Bluebell: An Alliance of Relational Lifting and Independence for Probabilistic Reasoning
Bibliographic record
Abstract
We present BlueBell , a program logic for reasoning about probabilistic programs where unary and relational styles of reasoning come together to create new reasoning tools. Unary-style reasoning is very expressive and is powered by foundational mechanisms to reason about probabilistic behavior like independence and conditioning . The relational style of reasoning, on the other hand, naturally shines when the properties of interest compare the behavior of similar programs (e.g. when proving differential privacy) managing to avoid having to characterize the output distributions of the individual programs. So far, the two styles of reasoning have largely remained separate in the many program logics designed for the deductive verification of probabilistic programs. In BlueBell , we unify these styles of reasoning through the introduction of a new modality called “joint conditioning” that can encode and illuminate the rich interaction between conditional independence and relational liftings ; the two powerhouses from the two styles of reasoning.
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 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 | 0.013 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.006 | 0.015 |
| Open science | 0.006 | 0.014 |
| Research integrity | 0.002 | 0.010 |
| Insufficient payload (model declined to judge) | 0.015 | 0.004 |
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".