arXiv subjects

Jie Min

Publications and source records attributed to Jie Min.

At least 19 recordsLinked to original sources

arXiv2026

Simplicial Volume and Scalar Curvature on Closed K\"ahler Surfaces

Let $M$ be a closed K\"ahler surface. We prove that every Riemannian metric $g$ on $M$ with $\operatorname{Sc}_g\geq-\lambda^2$, where $\lambda\geq 0$, satisfies $$ \lVert M\rVert\leq \frac{27}{2}\,\lambda^4\operatorname{vol}_g(M). $$ This proves Gromov's quantitative scalar-curvature--simplicial-volume conjecture for closed K\"ahler surfaces. We also construct infinitely many non-K\"ahler symplectic 4-manifolds of general type with positive simplicial volume for which the same estimate holds.

math.DG↗

arXiv2026

SSH-Net: A Deep Neural Network for Predicting Failure Time Distribution Functions under Competing Risks with Application to GPU Data

Competing risks are commonly observed in engineering fields and can bring challenges to time-to-event data modeling when the application scenarios are complicated. Recently, deep neural networks have received great attention for prediction with competing risks, due to their flexibility and high learning capability. However, the complexity of neural network structure brings extra difficulty in hyperparameter tuning based on different data inputs. Additionally, when an engineered system has complex physical structures with multiple hierarchical levels, treating all structural levels as a single group of inputs may fail to capture critical information. To address the issues, we propose a Structured Segmented Hazard Deep Neural Network (SSH-Net) for failure time prediction under cause-specific competing risks framework. Our approach associates neural network structure with data structures, and allows different covariate groups to impact the failure prediction through separate sub-networks. The neural network is constructed based on a cause-specific competing risks model. The SSH-Net outputs cause-specific hazard functions, and utilizes the penalized log-likelihood as the loss function. The prediction accuracy of SSH-Net is validated through simulation studies by evaluating the Brier score, the area under receiver operating characteristic curves (AUC), and the root mean square error (RMSE) of the predicted cause-specific cumulative incident function. We further demonstrate the model's ability to predict failure time distribution functions using the Titan GPU failure time data.

stat.ML↗

arXiv2025

TFCDiff: Robust ECG Denoising via Time-Frequency Complementary Diffusion

Ambulatory electrocardiogram (ECG) readings are prone to mixed noise from physical activities, including baseline wander (BW), muscle artifact (MA), and electrode motion artifact (EM). Developing a method to remove such complex noise and reconstruct high-fidelity signals is clinically valuable for diagnostic accuracy. However, denoising of multi-beat ECG segments remains understudied and poses technical challenges. To address this, we propose Time-Frequency Complementary Diffusion (TFCDiff), a novel approach that operates in the Discrete Cosine Transform (DCT) domain and uses the DCT coefficients of noisy signals as conditioning input. To refine waveform details, we incorporate Temporal Feature Enhancement Mechanism (TFEM) to reinforce temporal representations and preserve key physiological information. Comparative experiments on a synthesized dataset demonstrate that TFCDiff achieves state-of-the-art performance across five evaluation metrics. Furthermore, TFCDiff shows superior generalization on the unseen SimEMG Database, outperforming all benchmark models. Notably, TFCDiff processes raw 10-second sequences and maintains robustness under flexible random mixed noise (fRMN), enabling plug-and-play deployment in wearable ECG monitors for high-motion scenarios. Source code is available at https://github.com/Miroircivil/TFCDiff.

eess.SP↗

arXiv2025

Modeling Spatially Correlated Failure-time Data Under Two Distance Functions with an Application to Titan GPU Data

One common approach to statistical analysis of spatially correlated data relies on defining a correlation structure based solely on unknown parameters and the physical distance between the locations of observed values. However, some data have a complex spatial structure that cannot be adequately described with the physical distance alone. In this work, the spatial failure-time data of focus contains information on GPUs that are connected through a network fabric topology that differs from their physical layout and that is expected to introduce additional correlations. The proposed lifetime regression model includes random effects capturing the dependency due to physical location as well as random effects explaining the dependency due to logical connections between GPUs. The analysis of this GPU dataset serves as an example of models with multiple spatial random effects and the ideas presented can be extended to other applications with complex spatial structures. A Bayesian modeling scheme is recommended for this class of analyses. The examples in this work use the software package, Stan, to produce Markov chain Monte Carlo draws for parameter estimation. This modeling effort is validated through simulation which demonstrates accuracy in statistical inference. We also apply the developed framework to the large-scale Titan GPU failure time data.

stat.AP↗

arXiv2025

What Quality Engineers Need to Know about Degradation Models

Degradation models play a critical role in quality engineering by enabling the assessment and prediction of system reliability based on data. The objective of this paper is to provide an accessible introduction to degradation models. We explore commonly used degradation data types, including repeated measures degradation data and accelerated destructive degradation test data, and review modeling approaches such as general path models and stochastic process models. Key inference problems, including reliability estimation and prediction, are addressed. Applications across diverse fields, including material science, renewable energy, civil engineering, aerospace, and pharmaceuticals, illustrate the broad impact of degradation models in industry. We also discuss best practices for quality engineers, software implementations, and challenges in applying these models. This paper aims to provide quality engineers with a foundational understanding of degradation models, equipping them with the knowledge necessary to apply these techniques effectively in real-world scenarios.

stat.AP↗

arXiv2025

Performance Evaluation of Large Language Models in Statistical Programming

The programming capabilities of large language models (LLMs) have revolutionized automatic code generation and opened new avenues for automatic statistical analysis. However, the validity and quality of these generated codes need to be systematically evaluated before they can be widely adopted. Despite their growing prominence, a comprehensive evaluation of statistical code generated by LLMs remains scarce in the literature. In this paper, we assess the performance of LLMs, including two versions of ChatGPT and one version of Llama, in the domain of SAS programming for statistical analysis. Our study utilizes a set of statistical analysis tasks encompassing diverse statistical topics and datasets. Each task includes a problem description, dataset information, and human-verified SAS code. We conduct a comprehensive assessment of the quality of SAS code generated by LLMs through human expert evaluation based on correctness, effectiveness, readability, executability, and the accuracy of output results. The analysis of rating scores reveals that while LLMs demonstrate usefulness in generating syntactically correct code, they struggle with tasks requiring deep domain understanding and may produce redundant or incorrect results. This study offers valuable insights into the capabilities and limitations of LLMs in statistical programming, providing guidance for future advancements in AI-assisted coding systems for statistical analysis.

stat.AP↗

arXiv2025

Bridging the Data Gap in AI Reliability Research and Establishing DR-AIR, a Comprehensive Data Repository for AI Reliability

Artificial intelligence (AI) technology and systems have been advancing rapidly. However, ensuring the reliability of these systems is crucial for fostering public confidence in their use. This necessitates the modeling and analysis of reliability data specific to AI systems. A major challenge in AI reliability research, particularly for those in academia, is the lack of readily available AI reliability data. To address this gap, this paper focuses on conducting a comprehensive review of available AI reliability data and establishing DR-AIR: a data repository for AI reliability. Specifically, we introduce key measurements and data types for assessing AI reliability, along with the methodologies used to collect these data. We also provide a detailed description of the currently available datasets with illustrative examples. Furthermore, we outline the setup of the DR-AIR repository and demonstrate its practical applications. This repository provides easy access to datasets specifically curated for AI reliability research. We believe these efforts will significantly benefit the AI research community by facilitating access to valuable reliability data and promoting collaboration across various academic domains within AI. We conclude our paper with a call to action, encouraging the research community to contribute and share AI reliability data to further advance this critical field of study.

stat.AP↗

arXiv2024

Applied Statistics in the Era of Artificial Intelligence: A Review and Vision

The advent of artificial intelligence (AI) technologies has significantly changed many domains, including applied statistics. This review and vision paper explores the evolving role of applied statistics in the AI era, drawing from our experiences in engineering statistics. We begin by outlining the fundamental concepts and historical developments in applied statistics and tracing the rise of AI technologies. Subsequently, we review traditional areas of applied statistics, using examples from engineering statistics to illustrate key points. We then explore emerging areas in applied statistics, driven by recent technological advancements, highlighting examples from our recent projects. The paper discusses the symbiotic relationship between AI and applied statistics, focusing on how statistical principles can be employed to study the properties of AI models and enhance AI systems. We also examine how AI can advance applied statistics in terms of modeling and analysis. In conclusion, we reflect on the future role of statisticians. Our paper aims to shed light on the transformative impact of AI on applied statistics and inspire further exploration in this dynamic field.

stat.AP↗

arXiv2024

VISTA: Enhancing Long-Duration and High-Resolution Video Understanding by Video Spatiotemporal Augmentation

Current large multimodal models (LMMs) face significant challenges in processing and comprehending long-duration or high-resolution videos, which is mainly due to the lack of high-quality datasets. To address this issue from a data-centric perspective, we propose VISTA, a simple yet effective Video Spatiotemporal Augmentation framework that synthesizes long-duration and high-resolution video instruction-following pairs from existing video-caption datasets. VISTA spatially and temporally combines videos to create new synthetic videos with extended durations and enhanced resolutions, and subsequently produces question-answer pairs pertaining to these newly synthesized videos. Based on this paradigm, we develop seven video augmentation methods and curate VISTA-400K, a video instruction-following dataset aimed at enhancing long-duration and high-resolution video understanding. Finetuning various video LMMs on our data resulted in an average improvement of 3.3% across four challenging benchmarks for long-video understanding. Furthermore, we introduce the first comprehensive high-resolution video understanding benchmark HRVideoBench, on which our finetuned models achieve a 6.5% performance gain. These results highlight the effectiveness of our framework.

cs.CV↗

arXiv2024

The contact cut graph and a Weinstein $\mathcal{L}$-invariant

We define and study the contact cut graph which is an analogue of Hatcher and Thurston's cut graph for contact geometry, inspired by contact Heegaard splittings. We show how oriented paths in the contact cut graph correspond to Lefschetz fibrations and multisection with divides diagrams. We also give a correspondence for achiral Lefschetz fibrations. We use these correspondences to define a new invariant of Weinstein domains, the Weinstein $\mathcal{L}$-invariant, that is a symplectic analogue of the Kirby-Thompson's $\mathcal{L}$-invariant of smooth $4$-manifolds. We discuss the relation of Lefschetz stabilization with the Weinstein $\mathcal{L}$-invariant. We present topological and geometric constraints of Weinstein domains with $\mathcal{L}=0$. We also give two families of examples of multisections with divides that have arbitrarily large $\mathcal{L}$-invariant.

math.GT↗

arXiv2024

GeoDiffuser: Geometry-Based Image Editing with Diffusion Models

The success of image generative models has enabled us to build methods that can edit images based on text or other user input. However, these methods are bespoke, imprecise, require additional information, or are limited to only 2D image edits. We present GeoDiffuser, a zero-shot optimization-based method that unifies common 2D and 3D image-based object editing capabilities into a single method. Our key insight is to view image editing operations as geometric transformations. We show that these transformations can be directly incorporated into the attention layers in diffusion models to implicitly perform editing operations. Our training-free optimization method uses an objective function that seeks to preserve object style but generate plausible images, for instance with accurate lighting and shadows. It also inpaints disoccluded parts of the image where the object was originally located. Given a natural image and user input, we segment the foreground object using SAM and estimate a corresponding transform which is used by our optimization approach for editing. GeoDiffuser can perform common 2D and 3D edits like object translation, 3D rotation, and removal. We present quantitative results, including a perceptual study, that shows how our approach is better than existing methods. Visit https://ivl.cs.brown.edu/research/geodiffuser.html for more information.

cs.CV↗

arXiv2024

Multivariate Functional Clustering with Variable Selection and Application to Sensor Data from Engineering Systems

Multi-sensor data that track system operating behaviors are widely available nowadays from various engineering systems. Measurements from each sensor over time form a curve and can be viewed as functional data. Clustering of these multivariate functional curves is important for studying the operating patterns of systems. One complication in such applications is the possible presence of sensors whose data do not contain relevant information. Hence it is desirable for the clustering method to equip with an automatic sensor selection procedure. Motivated by a real engineering application, we propose a functional data clustering method that simultaneously removes noninformative sensors and groups functional curves into clusters using informative sensors. Functional principal component analysis is used to transform multivariate functional data into a coefficient matrix for data reduction. We then model the transformed data by a Gaussian mixture distribution to perform model-based clustering with variable selection. Three types of penalties, the individual, variable, and group penalties, are considered to achieve automatic variable selection. Extensive simulations are conducted to assess the clustering and variable selection performance of the proposed methods. The application of the proposed methods to an engineering system with multiple sensors shows the promise of the methods and reveals interesting patterns in the sensor data.

stat.ME↗

arXiv2023

A Spatially Correlated Competing Risks Time-to-Event Model for Supercomputer GPU Failure Data

Graphics processing units (GPUs) are widely used in many high-performance computing (HPC) applications such as imaging/video processing and training deep-learning models in artificial intelligence. GPUs installed in HPC systems are often heavily used, and GPU failures occur during HPC system operations. Thus, the reliability of GPUs is of interest for the overall reliability of HPC systems. The Cray XK7 Titan supercomputer was one of the top ten supercomputers in the world. The failure event times of more than 30,000 GPUs in Titan were recorded and previous data analysis suggested that the failure time of a GPU may be affected by the GPU's connectivity location inside the supercomputer among other factors. In this paper, we conduct in-depth statistical modeling of GPU failure times to study the effect of location on GPU failures under competing risks with covariates and spatially correlated random effects. In particular, two major failure types of GPUs in Titan are considered. The connectivity locations of cabinets are modeled as spatially correlated random effects, and the positions of GPUs inside each cabinet are treated as covariates. A Bayesian framework is used for statistical inference. We also compare different methods of estimation such as the maximum likelihood, which is implemented via an expectation-maximization algorithm. Our results provide interesting insights into GPU failures in HPC systems.

stat.AP↗

arXiv2023

Almost toric presentations of symplectic log Calabi-Yau pairs

It is known that the union of fibers over elliptic singularities of an almost toric fibered (ATF) closed symplectic four-manifold forms a symplectic log Calabi-Yau (LCY) divisor. In this paper, we show the converse: any symplectic LCY divisor can be realized as the boundary divisor of an ATF. For divisors in elliptic ruled surfaces, this realization occurs over the M\"obius strip; for divisors in rational surfaces, the realization occurs over the disk and becomes canonical once we choose an additional datum, called the framing, on the space of LCYs in rational surfaces. The construction for rational surfaces is achieved by considering the symplectic analogue of the toric model used in algebraic geometry, which motivates the introduction of a new combinatorial object that we call the bitten Delzant polygon.

math.SG↗

arXiv2022

Enumerative aspect of symplectic log Calabi-Yau divisors and almost toric fibrations

In this paper we are interested in the isotopy classes of symplectic log Calabi-Yau divisors in a fixed symplectic rational surface. We give several equivalent definitions and prove the stability, finiteness and rigidity results. Motivated by the problem of counting toric actions, we obtain a general counting formula of symplectic log Calabi-Yau divisors in a restrictive region of $c_1$-nef cone. A detailed count in the case of 2- and 3-point blow-ups of complex projective space for all symplectic forms is also given. In our framework the complexity of the combinatorics of analyzing Delzant polygons is reduced to the arrangement of homology classes. Then we study its relation with almost toric fibrations. We raise the problem of realizing all symplectic log Calabi-Yau divisors by some almost toric fibrations and verify it together with another conjecture of Symington in a special region.

math.SG↗

arXiv2022

Perpetual maintenance of machines with different urgency requirements

A garden $G$ is populated by $n\ge 1$ bamboos $b_1, b_2, ..., b_n$ with the respective daily growth rates $h_1 \ge h_2 \ge \dots \ge h_n$. It is assumed that the initial heights of bamboos are zero. The robotic gardener maintaining the garden regularly attends bamboos and trims them to height zero according to some schedule. The Bamboo Garden Trimming Problem (BGT) is to design a perpetual schedule of cuts to maintain the elevation of the bamboo garden as low as possible. The bamboo garden is a metaphor for a collection of machines which have to be serviced, with different frequencies, by a robot which can service only one machine at a time. The objective is to design a perpetual schedule of servicing which minimizes the maximum (weighted) waiting time for servicing. We consider two variants of BGT. In discrete BGT the robot trims only one bamboo at the end of each day. In continuous BGT the bamboos can be cut at any time, however, the robot needs time to move from one bamboo to the next. For discrete BGT, we show tighter approximation algorithms for the case when the growth rates are balanced and for the general case. The former algorithm settles one of the conjectures about the Pinwheel problem. The general approximation algorithm improves on the previous best approximation ratio. For continuous BGT, we propose approximation algorithms which achieve approximation ratios $O(\log \lceil h_1/h_n\rceil)$ and $O(\log n)$.

cs.DS↗

arXiv2022

Circular spherical divisors and their contact topology

This paper investigates the symplectic and contact topology associated to circular spherical divisors. We classify, up to toric equivalence, all concave circular spherical divisors $ D $ that can be embedded symplectically into a closed symplectic 4-manifold and show they are all realized as symplectic log Calabi-Yau pairs if their complements are minimal. We then determine the Stein fillability and rational homology type of all minimal symplectic fillings for the boundary torus bundles of such $D$. When $ D $ is anticanonical and convex, we give explicit betti number bounds for Stein fillings of its boundary contact torus bundle.

math.SG↗

arXiv2021

Statistical Perspectives on Reliability of Artificial Intelligence Systems

Artificial intelligence (AI) systems have become increasingly popular in many areas. Nevertheless, AI technologies are still in their developing stages, and many issues need to be addressed. Among those, the reliability of AI systems needs to be demonstrated so that the AI systems can be used with confidence by the general public. In this paper, we provide statistical perspectives on the reliability of AI systems. Different from other considerations, the reliability of AI systems focuses on the time dimension. That is, the system can perform its designed functionality for the intended period. We introduce a so-called SMART statistical framework for AI reliability research, which includes five components: Structure of the system, Metrics of reliability, Analysis of failure causes, Reliability assessment, and Test planning. We review traditional methods in reliability data analysis and software reliability, and discuss how those existing methods can be transformed for reliability modeling and assessment of AI systems. We also describe recent developments in modeling and analysis of AI reliability and outline statistical research challenges in this area, including out-of-distribution detection, the effect of the training set, adversarial attacks, model accuracy, and uncertainty quantification, and discuss how those topics can be related to AI reliability, with illustrative examples. Finally, we discuss data collection and test planning for AI reliability assessment and how to improve system designs for higher AI reliability. The paper closes with some concluding remarks.

cs.SE↗