Optimal stacking weights

Obtains optimal stacking weights given leave-one-out predictive densities for each candidate model.

Usage

get_stacking_weights(log_loopd, solver = NULL, verbose = TRUE)

Arguments

log_loopd: an \(n \times M\) matrix with \(i\)-th row containing the leave-one-out predictive densities for the \(i\)-th data point for the \(M\) candidate models.
solver: specifies the solver to use for obtaining optimal weights. Default is "CLARABEL". Internally calls CVXR::psolve().
verbose: if TRUE, prints output of optimization routine.

Value

A list with elements:

weights: optimal stacking weights as a numeric vector of length \(M\)
status: solver status, returns "optimal" if solver succeeded.
solver: name of the solver used.

References

Yao Y, Vehtari A, Simpson D, Gelman A (2018). "Using Stacking to Average Bayesian Predictive Distributions (with Discussion)." Bayesian Analysis, 13(3), 917-1007. doi:10.1214/17-BA1091 .

Author

Soumyakanti Pan span18@ucla.edu,
Sudipto Banerjee sudipto@ucla.edu

Examples

set.seed(1234)
data(simGaussian)
dat <- simGaussian[1:100, ]

mod1 <- spLMstack(y ~ x1, data = dat,
                  coords = as.matrix(dat[, c("s1", "s2")]),
                  cor.fn = "matern",
                  params.list = list(phi = c(1.5, 3),
                                     nu = c(0.5, 1),
                                     noise_sp_ratio = c(1)),
                  n.samples = 1000, loopd.method = "exact",
                  parallel = FALSE, verbose = TRUE)
#> --------------------------------------------------
#> Solver diagnostics:
#> Installed solvers: CLARABEL, SCS, OSQP, HIGHS
#> Requested solver: DEFAULT (CLARABEL -> ECOS -> SCS)
#> Solver search order: CLARABEL -> SCS
#> --------------------------------------------------
#> ────────────────────────────────── CVXR v1.8.1 ─────────────────────────────────
#> ℹ Problem: 1 variable, 2 constraints (DCP)
#> ℹ Compilation: "CLARABEL" via CVXR::FlipObjective -> CVXR::Dcp2Cone -> CVXR::CvxAttr2Constr -> CVXR::ConeMatrixStuffing -> CVXR::Clarabel_Solver
#> ℹ Compile time: 0.789s
#> ─────────────────────────────── Numerical solver ───────────────────────────────
#> ──────────────────────────────────── Summary ───────────────────────────────────
#> ✔ Status: optimal
#> ✔ Optimal value: -50.8551
#> ℹ Compile time: 0.789s
#> ℹ Solver time: 0.026s
#> 
#> STACKING WEIGHTS:
#> 
#>           | phi | nu  | noise_sp_ratio | weight |
#> +---------+-----+-----+----------------+--------+
#> | Model 1 |  1.5|  0.5|               1| 0.000  |
#> | Model 2 |  3.0|  0.5|               1| 0.284  |
#> | Model 3 |  1.5|  1.0|               1| 0.000  |
#> | Model 4 |  3.0|  1.0|               1| 0.716  |
#> +---------+-----+-----+----------------+--------+
#> 

loopd_mat <- do.call('cbind', mod1$loopd)
w_hat <- get_stacking_weights(loopd_mat)
#> --------------------------------------------------
#> Solver diagnostics:
#> Installed solvers: CLARABEL, SCS, OSQP, HIGHS
#> Requested solver: DEFAULT (CLARABEL -> ECOS -> SCS)
#> Solver search order: CLARABEL -> SCS
#> --------------------------------------------------
#> ────────────────────────────────── CVXR v1.8.1 ─────────────────────────────────
#> ℹ Problem: 1 variable, 2 constraints (DCP)
#> ℹ Compilation: "CLARABEL" via CVXR::FlipObjective -> CVXR::Dcp2Cone -> CVXR::CvxAttr2Constr -> CVXR::ConeMatrixStuffing -> CVXR::Clarabel_Solver
#> ℹ Compile time: 0.21s
#> ─────────────────────────────── Numerical solver ───────────────────────────────
#> ──────────────────────────────────── Summary ───────────────────────────────────
#> ✔ Status: optimal
#> ✔ Optimal value: -50.8551
#> ℹ Compile time: 0.21s
#> ℹ Solver time: 0.056s
print(round(w_hat$weights, 4))
#> [1] 0.0000 0.2845 0.0000 0.7155
print(w_hat$solver)
#> [1] "CVXR:CLARABEL"
print(w_hat$status)
#> [1] "optimal"