Shijie Zhong

Yufei Li, Yisen Gao, Jiaxuan Xiong et al.

Data critical to real-world decision-making is increasingly found within organizations. Such data is heterogeneous, constantly evolving, and only imperfectly captured. However, current data management systems remain largely passive, retrieving what is explicitly stored while offering limited support for uncovering implicit structure or reasoning under noise, incompleteness, and continuous updates. We argue that next-generation data management requires neural capabilities, which can uncover complex latent relationships, distinguish reliable signals from noise, and remain consistent as the underlying data state evolves. To support this direction, we introduce NGDBench, a benchmark across five domains that unifies structured and unstructured sources. NGDBench adopts a graph view because graphs provide a flexible abstraction for modeling complex systems, capturing latent relationships, and subsuming structured formats such as relational tables. Each instance pairs a clean latent graph with a realistically perturbed observed graph. NGDBench supports full Cypher queries and dynamic data management operations. Evaluations of state-of-the-art Text-to-Cypher by LLMs and GraphRAG pipelines reveal that current neural query methods remain sensitive to noise and struggle with dynamic state tracking, highlighting the need for resilient, inference-capable data management. Our code is available at https://github.com/HKUST-KnowComp/NGDBench.

Shijie Zhong, Jiangfeng Fu

In uncertainty quantification, evaluating sensitivity measures under specific conditions (i.e., conditional Sobol' indices) is essential for systems with parameterized responses, such as spatial fields or varying operating conditions. Traditional approaches often rely on point-wise modeling, which is computationally expensive and may lack consistency across the parameter space. This paper demonstrates that for a pre-trained global Polynomial Chaos Expansion (PCE) model, the analytical conditional Sobol' indices are inherently embedded within its basis functions. By leveraging the tensor-product property of PCE bases, we reformulate the global expansion into a set of analytical coefficient fields that depend on the conditioning variables. Based on the preservation of orthogonality under conditional probability measures, we derive closed-form expressions for conditional variances and Sobol' indices. This framework bypasses the need for repetitive modeling or additional sampling, transforming conditional sensitivity analysis into a purely algebraic post-processing step. Numerical benchmarks indicate that the proposed method ensures physical coherence and offers superior numerical robustness and computational efficiency compared to conventional point-wise approaches.

Shijie Zhong, Jiangfeng Fu, Yikun Yang

The maximum mean discrepancy (MMD) is a kernel-based nonparametric statistic for two-sample testing, whose inferential accuracy depends critically on variance characterization. Existing work provides various finite-sample estimators of the MMD variance, often differing under the null and alternative hypotheses and across balanced or imbalanced sampling schemes. In this paper, we study the variance of the MMD statistic through its U-statistic representation and Hoeffding decomposition, and establish a unified finite-sample characterization covering different hypotheses and sample configurations. Building on this analysis, we propose an exact acceleration method for the univariate case under the Laplacian kernel, which reduces the overall computational complexity from $\mathcal O(n^2)$ to $\mathcal O(n \log n)$.

Shijie Zhong, Wanggang Shen, Tommie Catanach et al.

Optimal experimental design (OED) provides a systematic approach to quantify and maximize the value of experimental data. Under a Bayesian approach, conventional OED maximizes the expected information gain (EIG) on model parameters. However, we are often interested in not the parameters themselves, but predictive quantities of interest (QoIs) that depend on the parameters in a nonlinear manner. We present a computational framework of predictive goal-oriented OED (GO-OED) suitable for nonlinear observation and prediction models, which seeks the experimental design providing the greatest EIG on the QoIs. In particular, we propose a nested Monte Carlo estimator for the QoI EIG, featuring Markov chain Monte Carlo for posterior sampling and kernel density estimation for evaluating the posterior-predictive density and its Kullback-Leibler divergence from the prior-predictive. The GO-OED design is then found by maximizing the EIG over the design space using Bayesian optimization. We demonstrate the effectiveness of the overall nonlinear GO-OED method, and illustrate its differences versus conventional non-GO-OED, through various test problems and an application of sensor placement for source inversion in a convection-diffusion field.