Full DAG Sampling Method

# Full DAG Sampling Method

The sampler performs vectorized forward sampling over proposal_view.topological_order.

Each node has:

• a base prior P0(X_i);
• zero or more pairwise CPD edges P(X_i | X_p);
• optional full-CPT overlays P(X_i | X_pa);
• optional conditional masks for hard or soft local consistency constraints.

For target node X_i, candidate value v receives:

`text log q_i(v) = log P0_i(v) + gamma_i * sum_pairwise w_e [log P_e(v | x_p) - log P0_i(v)] + gamma_i * sum_full_cpt w_c [log P_c(v | x_pa) - log P0_i(v)] `

The shrinkage term is:

`text gamma_i = 1 / max(1, sqrt(sum_j weight_j^2)) `

This keeps dense multi-parent nodes from becoming too sharp. Full CPTs can mark replace_pairwise_parent_edges=true; in that case pairwise edges from those parents to the same target are skipped to avoid double counting.

Conditional masks multiply the proposal distribution before the draw (the implementation samples by inverse CDF on the unnormalized masked proposal, which selects values with exactly the normalized probabilities):

• bad_values with bad_value_multiplier=0 are hard guards.
• downweight_values are soft penalties.
• preferred_values with penalize_values_outside_preferred_set=true are

Default sampling uses emit_only=True, which excludes nodes where emit:false. Use --include-hidden or decode_row(..., include_hidden=True) for all graph assignments.