# Interpretable Probability Estimation with LLMs via Shapley Reconstruction

arXiv: https://arxiv.org/abs/2601.09151 · HTML: https://mlsanity.com/paper/2601.09151/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Effective Text Rankers with Pairwise Ranking Prompting](https://mlsanity.com/paper/2306.17563/) (2023)
- [TabLLM: Few-shot Classification of Tabular Data with Large Language Models](https://mlsanity.com/paper/2210.10723/) (2022)
- [Aligning with Human Judgement: The Role of Pairwise Preference in Large Language Model Evaluators](https://mlsanity.com/paper/2403.16950/) (2024)
- [FinBen: A Holistic Financial Benchmark for Large Language Models](https://mlsanity.com/paper/2402.12659/) (2024)
- [Table Meets LLM: Can Large Language Models Understand Structured Table Data? A Benchmark and Empirical Study](https://mlsanity.com/paper/2305.13062/) (2023)
- [TokenSHAP: Interpreting Large Language Models with Monte Carlo Shapley Value Estimation](https://mlsanity.com/paper/2407.10114/) (2024)
- [BIRD: A Trustworthy Bayesian Inference Framework for Large Language Models](https://mlsanity.com/paper/2404.12494/) (2024)
- [Extracting Probabilistic Knowledge from Large Language Models for Bayesian Network Parameterization](https://mlsanity.com/paper/2505.15918/) (2025)
- [Large Language Model Capabilities in Perioperative Risk Prediction and Prognostication](https://mlsanity.com/paper/2401.01620/) (2024)
- [SyntaxShap: Syntax-aware Explainability Method for Text Generation](https://mlsanity.com/paper/2402.09259/) (2024)
- [Predicting Language Models' Success at Zero-Shot Probabilistic Prediction](https://mlsanity.com/paper/2509.15356/) (2025)

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

- [CA-BED: Conversation-Aware Bayesian Experimental Design](https://mlsanity.com/paper/2606.01182/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) demonstrate potential to estimate the probability of uncertain events, by leveraging their extensive knowledge and reasoning capabilities. This ability can be applied to support intelligent decision-making across diverse fields, such as financial forecasting and preventive healthcare. However, directly prompting LLMs for probability estimation faces significant challenges: their outputs are often noisy, and the underlying predicting process is opaque. In this paper, we propose PRISM: Probability Reconstruction via Shapley Measures, a framework that brings transparency and precision to LLM-based probability estimation. PRISM decomposes an LLM's prediction by quantifying the marginal contribution of each input factor using Shapley values. These factor-level contributions are then aggregated to reconstruct a calibrated final estimate. In our experiments, we demonstrate PRISM improves predictive accuracy over direct prompting and other baselines, across multiple domains including finance, healthcare, and agriculture. Beyond performance, PRISM provides a transparent prediction pipeline: our case studies visualize how individual factors shape the final estimate, helping build trust in LLM-based decision support systems.