# LLM-Forest: Ensemble Learning of LLMs with Graph-Augmented Prompts for Data Imputation

arXiv: https://arxiv.org/abs/2410.21520 · HTML: https://mlsanity.com/paper/2410.21520/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 76 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 27 of 27)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [SciBERT: A Pretrained Language Model for Scientific Text](https://mlsanity.com/paper/1903.10676/) (2019)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [TAPAS: Weakly Supervised Table Parsing via Pre-training](https://mlsanity.com/paper/2004.02349/) (2020)
- [TaBERT: Pretraining for Joint Understanding of Textual and Tabular Data](https://mlsanity.com/paper/2005.08314/) (2020)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [StructGPT: A General Framework for Large Language Model to Reason over Structured Data](https://mlsanity.com/paper/2305.09645/) (2023)
- [Binding Language Models in Symbolic Languages](https://mlsanity.com/paper/2210.02875/) (2022)
- [Chain-of-Table: Evolving Tables in the Reasoning Chain for Table Understanding](https://mlsanity.com/paper/2401.04398/) (2024)
- [Large Language Models are Versatile Decomposers: Decompose Evidence and Questions for Table-based Reasoning](https://mlsanity.com/paper/2301.13808/) (2023)
- [Large Language Models(LLMs) on Tabular Data: Prediction, Generation, and Understanding -- A Survey](https://mlsanity.com/paper/2402.17944/) (2024)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [Large Language Model for Table Processing: A Survey](https://mlsanity.com/paper/2402.05121/) (2024)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [TableRAG: Million-Token Table Understanding with Language Models](https://mlsanity.com/paper/2410.04739/) (2024)
- [TAP4LLM: Table Provider on Sampling, Augmenting, and Packing Semi-structured Data for Large Language Model Reasoning](https://mlsanity.com/paper/2312.09039/) (2023)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [A Pre-trained Sequential Recommendation Framework: Popularity Dynamics for Zero-shot Transfer](https://mlsanity.com/paper/2401.01497/) (2024)
- [Vision-Language and Large Language Model Performance in Gastroenterology: GPT, Claude, Llama, Phi, Mistral, Gemma, and Quantized Models](https://mlsanity.com/paper/2409.00084/) (2024)
- [TableQuery: Querying tabular data with natural language](https://mlsanity.com/paper/2202.00454/) (2022)
- [What Do LLMs Need to Understand Graphs: A Survey of Parametric Representation of Graphs](https://mlsanity.com/paper/2410.12126/) (2024)

## Built on by (most cited first, 25 of 25)

- [Harnessing Multiple Large Language Models: A Survey on LLM Ensemble](https://mlsanity.com/paper/2502.18036/) (2025)
- [Your Group-Relative Advantage Is Biased](https://mlsanity.com/paper/2601.08521/) (2026)
- [SelfElicit: Your Language Model Secretly Knows Where is the Relevant Evidence](https://mlsanity.com/paper/2502.08767/) (2025)
- [RAG over Tables: Hierarchical Memory Index, Multi-Stage Retrieval, and Benchmarking](https://mlsanity.com/paper/2504.01346/) (2025)
- [Adaptive Batch-Wise Sample Scheduling for Direct Preference Optimization](https://mlsanity.com/paper/2506.17252/) (2025)
- [PyG-SSL: A Graph Self-Supervised Learning Toolkit](https://mlsanity.com/paper/2412.21151/) (2024)
- [Can Graph Neural Networks Learn Language with Extremely Weak Text Supervision?](https://mlsanity.com/paper/2412.08174/) (2024)
- [Real-Time Aligned Reward Model beyond Semantics](https://mlsanity.com/paper/2601.22664/) (2026)
- [Counterfactual Credit Policy Optimization for Multi-Agent Collaboration](https://mlsanity.com/paper/2603.21563/) (2026)
- [Can LLMs Clean Up Your Mess? A Survey of Application-Ready Data Preparation with LLMs](https://mlsanity.com/paper/2601.17058/) (2026)
- [LLMBoost: Make Large Language Models Stronger with Boosting](https://mlsanity.com/paper/2512.22309/) (2025)
- [NIRVANA: Structured Pruning Reimagined for Large Language Model Compression](https://mlsanity.com/paper/2509.14230/) (2025)
- [Weak-Driven Learning: How Weak Agents make Strong Agents Stronger](https://mlsanity.com/paper/2602.08222/) (2026)
- [Scoring, Reasoning, and Selecting the Best! Ensembling Large Language Models via a Peer-Review Process](https://mlsanity.com/paper/2512.23213/) (2025)
- [STEM-POM: Evaluating Language Models Math-Symbol Reasoning in Document Parsing](https://mlsanity.com/paper/2411.00387/) (2024)
- [Multi-modal Relational Item Representation Learning for Inferring Substitutable and Complementary Items](https://mlsanity.com/paper/2507.22268/) (2025)
- [How many patients could we save with LLM priors?](https://mlsanity.com/paper/2509.04250/) (2025)
- [Adaptive Robust Estimator for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2603.21574/) (2026)
- [Joint Treatment Effect Estimation from Incomplete Healthcare Data: Temporal Causal Normalizing Flows with LLM-driven Evolutionary MNAR Imputation](https://mlsanity.com/paper/2605.05125/) (2026)
- [Aligning Probabilistic Beliefs under Informative Missingness: LLM Steerability in Clinical Reasoning](https://mlsanity.com/paper/2512.00479/) (2025)
- [ProfiliTable: Profiling-Driven Tabular Data Processing via Agentic Workflows](https://mlsanity.com/paper/2605.12376/) (2026)
- [SafeImpute: Reliable Clinical Data Imputation via Conformal Selection](https://mlsanity.com/paper/2607.05613/) (2026)
- [Auto-Fill: Learning to Predict Missing Values Accurately with Specialist Language Models](https://mlsanity.com/paper/2607.19847/) (2026)
- [EdgeLM: Edge Demonstrations for Language Models' Table Understanding](https://mlsanity.com/paper/2608.04390/) (2026)
- [Harnessing Image Question Dependence for Better VLM Test-time Reinforcement Learning](https://mlsanity.com/paper/2609.13296/) (2026)

## Abstract (arXiv)

Missing data imputation is a critical challenge in various domains, such as healthcare and finance, where data completeness is vital for accurate analysis. Large language models (LLMs), trained on vast corpora, have shown strong potential in data generation, making them a promising tool for data imputation. However, challenges persist in designing effective prompts for a finetuning-free process and in mitigating biases and uncertainty in LLM outputs. To address these issues, we propose a novel framework, LLM-Forest, which introduces a "forest" of few-shot prompt learning LLM "trees" with their outputs aggregated via confidence-based weighted voting based on LLM self-assessment, inspired by the ensemble learning (Random Forest). This framework is established on a new concept of bipartite information graphs to identify high-quality relevant neighboring entries with both feature and value granularity. Extensive experiments on 9 real-world datasets demonstrate the effectiveness and efficiency of LLM-Forest.