Semi-Implicit Approaches for Large-Scale Bayesian Spatial Interpolation
Bibliographic record
Abstract
We propose correlated semi-implicit variational inference (Co-SIVI), a scalable approach for full posterior approximation in large spatial models with exponential-family likelihoods. Co-SIVI incorporates dependence directly into the conditional variational distribution of spatial random effects through an iterative weighted least squares algorithm that accommodates both Gaussian process and nearest-neighbor Gaussian process (NNGP) priors. For large samples, we further propose reparameterizing the variational family for the covariance parameters to better capture posterior dependence. Co-SIVI addresses an important limitation of semi-implicit variational inference (SIVI), for which dependence induced through the mixing distribution may be insufficient when spatial random effects are explicitly included in the variational family. In simulations with Gaussian, Poisson, Gamma, and Bernoulli outcomes, Co-SIVI closely reproduces Hamiltonian Monte Carlo (HMC) results at substantially lower computational cost, while SIVI performs similarly for marginalized Gaussian models. We apply SIVI and Co-SIVI, both with NNGP priors, to two large-scale datasets: temperature data modeled with a Gaussian likelihood and housing price data modeled with a Gamma likelihood. Overall, Co-SIVI provides a scalable and flexible alternative to HMC for full posterior approximation in large non-Gaussian spatial models.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".