Bootstrap for Bottom-Up ParceLiNGAM

Bootstrap for Bottom-Up ParceLiNGAM

Usage

lingam_parce_bootstrap(
  X,
  n_sampling,
  prior_knowledge = NULL,
  alpha = 0.1,
  independence = "hsic",
  ind_corr = 0.5,
  reg_method = "adaptive_lasso",
  lambda = "BIC",
  init_method = "ols",
  seed = NULL,
  verbose = TRUE,
  parallel = FALSE,
  n_cores = NULL,
  compute_total_effects = TRUE
)

Arguments

X

Numeric matrix (n_samples x n_features)

n_sampling

Number of bootstrap iterations

prior_knowledge

Prior knowledge matrix (NULL allowed)

alpha

Significance level, passed to lingam_parce()

independence

Independence measure, passed to lingam_parce()

ind_corr

F-correlation rejection threshold, passed to lingam_parce()

reg_method

Regression method ("ols", "lasso", "adaptive_lasso", "ridge")

lambda

Lambda selection ("lambda.min", "lambda.1se", "AIC", "BIC", "oracle")

init_method

Method for estimating the initial weights of adaptive LASSO regression ("ols" or "ridge")

seed

Random seed (NULL allowed)

verbose

Whether to display progress (logical)

parallel

Whether to use parallel processing (logical)

n_cores

Number of cores to use (integer, NULL allowed)

compute_total_effects

Whether to also estimate total causal effects for every variable pair on each bootstrap iteration (logical, default TRUE).

Value

A BootstrapResult (list); see lingam_direct_bootstrap() for the query helpers that operate on it (get_probabilities(), get_causal_direction_counts(), get_directed_acyclic_graph_counts(), get_total_causal_effects()).

Details

Total effects are path sums, not regression estimates. Each iteration's total-effect matrix is built from calculate_total_effect() (summing products of adjacency-matrix coefficients along every directed path), matching the upstream Python implementation's bootstrap method (estimate_total_effect2). If a variable's row in the adjacency matrix contains NA (it is part of an unresolved block), all of its outgoing total effects are set to NA for that iteration, since its causal parents cannot be identified.

NA (unresolved) edges are treated as absent when aggregating. Both the adjacency matrix and the total-effect matrix have NA replaced by 0 before being stored in the returned BootstrapResult, matching the numpy comparison semantics used by the upstream implementation (where np.abs(nan) > threshold evaluates to FALSE). This means, for example, get_probabilities() reports the confounded pair's edge probability as the fraction of resamples in which the order happened to resolve, not as NA.

causal_orders is not populated (unlike lingam_direct_bootstrap()): ParceLiNGAM's causal order can include an unresolved block, which does not fit the fixed-length integer-vector format causal_orders requires. As a result, get_causal_order_stability() cannot be used with a BootstrapResult returned by this function.

Examples

# \donttest{
confounded <- generate_parce_sample(n = 500, seed = 1)

bs <- lingam_parce_bootstrap(confounded$data,
  n_sampling = 10L,
  reg_method = "ols",
  seed = 42
)
#> Bootstrap: 10 iterations, method=ols (sequential)
#>   iteration 1 / 10
#>   iteration 10 / 10
#> Completed in 19.4 seconds.
get_probabilities(bs)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]  0.0  0.2  0.4  0.4  0.0  0.0
#> [2,]  0.4  0.0  0.4  0.4  0.1  0.3
#> [3,]  0.0  0.0  0.0  0.0  0.0  0.0
#> [4,]  0.0  0.1  0.1  0.0  0.0  0.0
#> [5,]  0.6  0.6  0.6  0.6  0.0  0.4
#> [6,]  0.4  0.3  0.4  0.4  0.2  0.0
# }