arXiv subjects

Linglong Kong

Publications and source records attributed to Linglong Kong.

At least 19 recordsLinked to original sources

arXiv2026

Generating Benchmark Health Data Using a Tabular Diffusion Transformer

Cross-Tabular Data Generation (CTDG) seeks to learn a generative model from multiple heterogeneous tables and produce new synthetic tabular datasets. However, existing synthetic tabular data generation methods are largely restricted to single-input-table scenarios and struggle to effectively handle multiple heterogeneous tables with diverse feature sets. To address this limitation, we propose a two-stage framework for cross-tabular data generation. In the first stage, each heterogeneous raw table is transformed into a standardized statistical table with the same set of columns across all tables. Each statistical table captures the marginal distributions of the original columns and the pairwise correlations among them. In the second stage, a diffusion transformer model is trained to capture structural patterns across these homogeneous statistical tables and to generate synthetic statistical tables. Synthetic raw tables are subsequently reconstructed from the generated statistical tables via multivariate Gaussian sampling followed by an inverse probability integral transform. This two-stage CTDG framework enables the learning of a unified generative model from multiple heterogeneous tables and supports the generation of an unlimited number of realistic synthetic heterogeneous tables. Experimental results demonstrate high fidelity in the learned statistical representations and a favorable fidelity-diversity trade-off in the generated synthetic data, validating the effectiveness of the proposed approach.

cs.LG↗

arXiv2026

Prediction-powered Inference by Mixture of Experts

The rapidly expanding artificial intelligence (AI) industry has produced diverse yet powerful prediction tools, each with its own network architecture, training strategy, data-processing pipeline, and domain-specific strengths. These tools create new opportunities for semi-supervised inference, in which labeled data are limited and expensive to obtain, whereas unlabeled data are abundant and widely available. Given a collection of predictors, we treat them as a mixture of experts (MOE) and introduce an MOE-powered semi-supervised inference framework built upon prediction-powered inference (PPI). Motivated by the variance reduction principle underlying PPI, the proposed framework seeks the mixture of experts that achieves the smallest possible variance. Compared with standard PPI, the MOE-powered inference framework adapts to the unknown performance of individual predictors, benefits from their collective predictive power, and enjoys a best-expert guarantee. The framework is flexible and applies to mean estimation, linear regression, quantile estimation, and general M-estimation. We develop non-asymptotic theory for the MOE-powered inference framework and establish upper bounds on the coverage error of the resulting confidence intervals. Numerical experiments demonstrate the practical effectiveness of MOE-powered inference and corroborate our theoretical findings.

stat.ML↗

arXiv2026

Differentially Private Conformal Prediction

Conformal prediction (CP) has attracted broad attention as a simple and flexible framework for uncertainty quantification through prediction sets. In this work, we study how to deploy CP under differential privacy (DP) in a statistically efficient manner. We first introduce differential CP, a non-splitting conformal procedure that avoids the efficiency loss caused by data splitting and serves as a bridge between oracle CP and private conformal inference. By exploiting the stability properties of DP mechanisms, differential CP establishes a direct connection to oracle CP and inherits corresponding validity behavior. Building on this idea, we develop Differentially Private Conformal Prediction (DPCP), a fully private procedure that combines DP model training with a private quantile mechanism for calibration. We establish the end-to-end privacy guarantee of DPCP and investigate its coverage properties under additional regularity conditions. We further study the efficiency of both differential CP and DPCP under empirical risk minimization and general regression models, showing that DPCP can produce tighter prediction sets than existing private split conformal approaches under the same privacy budget. Numerical experiments on synthetic and real datasets demonstrate the practical effectiveness of the proposed methods.

stat.ML↗

arXiv2026

Principled Fast and Meta Knowledge Learners for Continual Reinforcement Learning

Inspired by the human learning and memory system, particularly the interplay between the hippocampus and cerebral cortex, this study proposes a dual-learner framework comprising a fast learner and a meta learner to address continual Reinforcement Learning~(RL) problems. These two learners are coupled to perform distinct yet complementary roles: the fast learner focuses on knowledge transfer, while the meta learner ensures knowledge integration. In contrast to traditional multi-task RL approaches that share knowledge through average return maximization, our meta learner incrementally integrates new experiences by explicitly minimizing catastrophic forgetting, thereby supporting efficient cumulative knowledge transfer for the fast learner. To facilitate rapid adaptation in new environments, we introduce an adaptive meta warm-up mechanism that selectively harnesses past knowledge. We conduct experiments in various pixel-based and continuous control benchmarks, revealing the superior performance of continual learning for our proposed dual-learner approach relative to baseline methods. The code is released in https://github.com/datake/FAME.

cs.LG↗

arXiv2026

Phase Transition for Budgeted Multi-Agent Synergy

Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. Each leaf agent is summarized by a compute-performance scaling exponent $\beta$; communication is captured by a message-length fidelity curve $\gamma(m)$; dependence is captured by an effective shared-error correlation $\rho$; and a context window $W$ imposes hard fan-in limits that make hierarchy necessary. For binary success/failure tasks with majority aggregation, we prove a sharp phase transition for deep $b$-ary trees with correlated inputs and lossy communication: a single scalar $\alpha_\rho$ (combining $\gamma(m)$, $\rho$, and fan-in $b$) determines whether weak signal is amplified to a nontrivial fixed point or washed out to chance. In the amplifying regime, we derive an organization exponent $s$ and show that budgeted synergy, i.e., outperforming the best single agent under the same total budget, occurs exactly when $s>\beta$, yielding closed-form compute allocation rules and explicit budget thresholds. We further characterize saturation via a mixing depth and provide a conservative clipped predictor that remains accurate across growth and saturation. A continuous-performance warm-up gives closed-form risks for star, chain, and tree organizations, making correlation- and communication-induced floors explicit and exposing the core design trade-offs in a smooth setting. Finally, we validate the predicted phase boundaries in controlled synthetic simulations and show how the same mechanisms explain the dominant bottlenecks reported in recent large-scale matched-budget studies of LLM agent-system scaling.

cs.AI↗

arXiv2025

SUP: An Inferable Private Multiple Testing Framework with Super Uniformity

Multiple testing is widely applied across scientific fields, particularly in genomic and health data analysis, where protecting sensitive personal information is imperative. However, developing private multiple testing algorithms for super uniform $p$-values remains an open question, as privacy mechanisms introduce intricate dependence among the peeled $p$-values and disrupt their super uniformity, complicating post-selection inference. To address this, we introduce a general Super Uniform Private (SUP) multiple testing framework with three key components. First, we develop a novel $ p $-value transformation that is compatible with diverse privacy regimes while retaining the super uniformity. Next, a reversed peeling algorithm is designed to reduce privacy budgets while facilitating inference. Then, we provide diverse rejection thresholds that are privacy-parameter-free and tailored for different Type-I errors, including the family-wise error rate (FWER) and the false discovery rate (FDR). Building upon these, we advance adaptive techniques to determine the peeling number and boost thresholds. Theoretically, we propose a technique overcoming the post-selection obstacle to Type-I error control, quantify the privacy-induced power loss of SUP relative to its non-private counterpart, and demonstrate that SUP surpasses existing private methods in terms of power. The results of extensive simulations and a real data application validate our theories.

stat.ME↗

arXiv2025

CBMA: Improving conformal prediction through Bayesian model averaging

Conformal prediction has emerged as a popular technique for facilitating valid predictive inference across a spectrum of machine learning models, under minimal assumption of exchangeability. Recently, Hoff (2023) showed that full conformal Bayes provides the most efficient prediction sets (smallest by expected volume) among all prediction sets that are valid at the $(1 - \alpha)$ level if the model is correctly specified. However, a critical issue arises when the Bayesian model itself may be mis-specified, resulting in prediction set that might be suboptimal, even though it still enjoys the frequentist coverage guarantee. To address this limitation, we propose an innovative solution that combines Bayesian model averaging (BMA) with conformal prediction. This hybrid not only leverages the strengths of Bayesian conformal prediction but also introduces a layer of robustness through model averaging. Theoretically, we prove that the resulting prediction set will converge to the optimal level of efficiency, if the true model is included among the candidate models. This assurance of optimality, even under potential model uncertainty, provides a significant improvement over existing methods, ensuring more reliable and precise uncertainty quantification.

math.ST↗

arXiv2025

Understanding Fairness and Prediction Error through Subspace Decomposition and Influence Analysis

Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.

stat.ML↗

arXiv2025

Conformal Inference For Missing Data under Multiple Robust Learning

We develop a novel approach to tackle the common but challenging problem of conformal inference for missing data in machine learning, focusing on Missing at Random (MAR) data. We propose a new procedure Conformal prediction for Missing data under Multiple Robust Learning (CM--MRL) that combines split conformal calibration with a multiple robust empirical-likelihood (EL) reweighting scheme. The method proceeds via a double calibration by reweighting the complete-case scores by EL so that their distribution matches the full calibration distribution implied by MAR, even when some working models are misspecified. We demonstrate the asymptotic behavior of our estimators through empirical process theory and provide reliable coverage for our prediction intervals, both marginally and conditionally and we further show an interval-length dominance result. We show the effectiveness of the proposed method by several numerical experiments in the presence of missing data.

stat.ME↗

arXiv2025

Toward Optimal Statistical Inference in Noisy Linear Quadratic Reinforcement Learning over a Finite Horizon

Recent developments in Reinforcement learning have significantly enhanced sequential decision-making in uncertain environments. Despite their strong performance guarantees, most existing work has focused primarily on improving the operational accuracy of learned control policies and the convergence rates of learning algorithms, with comparatively little attention to uncertainty quantification and statistical inference. Yet, these aspects are essential for assessing the reliability and variability of control policies, especially in high-stakes applications. In this paper, we study statistical inference for the policy gradient (PG) method for noisy Linear Quadratic Reinforcement learning (LQ RL) over a finite time horizon, where linear dynamics with both known and unknown drift parameters are controlled subject to a quadratic cost. We establish the theoretical foundations for statistical inference in LQ RL, deriving exact asymptotics for both the PG estimators and the corresponding objective loss. Furthermore, we introduce a principled inference framework that leverages online bootstrapping to construct confidence intervals for both the learned optimal policy and the corresponding objective losses. The method updates the PG estimates along with a set of randomly perturbed PG estimates as new observations arrive. We prove that the proposed bootstrapping procedure is distributionally consistent and that the resulting confidence intervals achieve both asymptotic and non-asymptotic validity. Notably, our results imply that the quantiles of the exact distribution can be approximated at a rate of $n^{-1/4}$, where $n$ is the number of samples used during the procedure. The proposed procedure is easy to implement and applicable to both offline and fully online settings. Numerical experiments illustrate the effectiveness of our approach across a range of noisy linear dynamical systems.

math.ST↗

arXiv2025

Non-Asymptotic Analysis of Online Local Private Learning with SGD

Differentially Private Stochastic Gradient Descent (DP-SGD) has been widely used for solving optimization problems with privacy guarantees in machine learning and statistics. Despite this, a systematic non-asymptotic convergence analysis for DP-SGD, particularly in the context of online problems and local differential privacy (LDP) models, remains largely elusive. Existing non-asymptotic analyses have focused on non-private optimization methods, and hence are not applicable to privacy-preserving optimization problems. This work initiates the analysis to bridge this gap and opens the door to non-asymptotic convergence analysis of private optimization problems. A general framework is investigated for the online LDP model in stochastic optimization problems. We assume that sensitive information from individuals is collected sequentially and aim to estimate, in real-time, a static parameter that pertains to the population of interest. Most importantly, we conduct a comprehensive non-asymptotic convergence analysis of the proposed estimators in finite-sample situations, which gives their users practical guidelines regarding the effect of various hyperparameters, such as step size, parameter dimensions, and privacy budgets, on convergence rates. Our proposed estimators are validated in the theoretical and practical realms by rigorous mathematical derivations and carefully constructed numerical experiments.

stat.ME↗

arXiv2025

Online differentially private inference in stochastic gradient descent

We propose a general privacy-preserving optimization-based framework for real-time environments without requiring trusted data curators. In particular, we introduce a noisy stochastic gradient descent algorithm for online statistical inference with streaming data under local differential privacy constraints. Unlike existing methods that either disregard privacy protection or require full access to the entire dataset, our proposed algorithm provides rigorous local privacy guarantees for individual-level data. It operates as a one-pass algorithm without re-accessing the historical data, thereby significantly reducing both time and space complexity. We also introduce online private statistical inference by conducting two construction procedures of valid private confidence intervals. We formally establish the convergence rates for the proposed estimators and present a functional central limit theorem to show the averaged solution path of these estimators weakly converges to a rescaled Brownian motion, providing a theoretical foundation for our online inference tool. Numerical simulation experiments demonstrate the finite-sample performance of our proposed procedure, underscoring its efficacy and reliability. Furthermore, we illustrate our method with an analysis of two datasets: the ride-sharing data and the US insurance data, showcasing its practical utility.

stat.ME↗

arXiv2025

Deep Fair Learning: A Unified Framework for Fine-tuning Representations with Sufficient Networks

Ensuring fairness in machine learning is a critical and challenging task, as biased data representations often lead to unfair predictions. To address this, we propose Deep Fair Learning, a framework that integrates nonlinear sufficient dimension reduction with deep learning to construct fair and informative representations. By introducing a novel penalty term during fine-tuning, our method enforces conditional independence between sensitive attributes and learned representations, addressing bias at its source while preserving predictive performance. Unlike prior methods, it supports diverse sensitive attributes, including continuous, discrete, binary, or multi-group types. Experiments on various types of data structure show that our approach achieves a superior balance between fairness and utility, significantly outperforming state-of-the-art baselines.

stat.ML↗

arXiv2025

Online federated learning framework for classification

In this paper, we develop a novel online federated learning framework for classification, designed to handle streaming data from multiple clients while ensuring data privacy and computational efficiency. Our method leverages the generalized distance-weighted discriminant technique, making it robust to both homogeneous and heterogeneous data distributions across clients. In particular, we develop a new optimization algorithm based on the Majorization-Minimization principle, integrated with a renewable estimation procedure, enabling efficient model updates without full retraining. We provide a theoretical guarantee for the convergence of our estimator, proving its consistency and asymptotic normality under standard regularity conditions. In addition, we establish that our method achieves Bayesian risk consistency, ensuring its reliability for classification tasks in federated environments. We further incorporate differential privacy mechanisms to enhance data security, protecting client information while maintaining model performance. Extensive numerical experiments on both simulated and real-world datasets demonstrate that our approach delivers high classification accuracy, significant computational efficiency gains, and substantial savings in data storage requirements compared to existing methods.

stat.ML↗

arXiv2025

A Deep Bayesian Nonparametric Framework for Robust Mutual Information Estimation

Mutual Information (MI) is a crucial measure for capturing dependencies between variables, but exact computation is challenging in high dimensions with intractable likelihoods, impacting accuracy and robustness. One idea is to use an auxiliary neural network to train an MI estimator; however, methods based on the empirical distribution function (EDF) can introduce sharp fluctuations in the MI loss due to poor out-of-sample performance, destabilizing convergence. We present a Bayesian nonparametric (BNP) solution for training an MI estimator by constructing the MI loss with a finite representation of the Dirichlet process posterior to incorporate regularization in the training process. With this regularization, the MI loss integrates both prior knowledge and empirical data to reduce the loss sensitivity to fluctuations and outliers in the sample data, especially in small sample settings like mini-batches. This approach addresses the challenge of balancing accuracy and low variance by effectively reducing variance, leading to stabilized and robust MI loss gradients during training and enhancing the convergence of the MI approximation while offering stronger theoretical guarantees for convergence. We explore the application of our estimator in maximizing MI between the data space and the latent space of a variational autoencoder. Experimental results demonstrate significant improvements in convergence over EDF-based methods, with applications across synthetic and real datasets, notably in 3D CT image generation, yielding enhanced structure discovery and reduced overfitting in data synthesis. While this paper focuses on generative models in application, the proposed estimator is not restricted to this setting and can be applied more broadly in various BNP learning procedures.

stat.ML↗

arXiv2025

A Consensus Privacy Metrics Framework for Synthetic Data

Synthetic data generation is one approach for sharing individual-level data. However, to meet legislative requirements, it is necessary to demonstrate that the individuals' privacy is adequately protected. There is no consolidated standard for measuring privacy in synthetic data. Through an expert panel and consensus process, we developed a framework for evaluating privacy in synthetic data. Our findings indicate that current similarity metrics fail to measure identity disclosure, and their use is discouraged. For differentially private synthetic data, a privacy budget other than close to zero was not considered interpretable. There was consensus on the importance of membership and attribute disclosure, both of which involve inferring personal information about an individual without necessarily revealing their identity. The resultant framework provides precise recommendations for metrics that address these types of disclosures effectively. Our findings further present specific opportunities for future research that can help with widespread adoption of synthetic data.

cs.CR↗

arXiv2024

Statistical Undersampling with Mutual Information and Support Points

Class imbalance and distributional differences in large datasets present significant challenges for classification tasks machine learning, often leading to biased models and poor predictive performance for minority classes. This work introduces two novel undersampling approaches: mutual information-based stratified simple random sampling and support points optimization. These methods prioritize representative data selection, effectively minimizing information loss. Empirical results across multiple classification tasks demonstrate that our methods outperform traditional undersampling techniques, achieving higher balanced classification accuracy. These findings highlight the potential of combining statistical concepts with machine learning to address class imbalance in practical applications.

stat.ML↗

arXiv2024

FedSTaS: Client Stratification and Client Level Sampling for Efficient Federated Learning

Federated learning (FL) is a machine learning methodology that involves the collaborative training of a global model across multiple decentralized clients in a privacy-preserving way. Several FL methods are introduced to tackle communication inefficiencies but do not address how to sample participating clients in each round effectively and in a privacy-preserving manner. In this paper, we propose \textit{FedSTaS}, a client and data-level sampling method inspired by \textit{FedSTS} and \textit{FedSampling}. In each federated learning round, \textit{FedSTaS} stratifies clients based on their compressed gradients, re-allocate the number of clients to sample using an optimal Neyman allocation, and sample local data from each participating clients using a data uniform sampling strategy. Experiments on three datasets show that \textit{FedSTaS} can achieve higher accuracy scores than those of \textit{FedSTS} within a fixed number of training rounds.

cs.LG↗