scm_weights_cpp: SCM Outer Weights (Joint Optimization of W and V)
In coresynth: Fast and Unified Synthetic Control Methods

scm_weights_cpp

R Documentation

SCM Outer Weights (Joint Optimization of W and V)

Description

Jointly optimises donor weights W (on the simplex) and the diagonal metric matrix V via coordinate descent on the pre-treatment prediction MSPE, following Abadie, Diamond & Hainmueller (2010).

Usage

scm_weights_cpp(
  X0,
  X1,
  Z0,
  Z1,
  max_iter = 100L,
  tol = 1e-04,
  t_train = -1L,
  z_rows = NULL,
  multistart = FALSE,
  cheap_face = FALSE,
  wolfe = FALSE
)

Arguments

`X0`	Covariate matrix for control units (k x N_co, typically pre-treatment outcomes)
`X1`	Covariate vector for the treated unit (k x 1)
`Z0`	Outcome matrix for control units in the pre-treatment window (T_pre x N_co)
`Z1`	Outcome vector for the treated unit in the pre-treatment window (T_pre x 1)
`max_iter`	Maximum coordinate-descent iterations (default 100)
`tol`	Convergence tolerance on MSPE improvement (default 1e-4)
`t_train`	Validation-window split for V selection. -1 (default): V selected on the full Z window (in-sample). Positive: rows t_train..(T_pre-1) of Z form the validation window used to select V (W is fitted on the full X throughout); after selecting V*, W is refit and the reported loss uses the full Z window.
`z_rows`	Optional 1-based row indices of Z defining the evaluation window for the outer V optimisation (the `v_window` argument of `scm_fit()`). `NULL` (default) evaluates on the full Z window. Takes precedence over `t_train`; the reported loss always uses the full Z window.
`multistart`	If `TRUE`, the outer V optimisation runs a deterministic multi-start search (screened start set, coordinate-descent polish, Nelder-Mead refinement) instead of a single coordinate-descent pass from the uniform V. The result is never worse (in outer loss) than the single-start path.
`cheap_face`	If `TRUE`, the inner simplex QP first tries a cheap bordered-KKT direct solve on each active-set face, falling back to the scale-robust null-space solve when that system is singular. Worth trying only in the outcomes-only regime (no user predictors, no predictor rescaling), where V is dense and the faces that carry the fit are well conditioned; it reproduces the null-space solution to round-off. `FALSE` (default) goes straight to the null-space solve, which is what predictor fits need for scale invariance and rank-deficient faces.
`wolfe`	If `TRUE`, every inner QP is solved with the Wolfe min-norm-point method, which returns a Caratheodory-sparse optimum (at most k+1 donors carry weight) instead of one arbitrary point of a degenerate optimal face. `FALSE` (default) uses the warm-started active-set solver.

Details

When t_train > 0, V is selected by minimising MSPE on a validation window (rows t_train..T_pre-1 of Z) while W is fitted on the full predictor matrix X. This is appropriate when X is a fixed predictor matrix that contains no validation-period outcome information (the user-supplied predictors case). For the outcomes-only case the proper Abadie (2021) S.3.2 train/validation split is implemented in R (.scm_oos_outcomes()): candidate W(V) are fitted on training-half outcomes only, by passing the training rows as X and the validation rows as Z to this function with t_train = -1.