Guang Cheng

Yidong Ouyang, Liyan Xie, Chongxuan Li et al.

The diffusion model has shown remarkable performance in modeling data distributions and synthesizing data. However, the vanilla diffusion model requires complete or fully observed data for training. Incomplete data is a common issue in various real-world applications, including healthcare and finance, particularly when dealing with tabular datasets. This work presents a unified and principled diffusion-based framework for learning from data with missing values under various missing mechanisms. We first observe that the widely adopted "impute-then-generate" pipeline may lead to a biased learning objective. Then we propose to mask the regression loss of Denoising Score Matching in the training phase. We prove the proposed method is consistent in learning the score of data distributions, and the proposed training objective serves as an upper bound for the negative likelihood in certain cases. The proposed framework is evaluated on multiple tabular datasets using realistic and efficacious metrics and is demonstrated to outperform state-of-the-art diffusion model on tabular data with "impute-then-generate" pipeline by a large margin.

Namjoon Suh, Xiaofeng Lin, Din-Yin Hsieh et al.

Diffusion model has become a main paradigm for synthetic data generation in many subfields of modern machine learning, including computer vision, language model, or speech synthesis. In this paper, we leverage the power of diffusion model for generating synthetic tabular data. The heterogeneous features in tabular data have been main obstacles in tabular data synthesis, and we tackle this problem by employing the auto-encoder architecture. When compared with the state-of-the-art tabular synthesizers, the resulting synthetic tables from our model show nice statistical fidelities to the real data, and perform well in downstream tasks for machine learning utilities. We conducted the experiments over $15$ publicly available datasets. Notably, our model adeptly captures the correlations among features, which has been a long-standing challenge in tabular data synthesis. Our code is available at https://github.com/UCLA-Trustworthy-AI-Lab/AutoDiffusion.

Yuantong Li, Guang Cheng, Xiaowu Dai

In this paper, we propose a new recommendation algorithm for addressing the problem of two-sided online matching markets with complementary preferences and quota constraints, where agents' preferences are unknown a priori and must be learned from data. The presence of mixed quota and complementary preferences constraints can lead to instability in the matching process, making this problem challenging to solve. To overcome this challenge, we formulate the problem as a bandit learning framework and propose the Multi-agent Multi-type Thompson Sampling (MMTS) algorithm. The algorithm combines the strengths of Thompson Sampling for exploration with a new double matching technique to provide a stable matching outcome. Our theoretical analysis demonstrates the effectiveness of MMTS as it can achieve stability and has a total $\widetilde{\mathcal{O}}(Q{\sqrt{K_{\max}T}})$-Bayesian regret with high probability, which exhibits linearity with respect to the total firm's quota $Q$, the square root of the maximum size of available type workers $\sqrt{K_{\max}}$ and time horizon $T$. In addition, simulation studies also demonstrate MMTS's effectiveness in various settings. We provide code used in our experiments \url{https://github.com/Likelyt/Double-Matching}.

Xianli Zeng, Edgar Dobriban, Guang Cheng

Increasing concerns about disparate effects of AI have motivated a great deal of work on fair machine learning. Existing works mainly focus on independence- and separation-based measures (e.g., demographic parity, equality of opportunity, equalized odds), while sufficiency-based measures such as predictive parity are much less studied. This paper considers predictive parity, which requires equalizing the probability of success given a positive prediction among different protected groups. We prove that, if the overall performances of different groups vary only moderately, all fair Bayes-optimal classifiers under predictive parity are group-wise thresholding rules. Perhaps surprisingly, this may not hold if group performance levels vary widely; in this case we find that predictive parity among protected groups may lead to within-group unfairness. We then propose an algorithm we call FairBayes-DPP, aiming to ensure predictive parity when our condition is satisfied. FairBayes-DPP is an adaptive thresholding algorithm that aims to achieve predictive parity, while also seeking to maximize test accuracy. We provide supporting experiments conducted on synthetic and empirical data.

Ximing Li, Chendi Wang, Guang Cheng

Marginal-based methods achieve promising performance in the synthetic data competition hosted by the National Institute of Standards and Technology (NIST). To deal with high-dimensional data, the distribution of synthetic data is represented by a probabilistic graphical model (e.g., a Bayesian network), while the raw data distribution is approximated by a collection of low-dimensional marginals. Differential privacy (DP) is guaranteed by introducing random noise to each low-dimensional marginal distribution. Despite its promising performance in practice, the statistical properties of marginal-based methods are rarely studied in the literature. In this paper, we study DP data synthesis algorithms based on Bayesian networks (BN) from a statistical perspective. We establish a rigorous accuracy guarantee for BN-based algorithms, where the errors are measured by the total variation (TV) distance or the $L^2$ distance. Related to downstream machine learning tasks, an upper bound for the utility error of the DP synthetic data is also derived. To complete the picture, we establish a lower bound for TV accuracy that holds for every $ε$-DP synthetic data generator.

Huiming Zhang, Haoyu Wei, Guang Cheng

In non-asymptotic learning, variance-type parameters of sub-Gaussian distributions are of paramount importance. However, directly estimating these parameters using the empirical moment generating function (MGF) is infeasible. To address this, we suggest using the sub-Gaussian intrinsic moment norm [Buldygin and Kozachenko (2000), Theorem 1.3] achieved by maximizing a sequence of normalized moments. Significantly, the suggested norm can not only reconstruct the exponential moment bounds of MGFs but also provide tighter sub-Gaussian concentration inequalities. In practice, we provide an intuitive method for assessing whether data with a finite sample size is sub-Gaussian, utilizing the sub-Gaussian plot. The intrinsic moment norm can be robustly estimated via a simple plug-in approach. Our theoretical findings are also applicable to reinforcement learning, including the multi-armed bandit scenario.

Zhanyu Wang, Guang Cheng, Jordan Awan

Differentially private (DP) mechanisms protect individual-level information by introducing randomness into the statistical analysis procedure. Despite the availability of numerous DP tools, there remains a lack of general techniques for conducting statistical inference under DP. We examine a DP bootstrap procedure that releases multiple private bootstrap estimates to infer the sampling distribution and construct confidence intervals (CIs). Our privacy analysis presents new results on the privacy cost of a single DP bootstrap estimate, applicable to any DP mechanism, and identifies some misapplications of the bootstrap in the existing literature. For the composition of the DP bootstrap, we present a numerical method to compute the exact privacy cost of releasing multiple DP bootstrap estimates, and using the Gaussian-DP (GDP) framework (Dong et al., 2022), we show that the release of $B$ DP bootstrap estimates from mechanisms satisfying $(μ/\sqrt{(2-2/\mathrm{e})B})$-GDP asymptotically satisfies $μ$-GDP as $B$ goes to infinity. Then, we perform private statistical inference by post-processing the DP bootstrap estimates. We prove that our point estimates are consistent, our standard CIs are asymptotically valid, and both enjoy optimal convergence rates. To further improve the finite performance, we use deconvolution with DP bootstrap estimates to accurately infer the sampling distribution. We derive CIs for tasks such as population mean estimation, logistic regression, and quantile regression, and we compare them to existing methods using simulations and real-world experiments on 2016 Canada Census data. Our private CIs achieve the nominal coverage level and offer the first approach to private inference for quantile regression.

Yuantong Li, Chi-hua Wang, Guang Cheng et al.

Two-sided online matching platforms are employed in various markets. However, agents' preferences in the current market are usually implicit and unknown, thus needing to be learned from data. With the growing availability of dynamic side information involved in the decision process, modern online matching methodology demands the capability to track shifting preferences for agents based on contextual information. This motivates us to propose a novel framework for this dynamic online matching problem with contextual information, which allows for dynamic preferences in matching decisions. Existing works focus on online matching with static preferences, but this is insufficient: the two-sided preference changes as soon as one side's contextual information updates, resulting in non-static matching. In this paper, we propose a dynamic matching bandit algorithm to adapt to this problem. The key component of the proposed dynamic matching algorithm is an online estimation of the preference ranking with a statistical guarantee. Theoretically, we show that the proposed dynamic matching algorithm delivers an agent-optimal stable matching result with high probability. In particular, we prove a logarithmic regret upper bound $\mathcal{O}(\log(T))$ and construct a corresponding instance-dependent matching regret lower bound. In the experiments, we demonstrate that dynamic matching algorithm is robust to various preference schemes, dimensions of contexts, reward noise levels, and context variation levels, and its application to a job-seeking market further demonstrates the practical usage of the proposed method.

Yucong Liu, Chi-Hua Wang, Guang Cheng

Devising procedures for auditing generative model privacy-utility tradeoff is an important yet unresolved problem in practice. Existing works concentrates on investigating the privacy constraint side effect in terms of utility degradation of the train on synthetic, test on real paradigm of synthetic data training. We push such understanding on privacy-utility tradeoff to next level by observing the privacy deregulation side effect on synthetic training data utility. Surprisingly, we discover the Utility Recovery Incapability of DP-CTGAN and PATE-CTGAN under privacy deregulation, raising concerns on their practical applications. The main message is Privacy Deregulation does NOT always imply Utility Recovery.

Shirong Xu, Will Wei Sun, Guang Cheng

Rankings are widely collected in various real-life scenarios, leading to the leakage of personal information such as users' preferences on videos or news. To protect rankings, existing works mainly develop privacy protection on a single ranking within a set of ranking or pairwise comparisons of a ranking under the $ε$-differential privacy. This paper proposes a novel notion called $ε$-ranking differential privacy for protecting ranks. We establish the connection between the Mallows model (Mallows, 1957) and the proposed $ε$-ranking differential privacy. This allows us to develop a multistage ranking algorithm to generate synthetic rankings while satisfying the developed $ε$-ranking differential privacy. Theoretical results regarding the utility of synthetic rankings in the downstream tasks, including the inference attack and the personalized ranking tasks, are established. For the inference attack, we quantify how $ε$ affects the estimation of the true ranking based on synthetic rankings. For the personalized ranking task, we consider varying privacy preferences among users and quantify how their privacy preferences affect the consistency in estimating the optimal ranking function. Extensive numerical experiments are carried out to verify the theoretical results and demonstrate the effectiveness of the proposed synthetic ranking algorithm.

Yidong Ouyang, Liyan Xie, Guang Cheng

Synthetic data generation has become an emerging tool to help improve the adversarial robustness in classification tasks since robust learning requires a significantly larger amount of training samples compared with standard classification tasks. Among various deep generative models, the diffusion model has been shown to produce high-quality synthetic images and has achieved good performance in improving the adversarial robustness. However, diffusion-type methods are typically slow in data generation as compared with other generative models. Although different acceleration techniques have been proposed recently, it is also of great importance to study how to improve the sample efficiency of generated data for the downstream task. In this paper, we first analyze the optimality condition of synthetic distribution for achieving non-trivial robust accuracy. We show that enhancing the distinguishability among the generated data is critical for improving adversarial robustness. Thus, we propose the Contrastive-Guided Diffusion Process (Contrastive-DP), which adopts the contrastive loss to guide the diffusion model in data generation. We verify our theoretical results using simulations and demonstrate the good performance of Contrastive-DP on image datasets.

Hongyu Zhu, Sichu Liang, Wentao Hu et al.

As a modern ensemble technique, Deep Forest (DF) employs a cascading structure to construct deep models, providing stronger representational power compared to traditional decision forests. However, its greedy multi-layer learning procedure is prone to overfitting, limiting model effectiveness and generalizability. This paper presents an optimized Deep Forest, featuring learnable, layerwise data augmentation policy schedules. Specifically, We introduce the Cut Mix for Tabular data (CMT) augmentation technique to mitigate overfitting and develop a population-based search algorithm to tailor augmentation intensity for each layer. Additionally, we propose to incorporate outputs from intermediate layers into a checkpoint ensemble for more stable performance. Experimental results show that our method sets new state-of-the-art (SOTA) benchmarks in various tabular classification tasks, outperforming shallow tree ensembles, deep forests, deep neural network, and AutoML competitors. The learned policies also transfer effectively to Deep Forest variants, underscoring its potential for enhancing non-differentiable deep learning modules in tabular signal processing.

Yang Yu, Shih-Kang Chao, Guang Cheng

We propose a distributed bootstrap method for simultaneous inference on high-dimensional massive data that are stored and processed with many machines. The method produces an $\ell_\infty$-norm confidence region based on a communication-efficient de-biased lasso, and we propose an efficient cross-validation approach to tune the method at every iteration. We theoretically prove a lower bound on the number of communication rounds $τ_{\min}$ that warrants the statistical accuracy and efficiency. Furthermore, $τ_{\min}$ only increases logarithmically with the number of workers and the intrinsic dimensionality, while nearly invariant to the nominal dimensionality. We test our theory by extensive simulation studies, and a variable screening task on a semi-synthetic dataset based on the US Airline On-Time Performance dataset. The code to reproduce the numerical results is available at GitHub: https://github.com/skchao74/Distributed-bootstrap.

Namjoon Suh, Guang Cheng

In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are reviewed in the nonparametric framework of regression (and classification in Appendix~{\color{blue}B}). These results rely on explicit constructions of neural networks, leading to fast convergence rates of excess risks. Nonetheless, their underlying analysis only applies to the global minimizer in the highly non-convex landscape of deep neural networks. This motivates us to review the training dynamics of neural networks in the second part. Specifically, we review papers that attempt to answer ``how the neural network trained via gradient-based methods finds the solution that can generalize well on unseen data.'' In particular, two well-known paradigms are reviewed: the Neural Tangent Kernel (NTK) paradigm, and Mean-Field (MF) paradigm. Last but not least, we review the most recent theoretical advancements in generative models including Generative Adversarial Networks (GANs), diffusion models, and in-context learning (ICL) in the Large Language Models (LLMs) from two perpsectives reviewed previously, i.e., approximation and training dynamics.

Xianli Zeng, Kevin Jiang, Guang Cheng et al.

Machine learning algorithms may have disparate impacts on protected groups. To address this, we develop methods for Bayes-optimal fair classification, aiming to minimize classification error subject to given group fairness constraints. We introduce the notion of \emph{linear disparity measures}, which are linear functions of a probabilistic classifier; and \emph{bilinear disparity measures}, which are also linear in the group-wise regression functions. We show that several popular disparity measures -- the deviations from demographic parity, equality of opportunity, and predictive equality -- are bilinear. We find the form of Bayes-optimal fair classifiers under a single linear disparity measure, by uncovering a connection with the Neyman-Pearson lemma. For bilinear disparity measures, we are able to find the explicit form of Bayes-optimal fair classifiers as group-wise thresholding rules with explicitly characterized thresholds. We develop similar algorithms for when protected attribute cannot be used at the prediction phase. Moreover, we obtain analogous theoretical characterizations of optimal classifiers for a multi-class protected attribute and for equalized odds. Leveraging our theoretical results, we design methods that learn fair Bayes-optimal classifiers under bilinear disparity constraints. Our methods cover three popular approaches to fairness-aware classification, via pre-processing (Fair Up- and Down-Sampling), in-processing (Fair cost-sensitive Classification) and post-processing (a Fair Plug-In Rule). Our methods control disparity directly while achieving near-optimal fairness-accuracy tradeoffs. We show empirically that our methods have state-of-the-art performance compared to existing algorithms. In particular, our pre-processing method can a reach higher accuracy than prior pre-processing methods at low disparity levels.

Yinan Cheng, Chi-Hua Wang, Vamsi K. Potluru et al.

Devising procedures for downstream task-oriented generative model selections is an unresolved problem of practical importance. Existing studies focused on the utility of a single family of generative models. They provided limited insights on how synthetic data practitioners select the best family generative models for synthetic training tasks given a specific combination of machine learning model class and performance metric. In this paper, we approach the downstream task-oriented generative model selections problem in the case of training fraud detection models and investigate the best practice given different combinations of model interpretability and model performance constraints. Our investigation supports that, while both Neural Network(NN)-based and Bayesian Network(BN)-based generative models are both good to complete synthetic training task under loose model interpretability constrain, the BN-based generative models is better than NN-based when synthetic training fraud detection model under strict model interpretability constrain. Our results provides practical guidance for machine learning practitioner who is interested in replacing their training dataset from real to synthetic, and shed lights on more general downstream task-oriented generative model selection problems.

Tian-Yi Zhou, Namjoon Suh, Guang Cheng et al.

Motivated by the abundance of functional data such as time series and images, there has been a growing interest in integrating such data into neural networks and learning maps from function spaces to R (i.e., functionals). In this paper, we study the approximation of functionals on reproducing kernel Hilbert spaces (RKHS's) using neural networks. We establish the universality of the approximation of functionals on the RKHS's. Specifically, we derive explicit error bounds for those induced by inverse multiquadric, Gaussian, and Sobolev kernels. Moreover, we apply our findings to functional regression, proving that neural networks can accurately approximate the regression maps in generalized functional linear models. Existing works on functional learning require integration-type basis function expansions with a set of pre-specified basis functions. By leveraging the interpolating orthogonal projections in RKHS's, our proposed network is much simpler in that we use point evaluations to replace basis function expansions.

Din-Yin Hsieh, Chi-Hua Wang, Guang Cheng

Exploring generative model training for synthetic tabular data, specifically in sequential contexts such as credit card transaction data, presents significant challenges. This paper addresses these challenges, focusing on attaining both high fidelity to actual data and optimal utility for machine learning tasks. We introduce five pre-processing schemas to enhance the training of the Conditional Probabilistic Auto-Regressive Model (CPAR), demonstrating incremental improvements in the synthetic data's fidelity and utility. Upon achieving satisfactory fidelity levels, our attention shifts to training fraud detection models tailored for time-series data, evaluating the utility of the synthetic data. Our findings offer valuable insights and practical guidelines for synthetic data practitioners in the finance sector, transitioning from real to synthetic datasets for training purposes, and illuminating broader methodologies for synthesizing credit card transaction time series.

Tung Sum Thomas Kwok, Chi-Hua Wang, Guang Cheng

Tabular data synthesis involves not only multi-table synthesis but also generating multi-modal data (e.g., strings and categories), which enables diverse knowledge synthesis. However, separating numerical and categorical data has limited the effectiveness of tabular data generation. The GReaT (Generate Realistic Tabular Data) framework uses Large Language Models (LLMs) to encode entire rows, eliminating the need to partition data types. Despite this, the framework's performance is constrained by two issues: (1) tabular data entries lack sufficient semantic meaning, limiting LLM's ability to leverage pre-trained knowledge for in-context learning, and (2) complex multi-table datasets struggle to establish effective relationships for collaboration. To address these, we propose GReaTER (Generate Realistic Tabular Data after data Enhancement and Reduction), which includes: (1) a data semantic enhancement system that improves LLM's understanding of tabular data through mapping, enabling better in-context learning, and (2) a cross-table connecting method to establish efficient relationships across complex tables. Experimental results show that GReaTER outperforms the GReaT framework.

Shirong Xu, Hengzhi He, Guang Cheng

In recent years, model collapse has become a critical issue in language model training, making it essential to understand the underlying mechanisms driving this phenomenon. In this paper, we investigate recursive parametric model training from a probabilistic perspective, aiming to characterize the conditions under which model collapse occurs and, crucially, how it can be mitigated. We conceptualize the recursive training process as a random walk of the model estimate, highlighting how the sample size influences the step size and how the estimation procedure determines the direction and potential bias of the random walk. Under mild conditions, we rigorously show that progressively increasing the sample size at each training step is necessary to prevent model collapse. In particular, when the estimation is unbiased, the required growth rate follows a superlinear pattern. This rate needs to be accelerated even further in the presence of substantial estimation bias. Building on this probabilistic framework, we also investigate the probability that recursive training on synthetic data yields models that outperform those trained solely on real data. Moreover, we extend these results to general parametric model family in an asymptotic regime. Finally, we validate our theoretical results through extensive simulations and a real-world dataset.

Yuyang Zhou, Guang Cheng, Kang Du et al.

The rapid evolution of cloud computing technologies and the increasing number of cloud applications have provided numerous benefits in our daily lives. However, the diversity and complexity of different components pose a significant challenge to cloud security, especially when dealing with sophisticated and advanced cyberattacks such as Denial of Service (DoS). Recent advancements in the large language models (LLMs) offer promising solutions for security intelligence. By exploiting the powerful capabilities in language understanding, data analysis, task inference, action planning, and code generation, we present LLM-PD, a novel defense architecture that proactively mitigates various DoS threats in cloud networks. LLM-PD can efficiently make decisions through comprehensive data analysis and sequential reasoning, as well as dynamically create and deploy actionable defense mechanisms. Furthermore, it can flexibly self-evolve based on experience learned from previous interactions and adapt to new attack scenarios without additional training. Our case study on three distinct DoS attacks demonstrates its remarkable ability in terms of defense effectiveness and efficiency when compared with other existing methods.

Xianli Zeng, Guang Cheng, Edgar Dobriban

Mitigating the disparate impact of statistical machine learning methods is crucial for ensuring fairness. While extensive research aims to reduce disparity, the effect of using a \emph{finite dataset} -- as opposed to the entire population -- remains unclear. This paper explores the statistical foundations of fair binary classification with two protected groups, focusing on controlling demographic disparity, defined as the difference in acceptance rates between the groups. Although fairness may come at the cost of accuracy even with infinite data, we show that using a finite sample incurs additional costs due to the need to estimate group-specific acceptance thresholds. We study the minimax optimal classification error while constraining demographic disparity to a user-specified threshold. To quantify the impact of fairness constraints, we introduce a novel measure called \emph{fairness-aware excess risk} and derive a minimax lower bound on this measure that all classifiers must satisfy. Furthermore, we propose FairBayes-DDP+, a group-wise thresholding method with an offset that we show attains the minimax lower bound. Our lower bound proofs involve several innovations. Experiments support that FairBayes-DDP+ controls disparity at the user-specified level, while being faster and having a more favorable fairness-accuracy tradeoff than several baselines.

Xianli Zeng, Joshua Ward, Guang Cheng

The increasing usage of machine learning models in consequential decision-making processes has spurred research into the fairness of these systems. While significant work has been done to study group fairness in the in-processing and post-processing setting, there has been little that theoretically connects these results to the pre-processing domain. This paper proposes that achieving group fairness in downstream models can be formulated as finding the optimal design matrix in which to modify a response variable in a Randomized Response framework. We show that measures of group fairness can be directly controlled for with optimal model utility, proposing a pre-processing algorithm called FairRR that yields excellent downstream model utility and fairness.

Shirong Xu, Will Wei Sun, Guang Cheng

In various real-world scenarios, such as recommender systems and political surveys, pairwise rankings are commonly collected and utilized for rank aggregation to derive an overall ranking of items. However, preference rankings can reveal individuals' personal preferences, highlighting the need to protect them from exposure in downstream analysis. In this paper, we address the challenge of preserving privacy while ensuring the utility of rank aggregation based on pairwise rankings generated from a general comparison model. A common privacy protection strategy in practice is the use of the randomized response mechanism to perturb raw pairwise rankings. However, a critical challenge arises because the privatized rankings no longer adhere to the original model, resulting in significant bias in downstream rank aggregation tasks. To address this, we propose an adaptive debiasing method for rankings from the randomized response mechanism, ensuring consistent estimation of true preferences and enhancing the utility of downstream rank aggregation. Theoretically, we provide insights into the relationship between overall privacy guarantees and estimation errors in private ranking data, and establish minimax rates for estimation errors. This enables the determination of optimal privacy guarantees that balance consistency in rank aggregation with privacy protection. We also investigate convergence rates of expected ranking errors for partial and full ranking recovery, quantifying how privacy protection affects the specification of top-$K$ item sets and complete rankings. Our findings are validated through extensive simulations and a real-world application.

Zhangjie Xia, Chi-Hua Wang, Guang Cheng

In the current era of big data and machine learning, it's essential to find ways to shrink the size of training dataset while preserving the training performance to improve efficiency. However, the challenge behind it includes providing practical ways to find points that can be deleted without significantly harming the training result and suffering from problems like underfitting. We therefore present the perfect deleted point problem for 1-step noisy SGD in the classical linear regression task, which aims to find the perfect deleted point in the training dataset such that the model resulted from the deleted dataset will be identical to the one trained without deleting it. We apply the so-called signal-to-noise ratio and suggest that its value is closely related to the selection of the perfect deleted point. We also implement an algorithm based on this and empirically show the effectiveness of it in a synthetic dataset. Finally we analyze the consequences of the perfect deleted point, specifically how it affects the training performance and privacy budget, therefore highlighting its potential. This research underscores the importance of data deletion and calls for urgent need for more studies in this field.

Zhaiming Shen, Menglun Wang, Guang Cheng et al.

Being able to successfully determine whether the testing samples has similar distribution as the training samples is a fundamental question to address before we can safely deploy most of the machine learning models into practice. In this paper, we propose TOOD detection, a simple yet effective tree-based out-of-distribution (TOOD) detection mechanism to determine if a set of unseen samples will have similar distribution as of the training samples. The TOOD detection mechanism is based on computing pairwise hamming distance of testing samples' tree embeddings, which are obtained by fitting a tree-based ensemble model through in-distribution training samples. Our approach is interpretable and robust for its tree-based nature. Furthermore, our approach is efficient, flexible to various machine learning tasks, and can be easily generalized to unsupervised setting. Extensive experiments are conducted to show the proposed method outperforms other state-of-the-art out-of-distribution detection methods in distinguishing the in-distribution from out-of-distribution on various tabular, image, and text data.

Joshua Ward, Yuxuan Yang, Chi-Hua Wang et al.

Membership Inference Attacks (MIAs) have emerged as a principled framework for auditing the privacy of synthetic data generated by tabular generative models, where many diverse methods have been proposed that each exploit different privacy leakage signals. However, in realistic threat scenarios, an adversary must choose a single method without a priori guarantee that it will be the empirically highest performing option. We study this challenge as a decision theoretic problem under uncertainty and conduct the largest synthetic data privacy benchmark to date. Here, we find that no MIA constitutes a strictly dominant strategy across a wide variety of model architectures and dataset domains under our threat model. Motivated by these findings, we propose ensemble MIAs and show that unsupervised ensembles built on individual attacks offer empirically more robust, regret-minimizing strategies than individual attacks.

Yuxiang Liu, Tian Wang, Gourab Kundu et al.

Transformer-based models such as BERT and E5 have significantly advanced text embedding by capturing rich contextual representations. However, many complex real-world queries require sophisticated reasoning to retrieve relevant documents beyond surface-level lexical matching, where encoder-only retrievers often fall short. Decoder-only large language models (LLMs), known for their strong reasoning capabilities, offer a promising alternative. Despite this potential, existing LLM-based embedding methods primarily focus on contextual representation and do not fully exploit the reasoning strength of LLMs. To bridge this gap, we propose Reasoning-Infused Text Embedding (RITE), a simple but effective approach that integrates logical reasoning into the text embedding process using generative LLMs. RITE builds upon existing language model embedding techniques by generating intermediate reasoning texts in the token space before computing embeddings, thereby enriching representations with inferential depth. Experimental results on BRIGHT, a reasoning-intensive retrieval benchmark, demonstrate that RITE significantly enhances zero-shot retrieval performance across diverse domains, underscoring the effectiveness of incorporating reasoning into the embedding process.

Joshua Ward, Chi-Hua Wang, Guang Cheng

Auditing the privacy leakage of synthetic data is an important but unresolved problem. Most existing privacy auditing frameworks for synthetic data rely on heuristics and unreasonable assumptions to attack the failure modes of generative models, exhibiting limited capability to describe and detect the privacy exposure of training data through synthetic data release. In this paper, we study designing Membership Inference Attacks (MIAs) that specifically exploit the observation that tabular generative models tend to significantly overfit to certain regions of the training distribution. Here, we propose Generative Likelihood Ratio Attack (Gen-LRA), a novel, computationally efficient No-Box MIA that, with no assumption of model knowledge or access, formulates its attack by evaluating the influence a test observation has in a surrogate model's estimation of a local likelihood ratio over the synthetic data. Assessed over a comprehensive benchmark spanning diverse datasets, model architectures, and attack parameters, we find that Gen-LRA consistently dominates other MIAs for generative models across multiple performance metrics. These results underscore Gen-LRA's effectiveness as a privacy auditing tool for the release of synthetic data, highlighting the significant privacy risks posed by generative model overfitting in real-world applications.

Shayleen Reynolds, Hengzhi He, Dung Daniel T. Ngo et al.

In recent years, LLM watermarking has emerged as an attractive safeguard against AI-generated content, with promising applications in many real-world domains. However, there are growing concerns that the current LLM watermarking schemes are vulnerable to expert adversaries wishing to reverse-engineer the watermarking mechanisms. Prior work in breaking or stealing LLM watermarks mainly focuses on the distribution-modifying algorithm of Kirchenbauer et al. (2023), which perturbs the logit vector before sampling. In this work, we focus on reverse-engineering the other prominent LLM watermarking scheme, distortion-free watermarking (Kuditipudi et al. 2024), which preserves the underlying token distribution by using a hidden watermarking key sequence. We demonstrate that, even under a more sophisticated watermarking scheme, it is possible to compromise the LLM and carry out a spoofing attack, i.e. generate a large number of (potentially harmful) texts that can be attributed to the original watermarked LLM. Specifically, we propose using adaptive prompting and a sorting-based algorithm to accurately recover the underlying secret key for watermarking the LLM. Our empirical findings on LLAMA-3.1-8B-Instruct, Mistral-7B-Instruct, Gemma-7b, and OPT-125M challenge the current theoretical claims on the robustness and usability of the distortion-free watermarking techniques.

Bochao Gu, Hengzhi He, Guang Cheng

In this paper, we propose a novel statistical framework for watermarking generative categorical data. Our method systematically embeds pre-agreed secret signals by splitting the data distribution into two components and modifying one distribution based on a deterministic relationship with the other, ensuring the watermark is embedded at the distribution-level. To verify the watermark, we introduce an insertion inverse algorithm and detect its presence by measuring the total variation distance between the inverse-decoded data and the original distribution. Unlike previous categorical watermarking methods, which primarily focus on embedding watermarks into a given dataset, our approach operates at the distribution-level, allowing for verification from a statistical distributional perspective. This makes it particularly well-suited for the modern paradigm of synthetic data generation, where the underlying data distribution, rather than specific data points, is of primary importance. The effectiveness of our method is demonstrated through both theoretical analysis and empirical validation.

Joshua Ward, Chi-Hua Wang, Guang Cheng

The promise of tabular generative models is to produce realistic synthetic data that can be shared and safely used without dangerous leakage of information from the training set. In evaluating these models, a variety of methods have been proposed to measure the tendency to copy data from the training dataset when generating a sample. However, these methods suffer from either not considering data-copying from a privacy threat perspective, not being motivated by recent results in the data-copying literature or being difficult to make compatible with the high dimensional, mixed type nature of tabular data. This paper proposes a new similarity metric and Membership Inference Attack called Data Plagiarism Index (DPI) for tabular data. We show that DPI evaluates a new intuitive definition of data-copying and characterizes the corresponding privacy risk. We show that the data-copying identified by DPI poses both privacy and fairness threats to common, high performing architectures; underscoring the necessity for more sophisticated generative modeling techniques to mitigate this issue.

Xiaofeng Lin, Chenheng Xu, Matthew Yang et al.

Generative Foundation Models (GFMs) have achieved remarkable success in producing high-quality synthetic data for images and text. However, their application to tabular data presents significant challenges due to the heterogeneous nature of table features. Current cross-table learning frameworks struggle because they lack a generative model backbone and an effective mechanism to decode heterogeneous feature values. To address these challenges, we propose the Cross-Table Synthesizer (CTSyn), a diffusion-based generative foundation model for tabular data generation. CTSyn comprises two key components. The first is an autoencoder network that consolidates diverse tables into a unified latent space. It dynamically reconstructs table values using a table schema embedding, allowing adaptation to heterogeneous datasets. The second is a conditional latent diffusion model that generates samples from the learned latent space, conditioned on the table schema. Through large-scale pre-training, CTSyn outperforms existing table synthesizers on standard benchmarks in both utility and diversity. These results position CTSyn as a promising framework for synthetic table generation and lay the groundwork for developing large-scale tabular foundation models.

Yuantong Li, Guang Cheng, Xiaowu Dai

Recommender systems play a crucial role in internet economies by connecting users with relevant products or services. However, designing effective recommender systems faces two key challenges: (1) the exploration-exploitation tradeoff in balancing new product exploration against exploiting known preferences, and (2) dynamic incentive compatibility in accounting for users' self-interested behaviors and heterogeneous preferences. This paper formalizes these challenges into a Dynamic Bayesian Incentive-Compatible Recommendation Protocol (DBICRP). To address the DBICRP, we propose a two-stage algorithm (RCB) that integrates incentivized exploration with an efficient offline learning component for exploitation. In the first stage, our algorithm explores available products while maintaining dynamic incentive compatibility to determine sufficient sample sizes. The second stage employs inverse proportional gap sampling integrated with an arbitrary machine learning method to ensure sublinear regret. Theoretically, we prove that RCB achieves $O(\sqrt{KdT})$ regret and satisfies Bayesian incentive compatibility (BIC) under a Gaussian prior assumption. Empirically, we validate RCB's strong incentive gain, sublinear regret, and robustness through simulations and a real-world application on personalized warfarin dosing. Our work provides a principled approach for incentive-aware recommendation in online preference learning settings.

Shirong Xu, Will Wei Sun, Guang Cheng

Synthetic data algorithms are widely employed in industries to generate artificial data for downstream learning tasks. While existing research primarily focuses on empirically evaluating utility of synthetic data, its theoretical understanding is largely lacking. This paper bridges the practice-theory gap by establishing relevant utility theory in a statistical learning framework. It considers two utility metrics: generalization and ranking of models trained on synthetic data. The former is defined as the generalization difference between models trained on synthetic and on real data. By deriving analytical bounds for this utility metric, we demonstrate that the synthetic feature distribution does not need to be similar as that of real data for ensuring comparable generalization of synthetic models, provided proper model specifications in downstream learning tasks. The latter utility metric studies the relative performance of models trained on synthetic data. In particular, we discover that the distribution of synthetic data is not necessarily similar as the real one to ensure consistent model comparison. Interestingly, consistent model comparison is still achievable even when synthetic responses are not well generated, as long as downstream models are separable by a generalization gap. Finally, extensive experiments on non-parametric models and deep neural networks have been conducted to validate these theoretical findings.

Chi-Hua Wang, Wenjie Li, Guang Cheng et al.

This paper presents a novel federated linear contextual bandits model, where individual clients face different K-armed stochastic bandits with high-dimensional decision context and coupled through common global parameters. By leveraging the sparsity structure of the linear reward , a collaborative algorithm named \texttt{Fedego Lasso} is proposed to cope with the heterogeneity across clients without exchanging local decision context vectors or raw reward data. \texttt{Fedego Lasso} relies on a novel multi-client teamwork-selfish bandit policy design, and achieves near-optimal regrets for shared parameter cases with logarithmic communication costs. In addition, a new conceptual tool called federated-egocentric policies is introduced to delineate exploration-exploitation trade-off. Experiments demonstrate the effectiveness of the proposed algorithms on both synthetic and real-world datasets.

Jiexin Duan, Xingye Qiao, Guang Cheng

In machine learning, crowdsourcing is an economical way to label a large amount of data. However, the noise in the produced labels may deteriorate the accuracy of any classification method applied to the labelled data. We propose an enhanced nearest neighbor classifier (ENN) to overcome this issue. Two algorithms are developed to estimate the worker quality (which is often unknown in practice): one is to construct the estimate based on the denoised worker labels by applying the $k$NN classifier to the expert data; the other is an iterative algorithm that works even without access to the expert data. Other than strong numerical evidence, our proposed methods are proven to achieve the same regret as its oracle version based on high-quality expert data. As a technical by-product, a lower bound on the sample size assigned to each worker to reach the optimal convergence rate of regret is derived.

Zhiying Fang, Yidong Ouyang, Ding-Xuan Zhou et al.

Deep learning models have been widely applied in various aspects of daily life. Many variant models based on deep learning structures have achieved even better performances. Attention-based architectures have become almost ubiquitous in deep learning structures. Especially, the transformer model has now defeated the convolutional neural network in image classification tasks to become the most widely used tool. However, the theoretical properties of attention-based models are seldom considered. In this work, we show that with suitable adaptations, the single-head self-attention transformer with a fixed number of transformer encoder blocks and free parameters is able to generate any desired polynomial of the input with no error. The number of transformer encoder blocks is the same as the degree of the target polynomial. Even more exciting, we find that these transformer encoder blocks in this model do not need to be trained. As a direct consequence, we show that the single-head self-attention transformer with increasing numbers of free parameters is universal. These surprising theoretical results clearly explain the outstanding performances of the transformer model and may shed light on future modifications in real applications. We also provide some experiments to verify our theoretical result.

Zhiying Fang, Guang Cheng

Convolutional neural networks have shown impressive abilities in many applications, especially those related to the classification tasks. However, for the regression problem, the abilities of convolutional structures have not been fully understood, and further investigation is needed. In this paper, we consider the mean squared error analysis for deep convolutional neural networks. We show that, for additive ridge functions, convolutional neural networks followed by one fully connected layer with ReLU activation functions can reach optimal mini-max rates (up to a log factor). The input dimension only appears in the constant of convergence rates. This work shows the statistical optimality of convolutional neural networks and may shed light on why convolutional neural networks are able to behave well for high dimensional input.

Yue Xing, Qifan Song, Guang Cheng

In some studies \citep[e.g.,][]{zhang2016understanding} of deep learning, it is observed that over-parametrized deep neural networks achieve a small testing error even when the training error is almost zero. Despite numerous works towards understanding this so-called "double descent" phenomenon \citep[e.g.,][]{belkin2018reconciling,belkin2019two}, in this paper, we turn into another way to enforce zero training error (without over-parametrization) through a data interpolation mechanism. Specifically, we consider a class of interpolated weighting schemes in the nearest neighbors (NN) algorithms. By carefully characterizing the multiplicative constant in the statistical risk, we reveal a U-shaped performance curve for the level of data interpolation in both classification and regression setups. This sharpens the existing result \citep{belkin2018does} that zero training error does not necessarily jeopardize predictive performances and claims a counter-intuitive result that a mild degree of data interpolation actually {\em strictly} improve the prediction performance and statistical stability over those of the (un-interpolated) $k$-NN algorithm. In the end, the universality of our results, such as change of distance measure and corrupted testing data, will also be discussed.

Shuang Wu, Chi-Hua Wang, Yuantong Li et al.

We propose a new bootstrap-based online algorithm for stochastic linear bandit problems. The key idea is to adopt residual bootstrap exploration, in which the agent estimates the next step reward by re-sampling the residuals of mean reward estimate. Our algorithm, residual bootstrap exploration for stochastic linear bandit (\texttt{LinReBoot}), estimates the linear reward from its re-sampling distribution and pulls the arm with the highest reward estimate. In particular, we contribute a theoretical framework to demystify residual bootstrap-based exploration mechanisms in stochastic linear bandit problems. The key insight is that the strength of bootstrap exploration is based on collaborated optimism between the online-learned model and the re-sampling distribution of residuals. Such observation enables us to show that the proposed \texttt{LinReBoot} secure a high-probability $\tilde{O}(d \sqrt{n})$ sub-linear regret under mild conditions. Our experiments support the easy generalizability of the \texttt{ReBoot} principle in the various formulations of linear bandit problems and show the significant computational efficiency of \texttt{LinReBoot}.

Xianli Zeng, Edgar Dobriban, Guang Cheng

Machine learning algorithms are becoming integrated into more and more high-stakes decision-making processes, such as in social welfare issues. Due to the need of mitigating the potentially disparate impacts from algorithmic predictions, many approaches have been proposed in the emerging area of fair machine learning. However, the fundamental problem of characterizing Bayes-optimal classifiers under various group fairness constraints has only been investigated in some special cases. Based on the classical Neyman-Pearson argument (Neyman and Pearson, 1933; Shao, 2003) for optimal hypothesis testing, this paper provides a unified framework for deriving Bayes-optimal classifiers under group fairness. This enables us to propose a group-based thresholding method we call FairBayes, that can directly control disparity, and achieve an essentially optimal fairness-accuracy tradeoff. These advantages are supported by thorough experiments.

Yue Xing, Qifan Song, Guang Cheng

The recent proposed self-supervised learning (SSL) approaches successfully demonstrate the great potential of supplementing learning algorithms with additional unlabeled data. However, it is still unclear whether the existing SSL algorithms can fully utilize the information of both labelled and unlabeled data. This paper gives an affirmative answer for the reconstruction-based SSL algorithm \citep{lee2020predicting} under several statistical models. While existing literature only focuses on establishing the upper bound of the convergence rate, we provide a rigorous minimax analysis, and successfully justify the rate-optimality of the reconstruction-based SSL algorithm under different data generation models. Furthermore, we incorporate the reconstruction-based SSL into the existing adversarial training algorithms and show that learning from unlabeled data helps improve the robustness.

Marie Maros, Gesualdo Scutari, Ying Sun et al.

We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the $N$ total observations. We analyze the convergence rate and statistical guarantees of a distributed projected gradient tracking-based algorithm under high-dimensional scaling, allowing the ambient dimension $d$ to grow with (and possibly exceed) the sample size $N$. Our theory shows that, under standard notions of restricted strong convexity and smoothness of the loss functions, suitable conditions on the network connectivity and algorithm tuning, the distributed algorithm converges globally at a {\it linear} rate to an estimate that is within the centralized {\it statistical precision} of the model, $O(s\log d/N)$. When $s\log d/N=o(1)$, a condition necessary for statistical consistency, an $\varepsilon$-optimal solution is attained after $\mathcal{O}(κ\log (1/\varepsilon))$ gradient computations and $O (κ/(1-ρ) \log (1/\varepsilon))$ communication rounds, where $κ$ is the restricted condition number of the loss function and $ρ$ measures the network connectivity. The computation cost matches that of the centralized projected gradient algorithm despite having data distributed; whereas the communication rounds reduce as the network connectivity improves. Overall, our study reveals interesting connections between statistical efficiency, network connectivity \& topology, and convergence rate in high dimensions.

Pratik Ramprasad, Yuantong Li, Zhuoran Yang et al.

The recent emergence of reinforcement learning has created a demand for robust statistical inference methods for the parameter estimates computed using these algorithms. Existing methods for statistical inference in online learning are restricted to settings involving independently sampled observations, while existing statistical inference methods in reinforcement learning (RL) are limited to the batch setting. The online bootstrap is a flexible and efficient approach for statistical inference in linear stochastic approximation algorithms, but its efficacy in settings involving Markov noise, such as RL, has yet to be explored. In this paper, we study the use of the online bootstrap method for statistical inference in RL. In particular, we focus on the temporal difference (TD) learning and Gradient TD (GTD) learning algorithms, which are themselves special instances of linear stochastic approximation under Markov noise. The method is shown to be distributionally consistent for statistical inference in policy evaluation, and numerical experiments are included to demonstrate the effectiveness of this algorithm at statistical inference tasks across a range of real RL environments.

Wenjie Li, Chi-Hua Wang, Guang Cheng et al.

In this paper, we make the key delineation on the roles of resolution and statistical uncertainty in hierarchical bandits-based black-box optimization algorithms, guiding a more general analysis and a more efficient algorithm design. We introduce the \textit{optimum-statistical collaboration}, an algorithm framework of managing the interaction between optimization error flux and statistical error flux evolving in the optimization process. We provide a general analysis of this framework without specifying the forms of statistical error and uncertainty quantifier. Our framework and its analysis, due to their generality, can be applied to a large family of functions and partitions that satisfy different local smoothness assumptions and have different numbers of local optimums, which is much richer than the class of functions studied in prior works. Our framework also inspires us to propose a better measure of the statistical uncertainty and consequently a variance-adaptive algorithm \texttt{VHCT}. In theory, we prove the algorithm enjoys rate-optimal regret bounds under different local smoothness assumptions; in experiments, we show the algorithm outperforms prior efforts in different settings.

Wenjie Li, Zhanyu Wang, Yichen Zhang et al.

In this work, we investigate the idea of variance reduction by studying its properties with general adaptive mirror descent algorithms in nonsmooth nonconvex finite-sum optimization problems. We propose a simple yet generalized framework for variance reduced adaptive mirror descent algorithms named SVRAMD and provide its convergence analysis in both the nonsmooth nonconvex problem and the P-L conditioned problem. We prove that variance reduction reduces the SFO complexity of adaptive mirror descent algorithms and thus accelerates their convergence. In particular, our general theory implies that variance reduction can be applied to algorithms using time-varying step sizes and self-adaptive algorithms such as AdaGrad and RMSProp. Moreover, the convergence rates of SVRAMD recover the best existing rates of non-adaptive variance reduced mirror descent algorithms without complicated algorithmic components. Extensive experiments in deep learning validate our theoretical findings.

Yue Xing, Ruizhi Zhang, Guang Cheng

Adversarially robust learning aims to design algorithms that are robust to small adversarial perturbations on input variables. Beyond the existing studies on the predictive performance to adversarial samples, our goal is to understand statistical properties of adversarially robust estimates and analyze adversarial risk in the setup of linear regression models. By discovering the statistical minimax rate of convergence of adversarially robust estimators, we emphasize the importance of incorporating model information, e.g., sparsity, in adversarially robust learning. Further, we reveal an explicit connection of adversarial and standard estimates, and propose a straightforward two-stage adversarial learning framework, which facilitates to utilize model structure information to improve adversarial robustness. In theory, the consistency of the adversarially robust estimator is proven and its Bahadur representation is also developed for the statistical inference purpose. The proposed estimator converges in a sharp rate under either low-dimensional or sparse scenario. Moreover, our theory confirms two phenomena in adversarially robust learning: adversarial robustness hurts generalization, and unlabeled data help improve the generalization. In the end, we conduct numerical simulations to verify our theory.

Yuantong Li, Chi-hua Wang, Guang Cheng

Motivated by the EU's "Right To Be Forgotten" regulation, we initiate a study of statistical data deletion problems where users' data are accessible only for a limited period of time. This setting is formulated as an online supervised learning task with \textit{constant memory limit}. We propose a deletion-aware algorithm \texttt{FIFD-OLS} for the low dimensional case, and witness a catastrophic rank swinging phenomenon due to the data deletion operation, which leads to statistical inefficiency. As a remedy, we propose the \texttt{FIFD-Adaptive Ridge} algorithm with a novel online regularization scheme, that effectively offsets the uncertainty from deletion. In theory, we provide the cumulative regret upper bound for both online forgetting algorithms. In the experiment, we showed \texttt{FIFD-Adaptive Ridge} outperforms the ridge regression algorithm with fixed regularization level, and hopefully sheds some light on more complex statistical models.

Jincheng Bai, Qifan Song, Guang Cheng

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep learning algorithms are lacking of theoretical support. On the other hand, another line of works have proposed theoretical frameworks that are computationally infeasible. In this paper, we train sparse deep neural networks with a fully Bayesian treatment under spike-and-slab priors, and develop a set of computationally efficient variational inferences via continuous relaxation of Bernoulli distribution. The variational posterior contraction rate is provided, which justifies the consistency of the proposed variational Bayes method. Notably, our empirical results demonstrate that this variational procedure provides uncertainty quantification in terms of Bayesian predictive distribution and is also capable to accomplish consistent variable selection by training a sparse multi-layer neural network.