmn$a0, fitted = predict(lasso.glmn,x))

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