Finite-Query Coherent Projection of Black-Box Conditional Predictions
Abstract
Local conditional predictions from a black box need not admit a common joint distribution. We study two aspects of their coherent projection: finite-access precision and directional fidelity. For arbitrary deterministic binary conditional tables, we establish matching expected minimax excess conditional-Kullback--Leibler risk Θ(min{R√(d/B),d2/B}) under independent uniform exact-table queries, with repeated draws charged, for a local bounded pairwise joint class. The result holds for sufficiently large d, R√d≤ M0, and Cd3≤ B≤(d2d−1)1/3, where M0 is fixed. A moment estimator attains the upper bound. The main technical contribution is a matching lower-bound construction that respects shared pairwise interactions and frozen exact-table responses, with comparison to the best projection of the same realized table. We then examine directional fidelity in a computable hard-marginal formulation that preserves direct black-box marginals. A preregistered TabPFN-v2 case study combines a Car anchor with a frozen two-dataset, three-split extension. All 1,152 extension optimization instances pass independent numerical checks at registered tolerances. Directional contrasts are dataset-dependent and asymmetric: optimizing one direction need not improve the other. Together, the analyses distinguish accurate approximation of a selected projection from improvement in conditional directions outside its fitted objective.
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BibTeX
@misc{wu2026finitequery,
title = {{Finite-Query Coherent Projection of Black-Box Conditional Predictions}},
author = {Yuyang Wu and Fanyu Zhou and Jinfeng Zhou and Guangying Lyu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30708},
eprint = {2610.30708},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30708},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite-Query Coherent Projection of Black-Box Conditional Predictions
AU - Yuyang Wu
AU - Fanyu Zhou
AU - Jinfeng Zhou
AU - Guangying Lyu
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30708
UR - https://arxiv.org/abs/2610.30708
AB - Local conditional predictions from a black box need not admit a common joint distribution. We study two aspects of their coherent projection: finite-access precision and directional fidelity. For arbitrary deterministic binary conditional tables, we establish matching expected minimax excess conditional-Kullback--Leibler risk Θ(min{R√(d/B),d^2/B}) under independent uniform exact-table queries, with repeated draws charged, for a local bounded pairwise joint class. The result holds for sufficiently large d, R√d≤ M_0, and Cd^3≤ B≤(d2^d−1)^1/3, where M_0 is fixed. A moment estimator attains the upper bound. The main technical contribution is a matching lower-bound construction that respects shared pairwise interactions and frozen exact-table responses, with comparison to the best projection of the same realized table. We then examine directional fidelity in a computable hard-marginal formulation that preserves direct black-box marginals. A preregistered TabPFN-v2 case study combines a Car anchor with a frozen two-dataset, three-split extension. All 1,152 extension optimization instances pass independent numerical checks at registered tolerances. Directional contrasts are dataset-dependent and asymmetric: optimizing one direction need not improve the other. Together, the analyses distinguish accurate approximation of a selected projection from improvement in conditional directions outside its fitted objective.
ER -