Optimal stacking weights

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

Usage

get_stacking_weights(log_loopd, solver = "ECOS")

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 "ECOS". Internally calls CVXR::psolve().

Value

A list of length 2.

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

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

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, solver = "ECOS", verbose = TRUE)
#> 
#> STACKING WEIGHTS:
#> 
#>           | phi | nu  | noise_sp_ratio | weight |
#> +---------+-----+-----+----------------+--------+
#> | Model 1 |  1.5|  0.5|               1| 0.000  |
#> | Model 2 |  3.0|  0.5|               1| 0.285  |
#> | Model 3 |  1.5|  1.0|               1| 0.000  |
#> | Model 4 |  3.0|  1.0|               1| 0.715  |
#> +---------+-----+-----+----------------+--------+
#> 

loopd_mat <- do.call('cbind', mod1$loopd)
w_hat <- get_stacking_weights(loopd_mat)
print(round(w_hat$weights, 4))
#> [1] 0.0000 0.2845 0.0000 0.7155
print(w_hat$status)
#> [1] "optimal"