# Cross-Domain Uncertainty Quantification for Selective Prediction: A Comprehensive Bound Ablation with Transfer-Informed Betting

arXiv: https://arxiv.org/abs/2603.08907 · HTML: https://mlsanity.com/paper/2603.08907/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 23 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Efficient Intent Detection with Dual Sentence Encoders](https://mlsanity.com/paper/2003.04807/) (2020)
- [An Evaluation Dataset for Intent Classification and Out-of-Scope Prediction](https://mlsanity.com/paper/1909.02027/) (2019)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [MASSIVE: A 1M-Example Multilingual Natural Language Understanding Dataset with 51 Typologically-Diverse Languages](https://mlsanity.com/paper/2204.08582/) (2022)
- [Efficient Few-Shot Learning Without Prompts](https://mlsanity.com/paper/2209.11055/) (2022)
- [RAGCache: Efficient Knowledge Caching for Retrieval-Augmented Generation](https://mlsanity.com/paper/2404.12457/) (2024)
- [There are natural scores: Full comment on Shafer, "Testing by betting: A strategy for statistical and scientific communication"](https://mlsanity.com/paper/2102.05569/) (2021)
- [Agentic Plan Caching: Test-Time Memory for Fast and Cost-Efficient LLM Agents](https://mlsanity.com/paper/2506.14852/) (2025)
- [vCache: Verified Semantic Prompt Caching](https://mlsanity.com/paper/2502.03771/) (2025)
- [Advancing Semantic Caching for LLMs with Domain-Specific Embeddings and Synthetic Data](https://mlsanity.com/paper/2504.02268/) (2025)
- [SemanticALLI: Caching Reasoning, Not Just Responses, in Agentic Systems](https://mlsanity.com/paper/2601.16286/) (2026)

## Built on by (most cited first, 1 of 1)

- [False Sense of Safety in Selective Signal Classification: Auditing Bound Tightness and Exchangeability for Risk Control](https://mlsanity.com/paper/2606.15153/) (2026)

## Abstract (arXiv)

We present a comprehensive ablation of nine finite-sample bound families for selective prediction with risk control, combining concentration inequalities (Hoeffding, Empirical Bernstein, Clopper-Pearson, Wasserstein DRO, CVaR) with multiple-testing corrections (union bound, Learn Then Test fixed-sequence) and betting-based confidence sequences (WSR). Our main theoretical contribution is Transfer-Informed Betting (TIB), which warm-starts the WSR wealth process using a source domain's risk profile, achieving tighter bounds in data-scarce settings with a formal dominance guarantee. We prove that the TIB wealth process remains a valid supermartingale under all source-target divergences, that TIB dominates standard WSR when domains match, and that no data-independent warm-start can achieve better convergence. The combination of betting-based confidence sequences, LTT monotone testing, and cross-domain transfer is, to our knowledge, a three-way novelty not present in the literature. We evaluate all nine bound families on four benchmarks-MASSIVE (n=1,102), NyayaBench (n=280), CLINC-150 (n=22.5K), and Banking77 (n=13K)-across 18 (alpha, delta) configurations. On MASSIVE at alpha=0.10, LTT eliminates the ln(K) union-bound penalty, achieving 94.0% guaranteed coverage versus 73.8% for Hoeffding-a 27% relative improvement. On NyayaBench, where the small calibration set makes Hoeffding-family bounds infeasible below alpha=0.20, Transfer-Informed Betting achieves 18.5% coverage at alpha=0.10, a 5.4x improvement over LTT + Hoeffding. We additionally compare with split-conformal prediction, showing that conformal methods produce prediction sets (avg. 1.67 classes) whereas selective prediction provides single-prediction risk guarantees. We apply these methods to agentic caching systems, formalizing a progressive trust model where the guarantee determines when cached responses can be served autonomously.