Gaussian Mean Field Variational Inference can Overestimate Predictive Variance
Mean Field Variational Inference (MFVI) is widely understood to underestimate posterior variance. By analysing conjugate Bayesian Linear Regression (BLR), we show that this characterization is incomplete: while MFVI underestimates the variance in parameter space, it can overestimate the predictive variance compared to the exact posterior. We show that if the MFVI posterior underestimates predictive variances in some directions, it necessarily overestimates them in others. Crucially, this overestimation occurs in directions where the training data concentrates. This leads to the surprising result that, for a test point drawn from the training distribution, MFVI's expected predictive varian...
| Authors | James Odgers, Ben Riegler, Siddharth Swaroop et al. |
|---|---|
| Primary category | stat.ML |
| Published | 24 June 2026 |
| Last updated at source | 24 June 2026 |
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