Practical bounds on the error of Bayesian posterior approximations: A nonasymptotic approach
Bibliographic record
Abstract
Bayesian inference typically requires the computation of an approximation to the posterior distribution.An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty estimates.Classical Monte Carlo methods, particularly Markov Chain Monte Carlo, remain the gold standard for approximate Bayesian inference because they have a robust finite-sample theory and reliable convergence diagnostics.However, alternative methods, which are more scalable or apply to problems where Markov Chain Monte Carlo cannot be used, lack the same finite-data approximation theory and tools for evaluating their accuracy.In this work, we develop a flexible new approach to bounding the error of mean and uncertainty estimates of scalable inference algorithms.Our strategy is to control the estimation errors in terms of Wasserstein distance, then bound the Wasserstein distance via a generalized notion of Fisher distance.Unlike computing the Wasserstein distance, which requires access to the normalized posterior distribution, the Fisher distance is tractable to compute because it requires access only to the gradient of the log posterior density.We demonstrate the usefulness of our Fisher distance approach by deriving bounds on the Wasserstein error of the Laplace approximation and Hilbert coresets.We anticipate that our approach will be applicable to many other approximate inference methods such as the integrated Laplace approximation, variational inference, and approximate Bayesian computation.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".