Calibrated Bayesian Selection of Schema Subgraphs for Database Question Answering
Abstract
An LLM answering a question about a relational database must know which tables hold the information. Showing too few makes the question unanswerable, while showing too many wastes context. Most schema-linking methods score each table alone, though the required tables are usually connected by foreign keys and can include connectors matching the question only weakly. We develop a hierarchical Bayesian model that combines question evidence with the foreign-key graph and returns empirically near-calibrated probabilities over complete sets of tables, not a single list, so later stages can tell when a selection is uncertain. Schema graphs are small enough to evaluate every subset exactly. With a fixed context budget the graph improves the chance of retaining every required table, and the benefit grows with schema size, turning positive at about seven tables. When the model also chooses how many tables to keep, a learned prior on subset size accounts for the whole improvement and the graph adds nothing. Fit the size prior first, and use the graph when the budget is fixed. The model's predictive sets cover the true set about as often as promised, where independent scoring is overconfident.
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BibTeX
@misc{richardson2026calibrated,
title = {{Calibrated Bayesian Selection of Schema Subgraphs for Database Question Answering}},
author = {Robert Richardson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.20294},
eprint = {2609.20294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20294},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Calibrated Bayesian Selection of Schema Subgraphs for Database Question Answering
AU - Robert Richardson
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2609.20294
UR - https://arxiv.org/abs/2609.20294
AB - An LLM answering a question about a relational database must know which tables hold the information. Showing too few makes the question unanswerable, while showing too many wastes context. Most schema-linking methods score each table alone, though the required tables are usually connected by foreign keys and can include connectors matching the question only weakly. We develop a hierarchical Bayesian model that combines question evidence with the foreign-key graph and returns empirically near-calibrated probabilities over complete sets of tables, not a single list, so later stages can tell when a selection is uncertain. Schema graphs are small enough to evaluate every subset exactly. With a fixed context budget the graph improves the chance of retaining every required table, and the benefit grows with schema size, turning positive at about seven tables. When the model also chooses how many tables to keep, a learned prior on subset size accounts for the whole improvement and the graph adds nothing. Fit the size prior first, and use the graph when the budget is fixed. The model's predictive sets cover the true set about as often as promised, where independent scoring is overconfident.
ER -