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Lexin Li

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7 papers

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NeurIPS Conference 2025 Conference Paper

Incentivizing Truthful Language Models via Peer Elicitation Games

Baiting Chen
Tong Zhu
Jiale Han
Lexin Li
Gang Li
Xiaowu Dai

Large Language Models (LLMs) have demonstrated strong generative capabilities but remain prone to inconsistencies and hallucinations. We introduce Peer Elicitation Games (PEG), a training-free, game-theoretic framework for aligning LLMs through a peer elicitation mechanism involving a generator and multiple discriminators instantiated from distinct base models. Discriminators interact in a peer evaluation setting, where utilities are computed using a determinant-based mutual information score that provably incentivizes truthful reporting without requiring ground-truth labels. We establish theoretical guarantees showing that each agent, via online learning, achieves sublinear regret in the sense their cumulative performance approaches that of the best fixed truthful strategy in hindsight. Moreover, we prove last-iterate convergence to a truthful Nash equilibrium, ensuring that the actual policies used by agents converge to stable and truthful behavior over time. Empirical evaluations across multiple benchmarks demonstrate significant improvements in factual accuracy. These results position PEG as a practical approach for eliciting truthful behavior from LLMs without supervision or fine-tuning.

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JMLR Journal 2024 Journal Article

Functional Directed Acyclic Graphs

Kuang-Yao Lee
Lexin Li
Bing Li

In this article, we introduce a new method to estimate a directed acyclic graph (DAG) from multivariate functional data. We build on the notion of faithfulness that relates a DAG with a set of conditional independences among the random functions. We develop two linear operators, the conditional covariance operator and the partial correlation operator, to characterize and evaluate the conditional independence. Based on these operators, we adapt and extend the PC-algorithm to estimate the functional directed graph, so that the computation time depends on the sparsity rather than the full size of the graph. We study the asymptotic properties of the two operators, derive their uniform convergence rates, and establish the uniform consistency of the estimated graph, all of which are obtained while allowing the graph size to diverge to infinity with the sample size. We demonstrate the efficacy of our method through both simulations and an application to a time-course proteomic dataset. [abs] [ pdf ][ bib ] &copy JMLR 2024. ( edit, beta )

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JMLR Journal 2024 Journal Article

Post-Regularization Confidence Bands for Ordinary Differential Equations

Xiaowu Dai
Lexin Li

Ordinary differential equation (ODE) is an important tool to study a system of biological and physical processes. A central question in ODE modeling is to infer the significance of individual regulatory effect of one signal variable on another. However, building confidence band for ODE with unknown regulatory relations is challenging, and it remains largely an open question. In this article, we construct the post-regularization confidence band for the individual regulatory function in ODE with unknown functionals and noisy data observations. Our proposal is the first of its kind, and is built on two novel ingredients. The first is a new localized kernel learning approach that combines reproducing kernel learning with local Taylor approximation, and the second is a new de-biasing method that tackles infinite-dimensional functionals and additional measurement errors. We show that the constructed confidence band has the desired asymptotic coverage probability, and the recovered regulatory network approaches the truth with probability tending to one. We establish the theoretical properties when the number of variables in the system can be either smaller or larger than the number of sampling time points, and we study the regime-switching phenomenon. We demonstrate the efficacy of the proposed method through both simulations and illustrations with two data applications. [abs] [ pdf ][ bib ] &copy JMLR 2024. ( edit, beta )

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TMLR Journal 2024 Journal Article

Sequential Best-Arm Identification with Application to P300 Speller

Xin Zhou
Botao Hao
Tor Lattimore
Jian Kang
Lexin Li

A brain-computer interface (BCI) is an advanced technology that facilitates direct communication between the human brain and a computer system, by enabling individuals to interact with devices using only their thoughts. The P300 speller is a primary type of BCI system, which allows users to spell words without using a physical keyboard, but instead by capturing and interpreting brain electroencephalogram (EEG) signals under different stimulus presentation paradigms. Traditional non-adaptive presentation paradigms, however, treat each word selection as an isolated event, resulting in a lengthy learning process. To enhance efficiency, we cast the problem as a sequence of best-arm identification tasks within the context of multi-armed bandits, where each task corresponds to the interaction between the user and the system for a single character or word. Leveraging large language models, we utilize the prior knowledge learned from previous tasks to inform and facilitate subsequent tasks. We propose a sequential top-two Thompson sampling algorithm under two scenarios: the fixed-confidence setting and the fixed-budget setting. We study the theoretical property of the proposed algorithm, and demonstrate its substantial empirical improvement through both simulations as well as the data generated from a P300 speller simulator that was built upon the real BCI experiments.

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JMLR Journal 2021 Journal Article

Double Generative Adversarial Networks for Conditional Independence Testing

Chengchun Shi
Tianlin Xu
Wicher Bergsma
Lexin Li

In this article, we study the problem of high-dimensional conditional independence testing, a key building block in statistics and machine learning. We propose an inferential procedure based on double generative adversarial networks (GANs). Specifically, we first introduce a double GANs framework to learn two generators of the conditional distributions. We then integrate the two generators to construct a test statistic, which takes the form of the maximum of generalized covariance measures of multiple transformation functions. We also employ data-splitting and cross-fitting to minimize the conditions on the generators to achieve the desired asymptotic properties, and employ multiplier bootstrap to obtain the corresponding p-value. We show that the constructed test statistic is doubly robust, and the resulting test both controls type-I error and has the power approaching one asymptotically. Also notably, we establish those theoretical guarantees under much weaker and practically more feasible conditions compared to the existing tests, and our proposal gives a concrete example of how to utilize some state-of-the-art deep learning tools, such as GANs, to help address a classical but challenging statistical problem. We demonstrate the efficacy of our test through both simulations and an application to an anti-cancer drug dataset. A Python implementation of the proposed procedure is available at https://github.com/tianlinxu312/dgcit. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

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JMLR Journal 2020 Journal Article

Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality

Miaoyan Wang
Lexin Li

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a multilinear Bernoulli model, develop a rank-constrained likelihood-based estimation method, and obtain the theoretical accuracy guarantees. In contrast to continuous-valued problems, the binary tensor problem exhibits an interesting phase transition phenomenon according to the signal-to-noise ratio. The error bound for the parameter tensor estimation is established, and we show that the obtained rate is minimax optimal under the considered model. Furthermore, we develop an alternating optimization algorithm with convergence guarantees. The efficacy of our approach is demonstrated through both simulations and analyses of multiple data sets on the tasks of tensor completion and clustering. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

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JMLR Journal 2017 Journal Article

STORE: Sparse Tensor Response Regression and Neuroimaging Analysis

Will Wei Sun
Lexin Li

Motivated by applications in neuroimaging analysis, we propose a new regression model, Sparse TensOr REsponse regression (STORE), with a tensor response and a vector predictor. STORE embeds two key sparse structures: element-wise sparsity and low-rankness. It can handle both a non-symmetric and a symmetric tensor response, and thus is applicable to both structural and functional neuroimaging data. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating updating algorithm. We establish a non- asymptotic estimation error bound for the actual estimator obtained from the proposed algorithm. This error bound reveals an interesting interaction between the computational efficiency and the statistical rate of convergence. When the distribution of the error tensor is Gaussian, we further obtain a fast estimation error rate which allows the tensor dimension to grow exponentially with the sample size. We illustrate the efficacy of our model through intensive simulations and an analysis of the Autism spectrum disorder neuroimaging data. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

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