Estimates the optimal complexity parameter for the SDTree using cross-validation. The transformations are estimated for each training set and validation set separately to ensure independence of the validation set.
cvSDTree(
formula = NULL,
data = NULL,
x = NULL,
y = NULL,
max_leaves = NULL,
cp = 0,
min_sample = 5,
mtry = NULL,
fast = TRUE,
Q_type = "trim",
trim_quantile = 0.5,
q_hat = 0,
Qf = NULL,
A = NULL,
gamma = 0.5,
gpu = FALSE,
mem_size = 1e+07,
max_candidates = 100,
nfolds = 3,
cp_seq = NULL,
mc.cores = 1,
Q_scale = TRUE
)Object of class formula or describing the model to fit
of the form y ~ x1 + x2 + ... where y is a numeric response and
x1, x2, ... are vectors of covariates. Interactions are not supported.
Training data of class data.frame containing the variables in the model.
Predictor data, alternative to formula and data.
Response vector, alternative to formula and data.
Maximum number of leaves for the grown tree.
Complexity parameter, minimum loss decrease to split a node.
A split is only performed if the loss decrease is larger than cp * initial_loss,
where initial_loss is the loss of the initial estimate using only a stump.
Minimum number of observations per leaf.
A split is only performed if both resulting leaves have at least
min_sample observations.
Number of randomly selected covariates to consider for a split,
if NULL all covariates are available for each split.
If TRUE, only the optimal splits in the new leaves are
evaluated and the previously optimal splits and their potential loss-decrease are reused.
If FALSE all possible splits in all the leaves are reevaluated after every split.
Type of deconfounding, one of 'trim', 'pca', 'no_deconfounding'.
'trim' corresponds to the Trim transform Cevid2020SpectralModelsSDModels
as implemented in the Doubly debiased lasso Guo2022DoublyConfoundingSDModels,
'pca' to the PCA transformationPaul2008PreconditioningProblemsSDModels.
See get_Q.
Quantile for Trim transform,
only needed for trim and DDL_trim, see get_Q.
Assumed confounding dimension, only needed for pca,
see get_Q.
Spectral transformation, if NULL
it is internally estimated using get_Q.
Numerical Anchor of class matrix. See get_W.
Strength of distributional robustness, \(\gamma \in [0, \infty]\).
See get_W.
If TRUE, the calculations are performed on the GPU.
If it is properly set up.
Amount of split candidates that can be evaluated at once. This is a trade-off between memory and speed can be decreased if either the memory is not sufficient or the gpu is to small.
Maximum number of split points that are proposed at each node for each covariate.
Number of folds for cross-validation. It is recommended to not use more than 5 folds if the number of covariates is larger than the number of observations. In this case the spectral transformation could differ to much if the validation data is substantially smaller than the training data.
Sequence of complexity parameters cp to compare using cross-validation,
if NULL a sequence from 0 to 0.6 with stepsize 0.002 is used.
Number of cores to use for parallel computation.
Should data be scaled to estimate the spectral transformation?
Default is TRUE to not reduce the signal of high variance covariates,
and we do not know of a scenario where this hurts.
A list containing
The optimal complexity parameter.
A table containing the complexity parameter, the mean and the standard deviation of the loss on the validation sets for the complexity parameters. If multiple complexity parameters result in the same loss, only the one with the largest complexity parameter is shown.
set.seed(1)
n <- 50
X <- matrix(rnorm(n * 5), nrow = n)
y <- sign(X[, 1]) * 3 + rnorm(n, 0, 5)
cp <- cvSDTree(x = X, y = y, Q_type = 'no_deconfounding')
cp
#> $cp_min
#> cp
#> 0.076
#>
#> $cp_table
#> cp SDLoss mean SDLoss sd
#> [1,] 0.044 30.89977 4.336556
#> [2,] 0.056 30.65170 5.398475
#> [3,] 0.058 30.60373 5.370633
#> [4,] 0.070 31.28713 5.866639
#> [5,] 0.076 29.12192 5.155334
#> [6,] 0.106 31.64469 3.284572
#> [7,] 0.132 32.25506 3.564472
#> [8,] 0.262 30.93818 5.837083
#> [9,] 0.326 31.50641 6.333261
#> [10,] 0.362 33.27446 3.286796
#> [11,] 0.600 34.64608 4.718930
#>