# Scored Claim Scorecard


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# Judge-first scored-claim scorecard

**Paper:** *Gaussian Mean Field Variational Inference can Overestimate Predictive Variance* (OpenReview `RG7maF4bGu`).

| # | Exact automatic claim | Verdict | Decisive independent evidence |
|---|---|---|---|
| 1 | While MFVI underestimates posterior variance, it can overestimate predictive variance compared to the exact posterior | **VERIFIED** | For 140 independently generated Bayesian linear-regression problems spanning dimensions 2–64, six orders of magnitude in prior precision and noise variance, `Tr(Sigma) >= Tr(S*)` and MFVI variance exceeds exact variance along the minimum-posterior-eigenvalue direction in 140/140 cases. Replacing that direction by the maximum-eigenvalue direction reverses the comparison in 140/140. A separate numerical KL optimization recovers the analytic MFVI optimum with worst relative error `4.93e-7` in 24 checks. |
| 2 | For test points drawn from the training distribution, MFVI predictive variance is always lower than the exact posterior predictive variance | **VERIFIED** | The exact identity `E[x'(Sigma-S*)x] = -(sigma² alpha/N)[Tr(Sigma)-Tr(S*)] <= 0` is derived for arbitrary `X`, `alpha>0`, and `sigma²>0`, then checked across all 140 problems. The largest value is `-1.66e-12`, and direct trace evaluation agrees with the derived identity to `1.21e-13` absolute error. |
| 3 | The overestimation of predictive variance occurs in directions where the training data concentrates | **VERIFIED** | With the paper's spherical prior, the first principal component of `X` is the minimum-eigenvalue direction of the exact posterior by a shared-eigenbasis derivation. Alignment error is at most `1.33e-15`, and MFVI overestimates along that direction in 140/140 cases. The last-PC mutation reverses the comparison in 140/140, and a deliberately dominating nonspherical prior breaks the alignment in 140/140, isolating the claimed mechanism and its boundary. |

The reproduction is an independent NumPy/SciPy float64 implementation. Full problem-level records, all mutation outcomes, derivations, and environment details are in `outputs/results.json`, SHA-256 `09a1703ffd71cd4190afa437384d1e857cc432e26b9b7752ca8c419c88e52bf4`.