Referential Integrity

The core mechanism that verifies every foreign key value in a child table has a corresponding primary key in the parent table. During synthesis, the generator must either:

• Sample from existing parent keys
• Generate parent records first, then reference them
• Use declarative mapping rules to maintain consistency

Without this, synthetic orders might reference non-existent customer IDs, breaking downstream analytics.

Orphan records occur when a child row references a parent key that doesn't exist. Prevention strategies include:

• Cascading synthesis: Generate tables in dependency order (parents before children)
• Referential lookup tables: Pre-compute valid key combinations before generation
• Constraint-aware sampling: Reject or re-sample invalid foreign keys during generation

This is critical for composite foreign keys spanning multiple columns.

In normalized schemas with transitive dependencies (Table A → Table B → Table C), integrity must propagate across the entire chain. A synthetic transaction must reference a valid account, which must reference a valid customer.

• Topological sort of table dependencies determines generation order
• Cyclic foreign keys require special handling with deferred constraint checking
• Denormalization may be temporarily applied to break complex cycles

Enforcing referential integrity must not distort the joint distribution between related tables. If 30% of real customers have orders, the synthetic data must preserve this ratio.

• Conditional generation ensures child table distributions match parent attributes
• Marginal preservation maintains column-level statistics across relationships
• Correlation structures between foreign key columns and other attributes remain intact

When synthetic data requires modification or regeneration of parent records, the system must propagate changes:

• CASCADE: Automatically update or delete dependent child records
• SET NULL: Nullify foreign keys when parent records are removed
• RESTRICT: Block parent modifications if children exist

These policies mirror production database rules and prevent integrity violations during iterative synthesis.

Advanced generators use rejection sampling or constrained optimization to ensure every generated row satisfies all foreign key constraints:

• Accept-reject: Discard invalid samples and retry until constraints pass
• Direct constrained generation: Build valid key combinations from known parent sets
• Probabilistic graphical models: Encode table relationships as a Bayesian network for coherent sampling

This guarantees 100% referential integrity without post-hoc patching.

A database rule that ensures a value in one table's column matches a value in another table's primary key column. In synthetic data generation, this constraint must be programmatically enforced to prevent the creation of orphan records—synthetic rows that reference non-existent parent rows. The synthesis engine must map the generated primary key space of the parent table to the foreign key column of the child table, preserving the exact cardinality and referential logic of the source schema.

The algorithmic safeguard that ensures no synthetic record in a child table references a non-existent parent record. Prevention strategies include:

• Sequential generation: Parent tables are synthesized first, and child table foreign keys are sampled exclusively from the generated parent primary keys.
• Conditional modeling: The child table generator is conditioned on the parent table's output, learning the conditional distribution P(child | parent).
• Rejection sampling: Invalid child records are discarded and resampled until a valid foreign key is assigned.

The degree to which a synthetic dataset accurately reproduces the statistical properties of the original data. In a relational context, fidelity must be measured not just on marginal distributions within single tables but also on joint distributions across tables. A high-fidelity multi-table synthesis preserves the true correlation structure between parent and child attributes, ensuring that downstream analytics and machine learning models trained on the synthetic data yield conclusions consistent with the real data.

A structured methodology combining statistical disclosure limitation techniques with risk assessment metrics to ensure synthetic datasets meet a predefined privacy threshold. When enforcing referential integrity, the framework must verify that the relational constraints themselves do not leak information. For example, preserving exact foreign key cardinalities could inadvertently reveal the size of sensitive subgroups. The framework balances utility (valid relationships) against privacy (plausible deniability of individual links).