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.

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.

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.

In this article, we propose a novel pessimism-based Bayesian learning method for optimal dynamic treatment regimes in the offline setting. When the coverage condition does not hold, which is common for offline data, the existing solutions would produce sub-optimal policies. The pessimism principle addresses this issue by discouraging recommendation of actions that are less explored conditioning on the state. However, nearly all pessimism-based methods rely on a key hyper-parameter that quantifies the degree of pessimism, and the performance of the methods can be highly sensitive to the choice of this parameter. We propose to integrate the pessimism principle with Thompson sampling and Bayesian machine learning for optimizing the degree of pessimism. We derive a credible set whose boundary uniformly lower bounds the optimal Q-function, and thus we do not require additional tuning of the degree of pessimism. We develop a general Bayesian learning method that works with a range of models, from Bayesian linear basis model to Bayesian neural network model. We develop the computational algorithm based on variational inference, which is highly efficient and scalable. We establish the theoretical guarantees of the proposed method, and show empirically that it outperforms the existing state-of-the-art solutions through both simulations and a real data example.

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.

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.

In this paper, we study a central problem in multimodal neuroimaging analysis, i.e., identification of significantly correlated brain regions between multiple imaging modalities. We propose a spatially varying correlation model and the associated inference procedure, which improves substantially over the common alternative solutions of voxel-wise and region-wise analysis. Compared with voxel-wise analysis, our method aggregates voxels with similar correlations into regions, takes into account spatial continuity of correlations at nearby voxels, and enjoys a much higher detection power. Compared with region-wise analysis, our method does not rely on any pre-specified brain region map, but instead finds homogenous correlation regions adaptively given the data. We applied our method to a multimodal positron emission tomography study, and found brain regions with significant correlation between tau and glucose metabolism that voxel-wise or region-wise analysis failed to identify. Our findings conform and lend additional support to prior hypotheses about how the two pathological proteins of Alzheimer's disease, tau and amyloid, interact with glucose metabolism in the aging human brain.

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.

Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disorder that has recently seen serious increase in the number of affected subjects. In the last decade, neuroimaging has been shown to be a useful tool to understand AD and its prodromal stage, amnestic mild cognitive impairment (MCI). The majority of AD/MCI studies have focused on disease diagnosis, by formulating the problem as classification with a binary outcome of AD/MCI or healthy controls. There have recently emerged studies that associate image scans with continuous clinical scores that are expected to contain richer information than a binary outcome. However, very few studies aim at modeling multiple clinical scores simultaneously, even though it is commonly conceived that multivariate outcomes provide correlated and complementary information about the disease pathology. In this article, we propose a sparse multi-response tensor regression method to model multiple outcomes jointly as well as to model multiple voxels of an image jointly. The proposed method is particularly useful to both infer clinical scores and thus disease diagnosis, and to identify brain subregions that are highly relevant to the disease outcomes. We conducted experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, and showed that the proposed method enhances the performance and clearly outperforms the competing solutions.

MOTIVATION: Association tests based on next-generation sequencing data are often under-powered due to the presence of rare variants and large amount of neutral or protective variants. A successful strategy is to aggregate genetic information within meaningful single-nucleotide polymorphism (SNP) sets, e.g. genes or pathways, and test association on SNP sets. Many existing methods for group-wise tests require specific assumptions about the direction of individual SNP effects and/or perform poorly in the presence of interactions. RESULTS: We propose a joint association test strategy based on two key components: a nonlinear supervised dimension reduction approach for effective SNP information aggregation and a novel kernel specially designed for qualitative genotype data. The new test demonstrates superior performance in identifying causal genes over existing methods across a large variety of disease models simulated from sequence data of real genes. In general, the proposed method provides an association test strategy that can (i) detect both rare and common causal variants, (ii) deal with both additive and interaction effect, (iii) handle both quantitative traits and disease dichotomies and (iv) incorporate non-genetic covariates. In addition, the new kernel can potentially boost the power of the entire family of kernel-based methods for genetic data analysis. AVAILABILITY: The method is implemented in MATLAB. Source code is available upon request. CONTACT: [email protected].

In digital advertising, attribution is the problem of assigning credit to one or more advertisements for driving the user to the desirable actions such as making a purchase. Rather than giving all the credit to the last ad a user sees, multi-touch attribution allows more than one ads to get the credit based on their corresponding contributions. Multi-touch attribution is one of the most important problems in digital advertising, especially when multiple media channels, such as search, display, social, mobile and video are involved. Due to the lack of statistical framework and a viable modeling approach, true data-driven methodology does not exist today in the industry. While predictive modeling has been thoroughly researched in recent years in the digital advertising domain, the attribution problem focuses more on accurate and stable interpretation of the influence of each user interaction to the final user decision rather than just user classification. Traditional classification models fail to achieve those goals.

MOTIVATION: It is important to predict the outcome of patients with diffuse large-B-cell lymphoma after chemotherapy, since the survival rate after treatment of this common lymphoma disease is <50%. Both clinically based outcome predictors and the gene expression-based molecular factors have been proposed independently in disease prognosis. However combining the high-dimensional genomic data and the clinically relevant information to predict disease outcome is challenging. RESULTS: We describe an integrated clinicogenomic modeling approach that combines gene expression profiles and the clinically based International Prognostic Index (IPI) for personalized prediction in disease outcome. Dimension reduction methods are proposed to produce linear combinations of gene expressions, while taking into account clinical IPI information. The extracted summary measures capture all the regression information of the censored survival phenotype given both genomic and clinical data, and are employed as covariates in the subsequent survival model formulation. A case study of diffuse large-B-cell lymphoma data, as well as Monte Carlo simulations, both demonstrate that the proposed integrative modeling improves the prediction accuracy, delivering predictions more accurate than those achieved by using either clinical data or molecular predictors alone.

MOTIVATION: Recent research has shown that gene expression profiles can potentially be used for predicting various clinical phenotypes, such as tumor class, drug response and survival time. While there has been extensive studies on tumor classification, there has been less emphasis on other phenotypic features, in particular, patient survival time or time to cancer recurrence, which are subject to right censoring. We consider in this paper an analysis of censored survival time based on microarray gene expression profiles. RESULTS: We propose a dimension reduction strategy, which combines principal components analysis and sliced inverse regression, to identify linear combinations of genes, that both account for the variability in the gene expression levels and preserve the phenotypic information. The extracted gene combinations are then employed as covariates in a predictive survival model formulation. We apply the proposed method to a large diffuse large-B-cell lymphoma dataset, which consists of 240 patients and 7399 genes, and build a Cox proportional hazards model based on the derived gene expression components. The proposed method is shown to provide a good predictive performance for patient survival, as demonstrated by both the significant survival difference between the predicted risk groups and the receiver operator characteristics analysis. AVAILABILITY: R programs are available upon request from the authors. SUPPLEMENTARY INFORMATION: http://dna.ucdavis.edu/~hli/bioinfo-surv-supp.pdf.