Shirong Xu

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.

Namjoon Suh, Yuning Yang, Din-Yin Hsieh et al.

We present TimeAutoDiff, a unified latent-diffusion framework for four fundamental time-series tasks: unconditional generation, missing-data imputation, forecasting, and time-varying-metadata conditional generation. The model natively supports heterogeneous features including continuous, binary, and categorical variables. We unify all tasks using a masked-modeling strategy in which a binary mask specifies which time-series cells are observed and which must be generated. TimeAutoDiff combines a lightweight variational autoencoder, which maps mixed-type features into a continuous latent sequence, with a diffusion model that learns temporal dynamics in this latent space. Two architectural choices provide strong speed and scalability benefits. The diffusion model samples an entire latent trajectory at once rather than denoising one timestep at a time, greatly reducing reverse-diffusion calls. In addition, the VAE compresses along the feature axis, enabling efficient modeling of wide tables in a low-dimensional latent space. Empirical evaluation shows that TimeAutoDiff matches or surpasses strong baselines in synthetic sequence fidelity and consistently improves imputation and forecasting performance. Metadata conditioning enables realistic scenario exploration, allowing users to edit metadata sequences and produce coherent counterfactual trajectories that preserve cross-feature dependencies. Ablation studies highlight the importance of the VAE's feature encoding and key components of the denoiser. A distance-to-closest-record audit further indicates that the model generalizes without excessive memorization. Code is available at https://github.com/namjoonsuh/TimeAutoDiff

Lan Tao, Shirong Xu, Chi-Hua Wang et al.

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.

Hengzhi He, Shirong Xu, Guang Cheng

Recent studies identified an intriguing phenomenon in recursive generative model training known as model collapse, where models trained on data generated by previous models exhibit severe performance degradation. Addressing this issue and developing more effective training strategies have become central challenges in generative model research. In this paper, we investigate this phenomenon within a novel framework, where generative models are iteratively trained on a combination of newly collected real data and synthetic data from the previous training step. To develop an optimal training strategy for integrating real and synthetic data, we evaluate the performance of a weighted training scheme in various scenarios, including Gaussian distribution estimation, generalized linear models, and nonparametric estimation. We theoretically characterize the impact of the mixing proportion and weighting scheme of synthetic data on the final model's performance. Our key finding is that, across different settings, the optimal weighting scheme under different proportions of synthetic data asymptotically follows a unified expression, revealing a fundamental trade-off between leveraging synthetic data and model performance. In some cases, the optimal weight assigned to real data corresponds to the reciprocal of the golden ratio. Finally, we validate our theoretical results on extensive simulated datasets and a real tabular dataset.

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.

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.

Shirong Xu, Jingnan Zhang, Junhui Wang

Paired comparison data, where users evaluate items in pairs, play a central role in ranking and preference learning tasks. While ordinal comparison data intuitively offer richer information than binary comparisons, this paper challenges that conventional wisdom. We propose a general parametric framework for modeling ordinal paired comparisons without ties. The model adopts a generalized additive structure, featuring a link function that quantifies the preference difference between two items and a pattern function that governs the distribution over ordinal response levels. This framework encompasses classical binary comparison models as special cases, by treating binary responses as binarized versions of ordinal data. Within this framework, we show that binarizing ordinal data can significantly improve the accuracy of ranking recovery. Specifically, we prove that under the counting algorithm, the ranking error associated with binary comparisons exhibits a faster exponential convergence rate than that of ordinal data. Furthermore, we characterize a substantial performance gap between binary and ordinal data in terms of a signal-to-noise ratio (SNR) determined by the pattern function. We identify the pattern function that minimizes the SNR and maximizes the benefit of binarization. Extensive simulations and a real application on the MovieLens dataset further corroborate our theoretical findings.

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.