Tuorui Peng | Searcharxiv

arXiv2026

Robust mean estimation under star-shaped constraints with heavy-tailed noise

We study the problem of robust mean estimation with adversarially contaminated data under star-shaped constraints in a heavy-tailed noise setting, where only a finite second moment $ \sigma ^2 $ is assumed. For a contamination level $ \varepsilon$ below some constant, we show that the minimax rate of the squared $ \ell_2 $ loss is $ \max( \delta ^{*2}, \varepsilon \sigma ^2) \wedge d^2 $ for a star-shaped set with diameter $ d $ (set $d = \infty$ if the set is unbounded), with $ \delta ^* $ determined via the local entropy $ \log M^\mathrm{ loc }(\delta ,c) $ as \begin{align*} \delta ^*:= \sup\bigg\{\delta \geq 0: N\frac{\delta ^2}{\sigma ^2}\leq \log M^\mathrm{ loc }(\delta ,c) \bigg\}, \end{align*} where $ c $ is a sufficiently large constant. Crucially, we require that the sample size satisfies $N \gtrsim \mathop{ \sup }\limits_{\delta \geq 0} \log M^\mathrm{ loc }(\delta ,c)$. We also show that the minimax rate is $ \max(\delta^{*2},\varepsilon ^2\sigma ^2) \wedge d^2 $ for known or sign-symmetric distributions, matching the rate achieved in the Gaussian case.

math.ST↗

arXiv2022

PMC-Patients: A Large-scale Dataset of Patient Summaries and Relations for Benchmarking Retrieval-based Clinical Decision Support Systems

Objective: Retrieval-based Clinical Decision Support (ReCDS) can aid clinical workflow by providing relevant literature and similar patients for a given patient. However, the development of ReCDS systems has been severely obstructed by the lack of diverse patient collections and publicly available large-scale patient-level annotation datasets. In this paper, we aim to define and benchmark two ReCDS tasks: Patient-to-Article Retrieval (ReCDS-PAR) and Patient-to-Patient Retrieval (ReCDS-PPR) using a novel dataset called PMC-Patients. Methods: We extract patient summaries from PubMed Central articles using simple heuristics and utilize the PubMed citation graph to define patient-article relevance and patient-patient similarity. We also implement and evaluate several ReCDS systems on the PMC-Patients benchmarks, including sparse retrievers, dense retrievers, and nearest neighbor retrievers. We conduct several case studies to show the clinical utility of PMC-Patients. Results: PMC-Patients contains 167k patient summaries with 3.1M patient-article relevance annotations and 293k patient-patient similarity annotations, which is the largest-scale resource for ReCDS and also one of the largest patient collections. Human evaluation and analysis show that PMC-Patients is a diverse dataset with high-quality annotations. The evaluation of various ReCDS systems shows that the PMC-Patients benchmark is challenging and calls for further research. Conclusion: We present PMC-Patients, a large-scale, diverse, and publicly available patient summary dataset with the largest-scale patient-level relation annotations. Based on PMC-Patients, we formally define two benchmark tasks for ReCDS systems and evaluate various existing retrieval methods. PMC-Patients can largely facilitate methodology research on ReCDS systems and shows real-world clinical utility.

cs.CL↗