Unified Inference Framework for Single and Multi-Player Performative Prediction: Method and Asymptotic Optimality

Performative prediction characterizes environments where predictive models alter the very data distributions they aim to forecast, triggering complex feedback loops. While prior research treats single-agent and multi-agent performativity as distinct phenomena, this paper introduces a unified statistical inference framework that bridges these contexts, treating the former as a special case of the latter. Our contribution is two-fold. First, we put forward the Repeated Risk Minimization (RRM) procedure for estimating the performative stability, and establish a rigorous inferential theory for admitting its asymptotic normality and confirming its asymptotic efficiency. Second, for the performative optimality, we introduce a novel two-step plug-in estimator that integrates the idea of Recalibrated Prediction Powered Inference (RePPI) with Importance Sampling, and further provide formal derivations for the Central Limit Theorems of both the underlying distributional parameters and the plug-in results. The theoretical analysis demonstrates that our estimator achieves the semiparametric efficiency bound and maintains robustness under mild distributional misspecification. This work provides a principled toolkit for reliable estimation and decision-making in dynamic, performative environments.

FactTest: Factuality Testing in Large Language Models with Statistical Guarantees

The propensity of Large Language Models (LLMs) to generate hallucinations and non-factual content undermines their reliability in high-stakes domains, where rigorous control over Type I errors (the conditional probability of incorrectly classifying hallucinations as truthful content) is essential. Despite its importance, formal verification of LLM factuality with such guarantees remains largely unexplored. In this paper, we introduce FactTest, a novel framework that statistically assesses whether an LLM can confidently provide correct answers to given questions with high-probability correctness guarantees. We formulate factuality testing as hypothesis testing problem to enforce an upper bound of Type I errors at user-specified significance levels. Notably, we prove that our framework also ensures strong Type II error control under mild conditions and can be extended to maintain its effectiveness when covariate shifts exist. %These analyses are amenable to the principled NP framework. Our approach is distribution-free and works for any number of human-annotated samples. It is model-agnostic and applies to any black-box or white-box LM. Extensive experiments on question-answering (QA) and multiple-choice benchmarks demonstrate that \approach effectively detects hallucinations and improves the model's ability to abstain from answering unknown questions, leading to an over 40% accuracy improvement.

Finite-Sample and Distribution-Free Fair Classification: Optimal Trade-off Between Excess Risk and Fairness, and the Cost of Group-Blindness

Algorithmic fairness in machine learning has recently garnered significant attention. However, two pressing challenges remain: (1) The fairness guarantees of existing fair classification methods often rely on specific data distribution assumptions and large sample sizes, which can lead to fairness violations when the sample size is moderate-a common situation in practice. (2) Due to legal and societal considerations, using sensitive group attributes during decision-making (referred to as the group-blind setting) may not always be feasible. In this work, we quantify the impact of enforcing algorithmic fairness and group-blindness in binary classification under group fairness constraints. Specifically, we propose a unified framework for fair classification that provides distribution-free and finite-sample fairness guarantees with controlled excess risk. This framework is applicable to various group fairness notions in both group-aware and group-blind scenarios. Furthermore, we establish a minimax lower bound on the excess risk, showing the minimax optimality of our proposed algorithm up to logarithmic factors. Through extensive simulation studies and real data analysis, we further demonstrate the superior performance of our algorithm compared to existing methods, and provide empirical support for our theoretical findings.