SLOPE 1.0.0

This update of SLOPE brings an entirely different C++ implementation of the
underlying package based on the C++ library
libslope. It comes with several large and
breaking changes with respect to the previous version of the package.

We realized that this may throw off some users, and hope that you will be
patient with dealing with the large number of breaking changes.

Breaking Changes

• The caretSLOPE() function that was deprecated has now been removed from the
  package.
• Fields unique, violations, and active_sets are no longer stored in the
  SLOPE object. These fields were typically only used for debugging purposes.
• The prox_method and method arguments in SLOPE() and sortedL1Prox(),
  respectively, have been removed. The proximal operator is now always computed
  using the fast stack-based algorithm. There was never any reason to use the
  slower PAVA algorithm.
• The ADMM solver has been removed from the package. Calling SLOPE() with
  solver = "admm" will now throws a warning and the value will be
  automatically set to "auto".
• alpha is now scaled by n (the number of observations) and differences with
  respect to the type of scaling are no longer taken into account.
• The object coefficients from SLOPE() is now a list of sparse matrices
  (rather than a three-dimensional array as before). Now it contains only the
  coefficients and not the intercepts. The intercepts are instead stored in
  intercepts in the returned object and are always present even if
  intercept = FALSE.
• The behavior of coef.SLOPE() has changed somewhat, and if
  simplify = FALSE, then the returned object is now instead a list of sparse
  matrices (rather than a three-dimensional array as before).
• The default value of q in SLOPE() has changed from
  0.1 * min(1, NROW(x) / NCOL(x)) to 0.1.
• Arguments sigma, n_sigma, and lambda_min_ratio in SLOPE() that were
  previously deprecated have been removed.
• SLOPE() now internally solves the problem normalized by scaling with the
  number of observations, which means that values returned in deviance and
  prmals and duals if diagnostics = TRUE are now scaled by n.
• path_length in SLOPE() now defaults to 100 (previously 20).
• tol_dev_ratio in SLOPE() now defaults to 0.999 (previously 0.995).
• Plots from plot.SLOPE() now use base R graphics rather than ggplot2. This
  means that the plots are more difficult to customize but plot much more faster
  when there are many variables and significantly reduces the dependency load of
  the package. For plots of trained SLOPE objects, which used to be faceted on
  the q parameter, the user now needs to use the standard base R graphics API
  to facet plots via par(mfrow = c(1, 2)) or similar.

Deprecated Functionality

• Arguments tol_rel_gap, tol_infeas, tol_abs, tol_rel, tol_rel_coef in
  SLOPE() are now deprecated. The solvers now all rely on the same tolerance
  criterion, which is set by tol and uses the duality gap normalized by the
  current primal value.
• Arguments screen and screen_alg are now deprecated and have no effect.
  Feature screening is always used. These arguments were only used for
  debugging.
• The argument verbosity in SLOPE() is now defunct and has no effect.
• The argument prox_method in SLOPE() and sortedL1Prox() is now defunct
  and has no effect.

New Features

• Centering x in SLOPE() is now allowed again, even when the matrix is
  sparse.
• Out-of-memory matrices are now allowed through the bigmemory package. Only
  support for dense matrices is available at the moment.
• Centers and scales can now be specified manually by providing vectors to
  center and scale in SLOPE().
• A new solver based on a hybrid method of proximal gradient descent and
  coordinate descent is available and used by default by the Gaussian and
  binomial families. Use it by specifying solver = "hybrid".
• Solver can now be set to "auto", in which case the package automatically
  chooses a solver.
• The returned duality gaps when diagnostics = TRUE are now true duality
  gaps, computed by guaranteeing that the dual variable is feasible (which was
  not the case previously).
• scale in SLOPE() gains a new option "max_abs" which scales the columns
  of x by their maximum absolute value.
• When alpha = "estimate", there is a now an iteration limit in case the
  algorithm does not converge to one set of features. Thanks @RomanParzer.
• plot.SLOPE() gains a new argument magnitudes, which causes the plot to
  only show the magnitudes of the coefficients (which helps if you want to
  visualize cluster structure).
• plot.SLOPE() gains a new argument add_labels, which add numbers for the
  coefficients to the plot. Set to FALSE by default.
• Relaxed SLOPE models can now be fit by specifying gamma in SLOPE().
• plot.trainedSLOPE() gains a new argument index, to select which of the
  hyperparameter combinations to plot for.
• There's a new function plotClusters(), which allows plotting the cluster
  structure in SLOPE. Thanks, @KrystynaGrzesiak!
• SLOPE() gains a new argument cd_type, to control the type of coordinate
  descent used for the hybrid solver, with options "cyclical" and
  "permuted".

Bug Fixes

• Return correct model when training for AUC in trainSLOPE().

Performance Improvements

The new hybrid algorithm that's implemented in libslope and now used in the
package constitutes a major upgrade in terms of performance.

• The solver is now much more memory-efficient and can avoid copies of the
  design matrix entirely by normalizing the columns just-in-time. This is the
  standard behavior. Future versions of the package will allow the user to
  specify whether to copy (and modify) the design matrix or not.

Dependencies

We have made an effort to reduce the footprint of the package and reduce the
number of dependencies.

• The package now relies on Eigen (through RcppEigen) rather than Armadillo,
  which means that there is no longer any reliance on BLAS and LAPACK libraries.
• The dependency on ggplot2 is removed.
• The vdiffr, tidyr, dplyr, bench, scales, and glmnet packages in
  the Suggests field that were used for testing are now removed.