[tpc] Save edge-rejection diagnostics to file in tskeleton (sepset path sanity check + test stats)

[felixleopoldo]

Summary

When tskeleton removes an edge x–y (i.e. a CI test returns pval >= alpha), no diagnostic information is currently persisted. This makes it hard to audit why an edge was rejected — especially in the presence of missing data where the MCAR/MAR/MNAR mechanism can cause spurious separations.

Proposed Feature

At the moment an edge is removed inside the repeat loop of tskeleton (currently workflow/rules/structure_learning_algorithms/tpc/R/tskeleton.R, around the pval >= alpha branch), write a row to a CSV file with the following columns:

Column	Description
x	Label of node x
y	Label of node y
sepset	Comma-separated labels of the separating set S
pval	P-value of the CI test that triggered removal
n_complete	Number of complete-case observations used in the test
sepset_on_path	Boolean — whether all elements of S satisfy the path condition (see below)

This logging should only be performed when verbose = TRUE.

Path condition for sepset_on_path

For each element z ∈ S, check whether z lies on some indirect simple path between x and y in the current skeleton G:

• Empty S → always TRUE (no elements to check)
• Each z → TRUE iff x can reach z in G \ {y} and y can reach z in G \ {x} (BFS/DFS on the undirected adjacency matrix)

sepset_on_path is TRUE only if every element of S passes. A FALSE value is a sanity-check warning: the CI test found independence via a node that isn't even on an indirect route between x and y, which may indicate a spurious test result (e.g. due to missing data artefacts).

Rationale: the direct edge x–y is not a path that can be "broken" by conditioning, so only indirect paths (length ≥ 2, no repeated vertices) are relevant. Checking reachability in G \ {y} and G \ {x} respectively is sufficient for this sanity check.

Acceptance Criteria

• A file path for the output CSV is passed into tskeleton (e.g. as an optional edge_log parameter; NULL disables logging)
• Logging only occurs when verbose = TRUE
• One row is appended per removed edge, at the point of removal (i.e. inside the pval >= alpha block)
• n_complete reuses the value already computed at the complete.cases call
• The path check handles the empty-S case correctly (returns TRUE)
• Writing is append-based (write.table(..., append = TRUE)) so partial runs remain readable
• script.R for the tpc module passes the log path through to tskeleton

Context / Motivation

• Debugging missing-data artefacts in the tpc algorithm where CI tests can misfire
• Understanding which edges were removed and whether the separating set is structurally plausible
• The n_complete and pval columns allow filtering out tests based on low sample size or marginal significance

Relevant Code

• workflow/rules/structure_learning_algorithms/tpc/R/tskeleton.R — pval >= alpha branch (edge removal + sepset assignment, ~line 527–529)
• workflow/rules/structure_learning_algorithms/tpc/script.R — entry point that calls tskeleton