Masking Causality and Conditional Dependence

Conditional independence testing is a critical component of feature screening, invariant statistical models, and causal discovery. Many of these algorithms rely on the sequential application of conditional independence tests, and their stability hinges on how their outcomes interact. We study this meta-dependence'' between conditional independence properties using the following geometric intuition: satisfying each conditional independence property constrains the space of possible joint distributions to a manifold. The meta-dependence'' of multiple conditional independences in a probability distribution is informed by its position relative to these manifolds. We provide a simple-to-compute measure of this meta-dependence using moment projections, with a closed-form expression for multivariate Gaussian distributions, and consolidate our findings empirically using both synthetic and real-world data. Our measure of meta-dependence does not rely on graphical properties of the distribution and can be computed directly from summary statistics such as a covariance matrix, allowing for various applications. We demonstrate one use case of meta-dependence, using a simple redundancy metric to tune significance thresholds and improve causal discovery.

Machine learning systems deployed for credit, hiring, and resource distribution are increasingly subject to regulatory oversight from policies such as the EU AI Act and GDPR. Current fairness governance practices rely on observational fairness metrics, post-hoc explainability, and immutable audit logs, but provide limited support for causal attribution and efficient evidentiary verification. We introduce Causal Evidentiary Governance (CEG), a framework in which regulated institutions commit to a versioned directed acyclic graph (DAG) that partitions causal pathways into allowable and disallowed groups. The Causal Harm Rate measures prediction variation attributable to disallowed causal pathways. Each decision is accompanied by a signed Decision-Evidence Packet (DEP), cryptographically binding the prediction to a digest of the published DAG and path-specific attributions. DEP digests can be appended to a Merkle tree to enable logarithmic-cost inclusion proofs. We validate CEG through a two-layer empirical methodology using demographic summaries from four years of PMA credit supervisory data to construct 10,000 synthetic credit applicants across four strategic DAG counterfactuals. Causal Harm Rate isolates injected causal effects more clearly than demographic parity or equalized odds. Cross-model validation and ablation studies assess robustness. Evaluation on the German Credit dataset shows that harm associated with specific causal pathways can be substantially understated by associational fairness metrics. Finally, a proof-of-concept implementation demonstrates operationally plausible throughput and highlights relevant performance tradeoffs.

We study causal logistic bandits with counterfactual fairness constraints. The causal structure is given through known factual and counterfactual feature maps that share an unknown logistic reward parameter, but the learner observes only factual rewards. Consequently, the directions determining counterfactual feasibility need not be identifiable from the available feedback. The closest prior analyses either omit a coverage condition or impose a comparatively strong one, and do not establish matching lower bounds. We first show that some coverage condition is necessary: without a coverage-type restriction, factually indistinguishable environments with different optimal fair actions force $Ω(T)$ expected joint loss. Under a weaker full-rank condition on the factual covariance pooled across actions, we identify a target-specific information scale $V_\star$ that measures the difficulty of estimating rewards and counterfactual effects from factual feedback. We construct worst-case families satisfying this condition on which every policy incurs expected joint loss $Ω\left(\left[V_\star\min\{\log K,d\}\right]^{1/3}T^{2/3}\right)$. We also give an explore--then--exploit procedure tuned using $V_\star$ and an adaptive algorithm that does not require its value. Both algorithms achieve $\max\{R_T,V_T\}=\widetilde{O}\left(\left[V_\star\min\{\log K,d\}\right]^{1/3}T^{2/3}+κd/σ_0^2\right)$, where $R_T$ is regret relative to the best fair action and $V_T$ denotes the cumulative stage-wise positive violations. Thus the upper and lower bounds match in their leading dependence on $T$, $V_\star$, and $\min\{\log K,d\}$, up to logarithmic factors.