Title: Valid Inference with Imperfect Synthetic Data
Venue: NeurIPS 2025
Accepted: yes
Keywords: Human-AI Collaboration

Statistical Inference

LLMs for Computational Social Sciences
Abstract: Predictions and generations from large language models are increasingly being explored as an aid in limited data regimes, such as in computational social science and human subjects research. 
While prior technical work has mainly explored the potential to use model-predicted labels for unlabeled data in a principled manner, there is increasing interest in using large language models to generate entirely new synthetic samples (e.g., synthetic simulations), such as in responses to surveys. However, it remains unclear 
by what means practitioners can combine such data with real data
and yet produce statistically valid conclusions upon them.
In this paper, we introduce a new estimator based on generalized method of moments, providing a hyperparameter-free solution with strong theoretical guarantees to address this challenge. Intriguingly, we find that interactions between the moment residuals of synthetic data and those of real data (i.e., when they are predictive of each other) can greatly improve estimates of the target parameter.
We validate the finite-sample performance of our estimator across different tasks in computational social science applications, demonstrating large empirical gains.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a novel methodology for generating synthetic data from Large Language Models (LLMs) that seeks to generate samples matching the distribution of human-labeled data. This is done by incorporating one human-labeled sample and specific request for a classification category into each LLM prompt. The paper also introduces a new estimator algorithm that seeks to correctly predict the true distribution from the (imperfect) artificial samples.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n- The paper seeks to address an important limitation in many social science contexts: Hand-labeled training data is expensive to produce and often limited in scope. Artificially-generated samples offer one way to overcome this limitation, but only if it is possible to infer the true distribution from an analysis of artificially generated samples (which are likely to contain unwanted biases)\n- The paper includes theoretical grounding for the proposed methodology, building upon established mathematical precedents\n- The authors ran multiple trials of all experiments, strengthening the reliability of the results\n- The introduction of a principled sampling method for artificial generated within the context of social science research is particularly valuable, and is worthy of deeper exploration\n\nWeaknesses\n- The prompting methods used by the researchers to generate artificial samples may not be as robust as the paper implies.\n- The assumption that prompting with T will result in text generations that exactly match the original distribution is incorrect, and in particular is highly dependent on the language model used. Highly distilled language models, in particular, tend to gravitate toward certain styles and patterns of generated text regardless of the prompt, and there is no guarantee that they will match T_i in all meaningful senses.\n- The authors do not address the question of how the selection of language model (e.g. GPT-4, GPT-4o, Qwen, Claude Sonnet, Llama, etc.) might impact the reliability of results, nor does the work explore the question of what will happen when the specific classification requested in the LLM prompt (e.g. hedging) represents a skill, behavior, or category that the language model is not equipped to- PPI++ is referenced within the paper and used as a key baseline, but this algorithm is not clearly explained within the text of the paper, making the comparisons difficult to understand. A more direct explanation of PPI++ within the paper body would reduce reviewer workload and make the paper more accessible to a broad audience. identify or generate.\n- The baseline comparisons used by the paper do not seem to be the correct way to evaluate this work. For example, PPI++ is used as a baseline, but it differs from the authors' methods along multiple dimensions (e.g. power tuning, the sampling method used to generate artificial data), making it difficult to draw meaningful conclusions from the results. In particular, it would have been nice to see a comparison of the authors' methods and PPI++ using the authors' novel sampling method for artificial data. It would also have been nice to see a comparison of PPI++ performance both with naively sampled artificial data and with data sampled using the authors' methodology.\n- The presentation of ideas within the paper do not flow naturally. Motivation for the research is not clearly established, many key points of information are not included in the paper proper and must be researched elsewhere in order for the paper to be properly understood. The title and abstract do not effectively convey the main contributions of the paper.\n\nQUESTIONS:\nPlease explain why the experiments using PPI++ were conducted using a different set of artificially generated samples than the ones used by the authors' algorithm.\n\nLIMITATIONS:\nLimitations are addressed briefly, but not in enough detail to be satisfactory. In particular, the authors do not address the (very real) risks that researchers acting based on the claims of the paper might attribute more reliability to the algorithms result than is justified. In other words, because the authors make strong claims relating to the algorithm's ability to identify the true distribution from artificially generated samples, there is a risk that researchers may succumb to overreliance on the algorithm's outputs, even when research is conducted that is outside the scope of the algorithm's optimal performance bounds (for example, when a small or unreliable language model is used, or when the specific classification requested by the prompt (e.g. \"hedging\") lies outside of the language model's capabilities. For this reason, the authors should clearly identify the bounds of their algorithm's validity: For which category of language models and for which types of classification problems can the authors' novel prompting method be considered accurate? How can this reliability be externally verified by other researchers? What are the potential outcomes or dangers of naive reliance upon the authors' algorithm in contexts where the algorithm does nor provide good results?", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-19"}

comments: SUMMARY:
Using human annotators to label domain-specific text can be highly expensive and time-consuming. Therefore, recent works have used LLMs to replace humans in labeling and data generation. While this can remove the original costs, we are still not sure about the benefits and correctness of the synthetic data. This paper models this process through the Generalized Method of Moments. The authors model the contribution of real, auxiliary, and synthetic data. Their comprehensive model shows we can utilize synthetic data to improve performance under essential conditions. They should have similar residuals to real data.

STRENGTHS AND WEAKNESSES:
**Weakness**

The main weakness of the paper is that it is hard to follow; some basic concepts are overexplained, while the important part and the contribution section are left ambiguous. A very critical concept, the Generalized Method of Moments, is not explained in the related work.

**Strength**

The contribution of the paper is significant. The authors have theoretically shown how to select synthetic datasets and when they can be beneficial. 

The experimental results also support their theoretical results. 

The paper has an interesting discussion section (4.5 and 5). 

My suggestion for the authors is to summarize the content in the early pages of the paper and expand on how the Generalized Method of Moments works and how it can help with this problem.

QUESTIONS:
Conditions under line 135 are not clear. Are the equations showing how T, X, and Y are generated, or are T and X when the text is labeled, and T and Y when the text is unlabeled? The current formulation is misleading.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 1
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a principled framework for incorporating fully synthetic data, generated by LLMs, into downstream statistical inference tasks. Motivated by applications in computational social science where labeled data is often scarce, the authors introduce a novel estimator based on the Generalized Method of Moments that combines labeled data, model-predicted data (proxies), and LLM-generated synthetic samples. The method exploits correlation structures introduced by conditioning synthetic samples on real data and provides theoretical guarantees on consistency and asymptotic normality. Empirical results on four real-world regression tasks demonstrate significant performance gains in low-label regimes.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n1. This paper tackles an important and emerging challenge, i.e., how to use LLM-generated synthetic data for reliable statistical inference.\n\n2. It introduces GMM estimator for this task and leverages the correlation between real and synthetic data for synthetic data generation. Experiments on diverse real-world tasks from political science and psychology show strong gains, especially in low-data settings.\n\n3. The paper is well-written and clearly structured. And the theoretical and empirical sections are well balanced.\n\n**Weaknesses**\n\n1. While the paper mentions that low-quality synthetic data won’t help, it doesn’t empirically explore the effect of varying LLM quality or prompt design.\n\n2. The experiments are focused on regression tasks with structured covariates; it’s unclear how well the framework generalizes to classification, causal inference, or time series.\n\n3. The framework relies on the availability of strong LLMs like GPT-4o. This may not generalize well to low-resource settings, such as open-source models.\n\n4. It would be helpful to see a comparison between the proposed conditioned sampling vs. naive zero-shot generation to justify the design decision.\n\nQUESTIONS:\n1. Can your framework support generation strategies that are not conditioned on real examples? For instance, can it be extended to few-shot or zero-shot prompting?\n\n2. What's the perfomance gap of between open-source models and GPT-4o?\n\n3. What's the diversity of the generated samples, which should also be dicsussed and verified.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-07"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper aims to find regression coefficients based on mostly-unlabeled data. It introduces `GMM+synth`, which relies on a black-box LLM to augment unlabeled data, and generate fully synthetic data. It uses a Generalized Methods of Moments approach for combining real, proxy, and synthetic data to get statistical estimates of the regression coefficients.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n1. Robust low sample size inference is an underexplored problem in ML\n2. The approach---building statistically valid estimators for incorporating possibly erroneous LLMs for augmentation---is appealing\n3. Writing is generally good\n\n## Weaknesses\nI have two general concerns\n1. Method. The method is rather involved, with ML model $f$ giving proxies, the LLM giving synthetic data, and then a GMM doing the statistical inference. There are many hidden choices---which ML model $f$ for proxy data? Which LLM for synthetic data? Which LLM prompts?---which the writers do not explore. To me as a reader, I'm not convinced the method is the best way to leverage the internal knowledge of an LLM.\n2. Experiments. Related to the above, the experiments are rather limited.\n   1. There is just one baseline\n   2. Tasks are simple. \n   3. Just a single LLM, and unclear how accurate GPT-o is for these tasks. The authors pose in Section 4.5 that we'll never be worse, as the model learns to ignore the synthetic data if it's uncorrelated. It would have been interesting to test this in practice, either with more difficult tasks or worse LLMs.\n\n### Minor\n1. Key observations in Experiments should be structured better. Right now, it jumps from Figures 3 and 4, to Figure 6 in the Appendix, to finally get to Figure 2, but then going back to Figure 3.\n\nQUESTIONS:\nSee weaknesses. Additionally:\n\n1. In L.135, do you mean $\\tilde{X}_k=f(\\tilde{T}_k)$, idem ditto for $Y$?\n2. If we have enough texts $T$, what is the intuition for why modelling synthetic $T$ helps?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 1, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-07"}