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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.

Data collaboration via Data Clean Room offers value but raises privacy concerns, which can be addressed through synthetic data and multi-table synthesizers. Common multi-table synthesizers fail to perform when subjects occur repeatedly in both tables. This is an urgent yet unresolved problem, since having both tables with repeating subjects is common. To improve performance in this scenario, we present the DEREC 3-step pre-processing pipeline to generalize adaptability of multi-table synthesizers. We also introduce the SIMPRO 3-aspect evaluation metrics, which leverage conditional distribution and large-scale simultaneous hypothesis testing to provide comprehensive feedback on synthetic data fidelity at both column and table levels. Results show that using DEREC improves fidelity, and multi-table synthesizers outperform single-table counterparts in collaboration settings. Together, the DEREC-SIMPRO pipeline offers a robust solution for generalizing data collaboration, promoting a more efficient, data-driven society.

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.

In this paper, we leverage the power of latent diffusion models to generate synthetic time series tabular data. Along with the temporal and feature correlations, the heterogeneous nature of the feature in the table has been one of the main obstacles in time series tabular data modeling. We tackle this problem by combining the ideas of the variational auto-encoder (VAE) and the denoising diffusion probabilistic model (DDPM). Our model named as \texttt{TimeAutoDiff} has several key advantages including (1) Generality: the ability to handle the broad spectrum of time series tabular data from single to multi-sequence datasets; (2) Good fidelity and utility guarantees: numerical experiments on six publicly available datasets demonstrating significant improvements over state-of-the-art models in generating time series tabular data, across four metrics measuring fidelity and utility; (3) Fast sampling speed: entire time series data generation as opposed to the sequential data sampling schemes implemented in the existing diffusion-based models, eventually leading to significant improvements in sampling speed, (4) Entity conditional generation: the first implementation of conditional generation of multi-sequence time series tabular data with heterogenous features in the literature, enabling scenario exploration across multiple scientific and engineering domains. Codes are in preparation for release to the public, but available upon request.

The evaluation of synthetic data generation is crucial, especially in the retail sector where data accuracy is paramount. This paper introduces a comprehensive framework for assessing synthetic retail data, focusing on fidelity, utility, and privacy. Our approach differentiates between continuous and discrete data attributes, providing precise evaluation criteria. Fidelity is measured through stability and generalizability. Stability ensures synthetic data accurately replicates known data distributions, while generalizability confirms its robustness in novel scenarios. Utility is demonstrated through the synthetic data's effectiveness in critical retail tasks such as demand forecasting and dynamic pricing, proving its value in predictive analytics and strategic planning. Privacy is safeguarded using Differential Privacy, ensuring synthetic data maintains a perfect balance between resembling training and holdout datasets without compromising security. Our findings validate that this framework provides reliable and scalable evaluation for synthetic retail data. It ensures high fidelity, utility, and privacy, making it an essential tool for advancing retail data science. This framework meets the evolving needs of the retail industry with precision and confidence, paving the way for future advancements in synthetic data methodologies.

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.

Generative Foundation Models (GFMs) have produced synthetic data with remarkable quality in modalities such as images and text. However, applying GFMs to tabular data poses significant challenges due to the inherent heterogeneity of table features. Existing cross-table learning frameworks are hindered by the absence of both a generative model backbone and a decoding mechanism for heterogeneous feature values. To overcome these limitations, we introduce the Cross-Table Synthesizer (CTSyn), a diffusion-based foundational model tailored for tabular data generation. CTSyn introduces three major components: an aggregator that consolidates heterogeneous tables into a unified latent space; a conditional latent diffusion model for sampling from this space; and type-specific decoders that reconstruct values of varied data types from sampled latent vectors. Extensive testing on real-world datasets reveals that CTSyn not only significantly outperforms existing table synthesizers in utility and diversity, but also uniquely enhances performances of downstream machine learning beyond what is achievable with real data, thus establishing a new paradigm for synthetic data generation.

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.

Diffusion models, a specific type of generative model, have achieved unprecedented performance in recent years and consistently produce high-quality synthetic samples. A critical prerequisite for their notable success lies in the presence of a substantial number of training samples, which can be impractical in real-world applications due to high collection costs or associated risks. Consequently, various finetuning and regularization approaches have been proposed to transfer knowledge from existing pre-trained models to specific target domains with limited data. This paper introduces the Transfer Guided Diffusion Process (TGDP), a novel approach distinct from conventional finetuning and regularization methods. We prove that the optimal diffusion model for the target domain integrates pre-trained diffusion models on the source domain with additional guidance from a domain classifier. We further extend TGDP to a conditional version for modeling the joint distribution of data and its corresponding labels, together with two additional regularization terms to enhance the model performance. We validate the effectiveness of TGDP on both simulated and real-world datasets., Comment: NeurIPS 2024

Offline Black-Box Optimization (BBO) aims at optimizing a black-box function using the knowledge from a pre-collected offline dataset of function values and corresponding input designs. However, the high-dimensional and highly-multimodal input design space of black-box function pose inherent challenges for most existing methods that model and operate directly upon input designs. These issues include but are not limited to high sample complexity, which relates to inaccurate approximation of black-box function; and insufficient coverage and exploration of input design modes, which leads to suboptimal proposal of new input designs. In this work, we consider finding a latent space that serves as a compressed yet accurate representation of the design-value joint space, enabling effective latent exploration of high-value input design modes. To this end, we formulate an learnable energy-based latent space, and propose Noise-intensified Telescoping density-Ratio Estimation (NTRE) scheme for variational learning of an accurate latent space model without costly Markov Chain Monte Carlo. The optimization process is then exploration of high-value designs guided by the learned energy-based model in the latent space, formulated as gradient-based sampling from a latent-variable-parameterized inverse model. We show that our particular parameterization encourages expanded exploration around high-value design modes, motivated by inversion thinking of a fundamental result of conditional covariance matrix typically used for variance reduction. We observe that our method, backed by an accurately learned informative latent space and an expanding-exploration model design, yields significant improvements over strong previous methods on both synthetic and real world datasets such as the design-bench suite.

We present BadGD, a unified theoretical framework that exposes the vulnerabilities of gradient descent algorithms through strategic backdoor attacks. Backdoor attacks involve embedding malicious triggers into a training dataset to disrupt the model's learning process. Our framework introduces three novel constructs: Max RiskWarp Trigger, Max GradWarp Trigger, and Max GradDistWarp Trigger, each designed to exploit specific aspects of gradient descent by distorting empirical risk, deterministic gradients, and stochastic gradients respectively. We rigorously define clean and backdoored datasets and provide mathematical formulations for assessing the distortions caused by these malicious backdoor triggers. By measuring the impact of these triggers on the model training procedure, our framework bridges existing empirical findings with theoretical insights, demonstrating how a malicious party can exploit gradient descent hyperparameters to maximize attack effectiveness. In particular, we show that these exploitations can significantly alter the loss landscape and gradient calculations, leading to compromised model integrity and performance. This research underscores the severe threats posed by such data-centric attacks and highlights the urgent need for robust defenses in machine learning. BadGD sets a new standard for understanding and mitigating adversarial manipulations, ensuring the reliability and security of AI systems., Comment: 25 pages, 1 figure

With the proliferation of generative AI and the increasing volume of generative data (also called as synthetic data), assessing the fidelity of generative data has become a critical concern. In this paper, we propose a discriminative approach to estimate the total variation (TV) distance between two distributions as an effective measure of generative data fidelity. Our method quantitatively characterizes the relation between the Bayes risk in classifying two distributions and their TV distance. Therefore, the estimation of total variation distance reduces to that of the Bayes risk. In particular, this paper establishes theoretical results regarding the convergence rate of the estimation error of TV distance between two Gaussian distributions. We demonstrate that, with a specific choice of hypothesis class in classification, a fast convergence rate in estimating the TV distance can be achieved. Specifically, the estimation accuracy of the TV distance is proven to inherently depend on the separation of two Gaussian distributions: smaller estimation errors are achieved when the two Gaussian distributions are farther apart. This phenomenon is also validated empirically through extensive simulations. In the end, we apply this discriminative estimation method to rank fidelity of synthetic image data using the MNIST dataset.

In this paper, we introduce a simple yet effective tabular data watermarking mechanism with statistical guarantees. We show theoretically that the proposed watermark can be effectively detected, while faithfully preserving the data fidelity, and also demonstrates appealing robustness against additive noise attack. The general idea is to achieve the watermarking through a strategic embedding based on simple data binning. Specifically, it divides the feature's value range into finely segmented intervals and embeds watermarks into selected ``green list" intervals. To detect the watermarks, we develop a principled statistical hypothesis-testing framework with minimal assumptions: it remains valid as long as the underlying data distribution has a continuous density function. The watermarking efficacy is demonstrated through rigorous theoretical analysis and empirical validation, highlighting its utility in enhancing the security of synthetic and real-world datasets.

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.

State machines play a pivotal role in augmenting the efficacy of protocol analyzing to unveil more vulnerabilities. However, the task of inferring state machines from network protocol implementations presents significant challenges. Traditional methods based on dynamic analysis often overlook crucial state transitions due to limited coverage, while static analysis faces difficulties with complex code structures and behaviors. To address these limitations, we propose an innovative state machine inference approach powered by Large Language Models (LLMs). Utilizing text-embedding technology, this method allows LLMs to dissect and analyze the intricacies of protocol implementation code. Through targeted prompt engineering, we systematically identify and infer the underlying state machines. Our evaluation across six protocol implementations demonstrates the method's high efficacy, achieving an accuracy rate exceeding 90% and successfully delineating differences on state machines among various implementations of the same protocol. Importantly, integrating this approach with protocol fuzzing has notably enhanced AFLNet's code coverage by 10% over RFCNLP, showcasing the considerable potential of LLMs in advancing network protocol security analysis. Our proposed method not only marks a significant step forward in accurate state machine inference but also opens new avenues for improving the security and reliability of protocol implementations.

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.

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.

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.

In various real-world scenarios, such as recommender systems and political surveys, pairwise rankings are commonly collected and utilized for rank aggregation to obtain an overall ranking of items. However, preference rankings can reveal individuals' personal preferences, underscoring the need to protect them from being released for 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. Using the randomized response mechanism to perturb raw pairwise rankings is a common privacy protection strategy used in practice. 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. Motivated by this, we propose to adaptively debiasing the rankings from the randomized response mechanism, ensuring consistent estimation of true preferences and enhancing the utility of downstream rank aggregation. Theoretically, we offer insights into the relationship between overall privacy guarantees and estimation errors from 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 influences the specification of top-$K$ item sets and complete rankings. Our findings are validated through extensive simulations and a real application.

The network flow watermarking technique associates the two communicating parties by actively modifying certain characteristics of the stream generated by the sender so that it covertly carries some special marking information. Some curious users communicating with the hidden server as a Tor client may attempt de-anonymization attacks to uncover the real identity of the hidden server by using this technique. This compromises the privacy of the anonymized communication system. Therefore, we propose a defense scheme against flow watermarking. The scheme is based on deep neural networks and utilizes generative adversarial networks to convert the original Inter-Packet Delays (IPD) into new IPDs generated by the model. We also adopt the concept of adversarial attacks to ensure that the detector will produce an incorrect classification when detecting these new IPDs. This approach ensures that these IPDs are considered "clean", effectively covering the potential watermarks. This scheme is effective against time-based flow watermarking techniques.

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, Bayes-optimal fair classifiers become group-wise thresholding rules. Our approach can also handle multiple fairness constraints (such as equalized odds), and the common scenario when the protected attribute cannot be used at the prediction phase. 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 compare favorably to existing algorithms., Comment: This paper replaces the preprint "Bayes-optimal classifiers under group fairness" by Xianli Zeng, Edgar Dobriban, and Guang Cheng (arXiv:2202.09724)

Large language models (LLMs) are powerful models that can learn concepts at the inference stage via in-context learning (ICL). While theoretical studies, e.g., \cite{zhang2023trained}, attempt to explain the mechanism of ICL, they assume the input $x_i$ and the output $y_i$ of each demonstration example are in the same token (i.e., structured data). However, in real practice, the examples are usually text input, and all words, regardless of their logic relationship, are stored in different tokens (i.e., unstructured data \cite{wibisono2023role}). To understand how LLMs learn from the unstructured data in ICL, this paper studies the role of each component in the transformer architecture and provides a theoretical understanding to explain the success of the architecture. In particular, we consider a simple transformer with one/two attention layers and linear regression tasks for the ICL prediction. We observe that (1) a transformer with two layers of (self-)attentions with a look-ahead attention mask can learn from the prompt in the unstructured data, and (2) positional encoding can match the $x_i$ and $y_i$ tokens to achieve a better ICL performance.

Pre-training is known to generate universal representations for downstream tasks in large-scale deep learning such as large language models. Existing literature, e.g., \cite{kim2020adversarial}, empirically observe that the downstream tasks can inherit the adversarial robustness of the pre-trained model. We provide theoretical justifications for this robustness inheritance phenomenon. Our theoretical results reveal that feature purification plays an important role in connecting the adversarial robustness of the pre-trained model and the downstream tasks in two-layer neural networks. Specifically, we show that (i) with adversarial training, each hidden node tends to pick only one (or a few) feature; (ii) without adversarial training, the hidden nodes can be vulnerable to attacks. This observation is valid for both supervised pre-training and contrastive learning. With purified nodes, it turns out that clean training is enough to achieve adversarial robustness in downstream tasks., Comment: To appear in AISTATS2024

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., Comment: 38 pages, 2 figures. Invited for review in Annual Review of Statistics and Its Application

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., Comment: The following article has been accepted by ICAIF22, Synthetic Data for AI in Finance; see https://sites.google.com/view/icaif-synthetic-2022/program

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., Comment: The following article has been accepted by 2nd Workshop on Synthetic Data for AI in Finance; see https://sites.google.com/view/icaif-synthetic/home

Machine learning (ML) has gained significant adoption in Android malware detection to address the escalating threats posed by the rapid proliferation of malware attacks. However, recent studies have revealed the inherent vulnerabilities of ML-based detection systems to evasion attacks. While efforts have been made to address this critical issue, many of the existing defensive methods encounter challenges such as lower effectiveness or reduced generalization capabilities. In this paper, we introduce a novel Android malware detection method, MalPurifier, which exploits adversarial purification to eliminate perturbations independently, resulting in attack mitigation in a light and flexible way. Specifically, MalPurifier employs a Denoising AutoEncoder (DAE)-based purification model to preprocess input samples, removing potential perturbations from them and then leading to correct classification. To enhance defense effectiveness, we propose a diversified adversarial perturbation mechanism that strengthens the purification model against different manipulations from various evasion attacks. We also incorporate randomized "protective noises" onto benign samples to prevent excessive purification. Furthermore, we customize a loss function for improving the DAE model, combining reconstruction loss and prediction loss, to enhance feature representation learning, resulting in accurate reconstruction and classification. Experimental results on two Android malware datasets demonstrate that MalPurifier outperforms the state-of-the-art defenses, and it significantly strengthens the vulnerable malware detector against 37 evasion attacks, achieving accuracies over 90.91%. Notably, MalPurifier demonstrates easy scalability to other detectors, offering flexibility and robustness in its implementation., Comment: 14 pages; In submission

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.

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.

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., Comment: 22 pages, short version is accepted by ICML workshop on Structured Probabilistic Inference & Generative Modeling 2023

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.

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.

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}., Comment: Proceedings of the 41th International Conference on Machine Learning, (ICML 2024)

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 $\epsilon$-DP synthetic data generator.

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 $\epsilon$-differential privacy. This paper proposes a novel notion called $\epsilon$-ranking differential privacy for protecting ranks. We establish the connection between the Mallows model (Mallows, 1957) and the proposed $\epsilon$-ranking differential privacy. This allows us to develop a multistage ranking algorithm to generate synthetic rankings while satisfying the developed $\epsilon$-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 $\epsilon$ 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., Comment: 59 pages, 8 figures

A characteristic mode (CM) method that relies on a global multi-trace formulation (MTF) of surface integral equations is proposed to compute the modes and the resonance frequencies of microstrip patch antennas with finite dielectric substrates and ground planes. Compared to the coupled formulation of electric field and Poggio-Miller-Chang-Harrington-Wu-Tsai integral equations, global MTF allows for more direct implementation of a sub-structure CM method. This is achieved by representing the coupling of the electromagnetic fields on the substrate and ground plane in the form of a numerical Green function matrix, which yields a more compact generalized eigenvalue equation. The resulting sub-structure CM method avoids the cumbersome computation of the multilayered medium Green function (unlike the CM methods that rely on mixed-potential integral equations) and the volumetric discretization of the substrate (unlike the CM methods that rely on volume-surface integral equations), and numerical results show that it is a reliable and accurate approach to predicting the modal behavior of electromagnetic fields on practical microstrip antennas.

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.

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.

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 $(\mu/\sqrt{(2-2/\mathrm{e})B})$-GDP asymptotically satisfies $\mu$-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.

Deep learning has gained huge empirical successes in large-scale classification problems. In contrast, there is a lack of statistical understanding about deep learning methods, particularly in the minimax optimality perspective. For instance, in the classical smooth decision boundary setting, existing deep neural network (DNN) approaches are rate-suboptimal, and it remains elusive how to construct minimax optimal DNN classifiers. Moreover, it is interesting to explore whether DNN classifiers can circumvent the curse of dimensionality in handling high-dimensional data. The contributions of this paper are two-fold. First, based on a localized margin framework, we discover the source of suboptimality of existing DNN approaches. Motivated by this, we propose a new deep learning classifier using a divide-and-conquer technique: DNN classifiers are constructed on each local region and then aggregated to a global one. We further propose a localized version of the classical Tsybakov's noise condition, under which statistical optimality of our new classifier is established. Second, we show that DNN classifiers can adapt to low-dimensional data structures and circumvent the curse of dimensionality in the sense that the minimax rate only depends on the effective dimension, potentially much smaller than the actual data dimension. Numerical experiments are conducted on simulated data to corroborate our theoretical results.

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., Comment: arXiv admin note: text overlap with arXiv:2202.09724

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.

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., Comment: This paper has been withdrawn by the author due to a revision decision