Zhiyue Zhang

Wenjie Liu, Siyuan Lang, Zhiyue Zhang

For Stefan problems, characterized by moving boundaries and discontinuous coefficients due to phase changes, the inherent nonconvexity of the objective functional frequently causes optimization difficulty in randomized neural network approximations; to address this, we propose a Perturbation-Correction Extreme Learning Machine (PCELM) framework, built upon the extreme learning machine framework. This method first establishes a basic approximation during an initialization step by minimizing the original nonconvex residual, typically achieving only moderate accuracy, and then, in a subsequent correction step, determines a correction term by solving a subproblem based on a perturbation expansion around this basic approximation, thereby transforming it into a convex optimization problem for the output coefficients that ensures rapid convergence. We further provide a rigorous a convexity analysis, demonstrating that PCELM method solves a convex sub-problem. Numerical experiments on various Stefan problems, including multi-phase and multi-dimensional Stefan problems, confirm that the proposed PCELM method successfully overcomes optimization plateaus, with the correction step consistently delivering a significant improvement of 2-6 orders of magnitude in the relative L2 accuracy.

Yao Zhao, Zhiyue Zhang, Yanxun Xu

Clinical evidence synthesis requires identifying relevant trials from large registries and aggregating results that account for population differences. While recent LLM-based approaches have automated components of systematic review, they do not support end-to-end evidence synthesis. Moreover, conventional meta-analysis weights studies by statistical precision without considering clinical compatibility reflected in eligibility criteria. We propose EligMeta, an agentic framework that integrates automated trial discovery with eligibility-aware meta-analysis, translating natural-language queries into reproducible trial selection and incorporating eligibility alignment into study weighting to produce cohort-specific pooled estimates. EligMeta employs a hybrid architecture separating LLM-based reasoning from deterministic execution: LLMs generate interpretable rules from natural-language queries and perform schema-constrained parsing of trial metadata, while all logical operations, weight computations, and statistical pooling are executed deterministically to ensure reproducibility. The framework structures eligibility criteria and computes similarity-based study weights reflecting population alignment between target and comparator trials. In a gastric cancer landscape analysis, EligMeta reduced 4,044 candidate trials to 39 clinically relevant studies through rule-based filtering, recovering all 13 guideline-cited trials. In an olaparib adverse events meta-analysis across four trials, eligibility-aware weighting shifted the pooled risk ratio from 2.18 (95% CI: 1.71-2.79) under conventional Mantel-Haenszel estimation to 1.97 (95% CI: 1.76-2.20), demonstrating quantifiable impact of incorporating eligibility alignment. EligMeta bridges automated trial discovery with eligibility-aware meta-analysis, providing a scalable and reproducible framework for evidence synthesis in precision medicine.

Yao Zhao, Yantian Ding, Zhiyue Zhang et al.

Retrieval Augmented Generation (RAG) systems often struggle with domain-specific knowledge due to performance deterioration of pre-trained embeddings and prohibitive computational costs of large language model (LLM)-based retrievers. While fine-tuning data augmentation embedding models offers a promising direction, its effectiveness is limited by the need for high-quality training data and reliable chunking strategies that preserve contextual integrity. We propose LMAR (Language Model Augmented Retriever), a model-agnostic framework that addresses these challenges by combining LLM-guided data synthesis with contrastive embedding adaptation and efficient text clustering. LMAR consists of a two-stage pipeline: (1) Triplet sampling and synthetic data augmentation, where LLMs act as both labeler and validator to ensure high-fidelity supervision throughout the pipeline. Experimental results across multiple domain-specific benchmark datasets demonstrate that LMAR outperforms multiple baseline models, while maintaining moderate hardware requirements and low latency. Its model-agnostic nature further enables seamless integration with emerging RAG architectures and text embedding models, ensuring continual improvements without redesigning the pipeline. These results highlight LMAR as a practical and cost-effective solution for scalable domain-specific adaptation.

Zhiyue Zhang, Yao Zhao, Yanxun Xu

In applications such as biomedical studies, epidemiology, and social sciences, recurrent events often co-occur with longitudinal measurements and a terminal event, such as death. Therefore, jointly modeling longitudinal measurements, recurrent events, and survival data while accounting for their dependencies is critical. While joint models for the three components exist in statistical literature, many of these approaches are limited by heavy parametric assumptions and scalability issues. Recently, incorporating deep learning techniques into joint modeling has shown promising results. However, current methods only address joint modeling of longitudinal measurements at regularly-spaced observation times and survival events, neglecting recurrent events. In this paper, we develop TransformerLSR, a flexible transformer-based deep modeling and inference framework to jointly model all three components simultaneously. TransformerLSR integrates deep temporal point processes into the joint modeling framework, treating recurrent and terminal events as two competing processes dependent on past longitudinal measurements and recurrent event times. Additionally, TransformerLSR introduces a novel trajectory representation and model architecture to potentially incorporate a priori knowledge of known latent structures among concurrent longitudinal variables. We demonstrate the effectiveness and necessity of TransformerLSR through simulation studies and analyzing a real-world medical dataset on patients after kidney transplantation.

Mao Hong, Zhiyue Zhang, Yue Wu et al.

Model-based offline reinforcement learning methods (RL) have achieved state-of-the-art performance in many decision-making problems thanks to their sample efficiency and generalizability. Despite these advancements, existing model-based offline RL approaches either focus on theoretical studies without developing practical algorithms or rely on a restricted parametric policy space, thus not fully leveraging the advantages of an unrestricted policy space inherent to model-based methods. To address this limitation, we develop MoMA, a model-based mirror ascent algorithm with general function approximations under partial coverage of offline data. MoMA distinguishes itself from existing literature by employing an unrestricted policy class. In each iteration, MoMA conservatively estimates the value function by a minimization procedure within a confidence set of transition models in the policy evaluation step, then updates the policy with general function approximations instead of commonly-used parametric policy classes in the policy improvement step. Under some mild assumptions, we establish theoretical guarantees of MoMA by proving an upper bound on the suboptimality of the returned policy. We also provide a practically implementable, approximate version of the algorithm. The effectiveness of MoMA is demonstrated via numerical studies.

Zhiyue Zhang, Kenneth Lange, Jason Xu

Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters. This has motivated the development of sparse clustering techniques that typically rely on k-means within outer algorithms of high computational complexity. Current techniques also require careful tuning of shrinkage parameters, further limiting their scalability. In this paper, we propose a novel framework for sparse k-means clustering that is intuitive, simple to implement, and competitive with state-of-the-art algorithms. We show that our algorithm enjoys consistency and convergence guarantees. Our core method readily generalizes to several task-specific algorithms such as clustering on subsets of attributes and in partially observed data settings. We showcase these contributions thoroughly via simulated experiments and real data benchmarks, including a case study on protein expression in trisomic mice.