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High-Dimensional Direct LiNGAM

Source: R/lingam_high_dim.r
lingam_high_dim.Rd

A variant of Direct LiNGAM for high-dimensional data (large p, or p > n). Causal order search is based on moment statistics of non-Gaussianity rather than pairwise independence measures, which is considerably faster for many variables. Unlike lingam_direct(), the algorithm is deterministic (no random restarts).

Usage

lingam_high_dim(X, J = 3L, K = 4L, alpha = 0.5, estimate_adj_mat = TRUE)

Arguments

X

Numeric matrix (n_samples x n_features), data frame or matrix

J

Assumed largest in-degree (single integer, must be >= 3)

K

Degree of the moment used to measure non-Gaussianity (single integer, must be >= 1)

alpha

Cutoff coefficient for pruning away false parents (single numeric value in [0, 1])

estimate_adj_mat

Whether to estimate the adjacency matrix (single logical value). If FALSE, causal-order search still runs but adjacency_matrix is returned as an NA-filled matrix (not NULL, so downstream S3 methods keep working).

Value

A LingamResult object (list), the same class returned by lingam_direct(), containing:

  • adjacency_matrix: adjacency matrix B (n_features x n_features). Convention: B[i, j] is the causal coefficient from variable j to variable i (j -> i). Zero elements indicate no causal relationship. All-NA when estimate_adj_mat = FALSE.

  • causal_order: estimated causal order (integer vector of 1-based indices). Earlier elements are more upstream.

Details

When n_samples <= n_features, the adjacency matrix cannot be estimated with the usual BIC-based Adaptive LASSO, so this function falls back to a cross-validated LASSO (glmnet::cv.glmnet) after emitting a warning. The upstream Python implementation uses LassoLarsCV for this fallback; cv.glmnet follows the same cross-validation design but is not numerically identical (different solver: coordinate descent vs. LARS).

The pruning statistic used during causal-order search (Wang & Drton 2020) is the minimum of a conditional non-Gaussianity statistic over every size-appropriate conditioning subset. The upstream Python implementation (cdt15/lingam) has a return statement mis-indented inside the loop over conditioning subsets, causing it to only ever evaluate the first subset. This R implementation intentionally does not replicate that bug and evaluates every subset, so causal_order and adjacency_matrix are not numerically identical to the upstream Python package.

References

Wang, Y. S. and Drton, M. (2020). High-dimensional causal discovery under non-Gaussianity. Biometrika, 107(1), 41-59.

Examples

sample <- generate_lingam_sample_6(n = 300, seed = 1)
result <- lingam_high_dim(sample$data)
result$causal_order
#> [1] 4 3 1 5 2 6
round(result$adjacency_matrix, 3)
#>       x0 x1     x2    x3 x4 x5
#> x0 0.000  0  0.000 2.918  0  0
#> x1 2.970  0  2.015 0.000  0  0
#> x2 0.000  0  0.000 5.991  0  0
#> x3 0.000  0  0.000 0.000  0  0
#> x4 8.037  0 -1.001 0.000  0  0
#> x5 4.021  0  0.000 0.000  0  0

# \donttest{
if (requireNamespace("glmnet", quietly = TRUE)) {
  # n <= p: falls back to cross-validated LASSO with a warning
  wide_sample <- generate_lingam_large_sample(p = 30, n = 25, seed = 1)
  wide_result <- lingam_high_dim(wide_sample$data)
  wide_result$causal_order
}
#> Warning: Since n_samples <= n_features, the adjacency matrix is estimated with cross-validated lasso (cv.glmnet) instead of BIC-based lambda selection.
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#> Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold
#>  [1]  2  1  3  8 20 13 27  4  5 12 26  6  7 16  9 15 14 23 10 18 21 11 22 24 29
#> [26] 30 25 19 17 28
# }