When Marginals Match but Structure Fails: Covariance Fidelity in Generative Models
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| Format: | Preprint |
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2026
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| _version_ | 1866914577199923200 |
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| author | Riasat, Nazia |
| author_facet | Riasat, Nazia |
| contents | Generative models are increasingly deployed as substitutes for real data in downstream scientific workflows, yet standard evaluation criteria remain focused on marginal distribution matching. We argue that this represents a fundamental gap: downstream inference is rarely a marginal operation, and a model that passes every univariate diagnostic can still produce structurally unreliable synthetic data. We introduce covariance-level dependence fidelity, measured by D_Sigma(P,Q) = ||Sigma_P - Sigma_Q||_F, as a principled, computable criterion for evaluating whether a generative model preserves the joint structure of data beyond its univariate marginals. Three results formalise this criterion. First, marginal fidelity provides no constraint on dependence structure: D_Sigma can be made arbitrarily large while all univariate marginals match exactly. Second, covariance divergence induces quantifiable downstream instability, including sign reversals in population regression coefficients. Third, bounding D_Sigma provides positive stability guarantees for dependence-sensitive procedures such as PCA via Davis-Kahan-type bounds. Empirical validation across three domains, image data (Fashion-MNIST VAE, n = 60,000), bulk RNA-seq (TCGA-BRCA, n = 1,111), and a small-sample stress test (Alzheimer's gene expression, n = 113), shows that D_Sigma/delta consistently distinguishes structure-discarding from structure-preserving generators in cases where standard marginal diagnostics show little separation, confirming that covariance-level fidelity provides information orthogonal to existing evaluation metrics across domains and sample sizes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_17041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When Marginals Match but Structure Fails: Covariance Fidelity in Generative Models Riasat, Nazia Machine Learning Artificial Intelligence Methodology 62H20, 62J05, 15A18, 62G99, 68T05, 60E05 I.2.6; G.3; G.1.3; I.5.1 Generative models are increasingly deployed as substitutes for real data in downstream scientific workflows, yet standard evaluation criteria remain focused on marginal distribution matching. We argue that this represents a fundamental gap: downstream inference is rarely a marginal operation, and a model that passes every univariate diagnostic can still produce structurally unreliable synthetic data. We introduce covariance-level dependence fidelity, measured by D_Sigma(P,Q) = ||Sigma_P - Sigma_Q||_F, as a principled, computable criterion for evaluating whether a generative model preserves the joint structure of data beyond its univariate marginals. Three results formalise this criterion. First, marginal fidelity provides no constraint on dependence structure: D_Sigma can be made arbitrarily large while all univariate marginals match exactly. Second, covariance divergence induces quantifiable downstream instability, including sign reversals in population regression coefficients. Third, bounding D_Sigma provides positive stability guarantees for dependence-sensitive procedures such as PCA via Davis-Kahan-type bounds. Empirical validation across three domains, image data (Fashion-MNIST VAE, n = 60,000), bulk RNA-seq (TCGA-BRCA, n = 1,111), and a small-sample stress test (Alzheimer's gene expression, n = 113), shows that D_Sigma/delta consistently distinguishes structure-discarding from structure-preserving generators in cases where standard marginal diagnostics show little separation, confirming that covariance-level fidelity provides information orthogonal to existing evaluation metrics across domains and sample sizes. |
| title | When Marginals Match but Structure Fails: Covariance Fidelity in Generative Models |
| topic | Machine Learning Artificial Intelligence Methodology 62H20, 62J05, 15A18, 62G99, 68T05, 60E05 I.2.6; G.3; G.1.3; I.5.1 |
| url | https://arxiv.org/abs/2603.17041 |