arXiv subjects
Publications and source records attributed to Yutao Ma.
Consider the chiral non-Hermitian random matrix ensemble with parameters $n$ and $v,$ and let $(ζ_i)_{1\le i\le n}$ be its $n$ eigenvalues with positive $x$-coordinate. In this paper, we establish deviation probabilities and moderate deviation probabilities for the spectral radius $(n/(n+v))^{1/2}\max_{1\le i\le n}|ζ_i|^2,$ as well as $(n/(n+v))^{1/2}\min_{1\le i\le n}|ζ_i|^2.$
In this paper, we consider the tail probabilities of extremals of $β$-Jacobi ensemble which plays an important role in multivariate analysis. The key steps in constructing estimators rely on the rate functions of large deviations. Therefore, under specific conditions, we consider stretching and shifting transformations applied to the $β$-Jacobi ensemble to ensure that its extremals satisfy the large deviations. The estimator we construct characterize the large deviation behavior and moderate deviation behavior of extremals under different assumptions.
This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $β$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the ultra-high dimensional setting, we give an exact approximation for the tail probabilities and construct an efficient estimator for the tail probabilities. Additionally, we conduct a numerical study to evaluate the practical performance of our algorithms. The simulation results demonstrate that our method offers an efficient and accurate approach for evaluating tail probabilities in practice.
Since language models (LMs) now outperform average humans on many challenging tasks, it has become increasingly difficult to develop challenging, high-quality, and realistic evaluations. We address this issue by examining LMs' capabilities to generate code for solving real scientific research problems. Incorporating input from scientists and AI researchers in 16 diverse natural science sub-fields, including mathematics, physics, chemistry, biology, and materials science, we created a scientist-curated coding benchmark, SciCode. The problems in SciCode naturally factorize into multiple subproblems, each involving knowledge recall, reasoning, and code synthesis. In total, SciCode contains 338 subproblems decomposed from 80 challenging main problems. It offers optional descriptions specifying useful scientific background information and scientist-annotated gold-standard solutions and test cases for evaluation. Claude3.5-Sonnet, the best-performing model among those tested, can solve only 4.6% of the problems in the most realistic setting. We believe that SciCode demonstrates both contemporary LMs' progress towards becoming helpful scientific assistants and sheds light on the development and evaluation of scientific AI in the future.
We consider $β$-Jacobi ensembles with parameters $p_1, p_2\geq n.$ We prove that the empirical measure of the rescaled Jacobi ensembles converges weakly to a modified Watcher law via the spectral measure method, which revisits the weak limits obtained in \cite{MaLDPJ} while replacing the condition $βn\!>\!> \log n$ by $βn\!>\!>1.$ We also provide the central limit theorem and the large deviation for the corresponding rescaled spectral measure.
Recent years have witnessed the rapid development of service-oriented computing technologies. The boom of Web services increases software developers' selection burden in developing new service-based systems such as mashups. Timely recommending appropriate component services for developers to build new mashups has become a fundamental problem in service-oriented software engineering. Existing service recommendation approaches are mainly designed for mashup development in the single-round scenario. It is hard for them to effectively update recommendation results according to developers' requirements and behaviours (e.g. instant service selection). To address this issue, the authors propose a service bundle recommendation framework based on deep learning, DLISR, which aims to capture the interactions among the target mashup to build, selected (component) services, and the following service to recommend. Moreover, an attention mechanism is employed in DLISR to weigh selected services when recommending a candidate service. The authors also design two separate models for learning interactions from the perspectives of content and invocation history, respectively, and a hybrid model called HISR. Experiments on a real-world dataset indicate that HISR can outperform several state-of-the-art service recommendation methods to develop new mashups iteratively.
Background: Cervical cancer seriously affects the health of the female reproductive system. Optical coherence tomography (OCT) emerged as a non-invasive, high-resolution imaging technology for cervical disease detection. However, OCT image annotation is knowledge-intensive and time-consuming, which impedes the training process of deep-learning-based classification models. Purpose: This study aims to develop a computer-aided diagnosis (CADx) approach to classifying in-vivo cervical OCT images based on self-supervised learning. Methods: In addition to high-level semantic features extracted by a convolutional neural network (CNN), the proposed CADx approach leverages unlabeled cervical OCT images' texture features learned by contrastive texture learning. We conducted ten-fold cross-validation on the OCT image dataset from a multi-center clinical study on 733 patients from China. Results: In a binary classification task for detecting high-risk diseases, including high-grade squamous intraepithelial lesion and cervical cancer, our method achieved an area-under-the-curve value of 0.9798 plus or minus 0.0157 with a sensitivity of 91.17 plus or minus 4.99% and a specificity of 93.96 plus or minus 4.72% for OCT image patches; also, it outperformed two out of four medical experts on the test set. Furthermore, our method achieved a 91.53% sensitivity and 97.37% specificity on an external validation dataset containing 287 3D OCT volumes from 118 Chinese patients in a new hospital using a cross-shaped threshold voting strategy. Conclusions: The proposed contrastive-learning-based CADx method outperformed the end-to-end CNN models and provided better interpretability based on texture features, which holds great potential to be used in the clinical protocol of "see-and-treat."
Most of the existing deep learning-based sequential recommendation approaches utilize the recurrent neural network architecture or self-attention to model the sequential patterns and temporal influence among a user's historical behavior and learn the user's preference at a specific time. However, these methods have two main drawbacks. First, they focus on modeling users' dynamic states from a user-centric perspective and always neglect the dynamics of items over time. Second, most of them deal with only the first-order user-item interactions and do not consider the high-order connectivity between users and items, which has recently been proved helpful for the sequential recommendation. To address the above problems, in this article, we attempt to model user-item interactions by a bipartite graph structure and propose a new recommendation approach based on a Position-enhanced and Time-aware Graph Convolutional Network (PTGCN) for the sequential recommendation. PTGCN models the sequential patterns and temporal dynamics between user-item interactions by defining a position-enhanced and time-aware graph convolution operation and learning the dynamic representations of users and items simultaneously on the bipartite graph with a self-attention aggregator. Also, it realizes the high-order connectivity between users and items by stacking multi-layer graph convolutions. To demonstrate the effectiveness of PTGCN, we carried out a comprehensive evaluation of PTGCN on three real-world datasets of different sizes compared with a few competitive baselines. Experimental results indicate that PTGCN outperforms several state-of-the-art models in terms of two commonly-used evaluation metrics for ranking.
The bug triaging process, an essential process of assigning bug reports to the most appropriate developers, is related closely to the quality and costs of software development. As manual bug assignment is a labor-intensive task, especially for large-scale software projects, many machine-learning-based approaches have been proposed to automatically triage bug reports. Although developer collaboration networks (DCNs) are dynamic and evolving in the real-world, most automated bug triaging approaches focus on static tossing graphs at a single time slice. Also, none of the previous studies consider periodic interactions among developers. To address the problems mentioned above, in this article, we propose a novel spatial-temporal dynamic graph neural network (ST-DGNN) framework, including a joint random walk (JRWalk) mechanism and a graph recurrent convolutional neural network (GRCNN) model. In particular, JRWalk aims to sample local topological structures in a graph with two sampling strategies by considering both node importance and edge importance. GRCNN has three components with the same structure, i.e., hourly-periodic, daily-periodic, and weekly-periodic components, to learn the spatial-temporal features of dynamic DCNs. We evaluated our approach's effectiveness by comparing it with several state-of-the-art graph representation learning methods in two domain-specific tasks that belong to node classification. In the two tasks, experiments on two real-world, large-scale developer collaboration networks collected from the Eclipse and Mozilla projects indicate that the proposed approach outperforms all the baseline methods.
Next (or successive) point-of-interest (POI) recommendation has attracted increasing attention in recent years. Most of the previous studies attempted to incorporate the spatiotemporal information and sequential patterns of user check-ins into recommendation models to predict the target user's next move. However, none of these approaches utilized the social influence of each user's friends. In this study, we discuss a new topic of next POI recommendation and present a deep attentive network for social-aware next POI recommendation called DAN-SNR. In particular, the DAN-SNR makes use of the self-attention mechanism instead of the architecture of recurrent neural networks to model sequential influence and social influence in a unified manner. Moreover, we design and implement two parallel channels to capture short-term user preference and long-term user preference as well as social influence, respectively. By leveraging multi-head self-attention, the DAN-SNR can model long-range dependencies between any two historical check-ins efficiently and weigh their contributions to the next destination adaptively. Also, we carried out a comprehensive evaluation using large-scale real-world datasets collected from two popular location-based social networks, namely Gowalla and Brightkite. Experimental results indicate that the DAN-SNR outperforms seven competitive baseline approaches regarding recommendation performance and is of high efficiency among six neural-network- and attention-based methods.
We establish various bounds on the solutions to a Stein equation for Poisson approximation in Wasserstein distance with non-linear transportation costs. The proofs are a refinement of those in [Barbour and Xia (2006)] using the results in [Liu and Ma (2009)]. As a corollary, we obtain an estimate of Poisson approximation error measured in L^2-Wasserstein distance.
For stochastic reaction-diffusion equations with Lévy noises and non-Lipschitz reaction terms, we prove that $W_1H$ transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the $L^1$-metric. The proofs are based on the Galerkin approximations.
Uterine cancer, also known as endometrial cancer, can seriously affect the female reproductive organs, and histopathological image analysis is the gold standard for diagnosing endometrial cancer. However, due to the limited capability of modeling the complicated relationships between histopathological images and their interpretations, these computer-aided diagnosis (CADx) approaches based on traditional machine learning algorithms often failed to achieve satisfying results. In this study, we developed a CADx approach using a convolutional neural network (CNN) and attention mechanisms, called HIENet. Because HIENet used the attention mechanisms and feature map visualization techniques, it can provide pathologists better interpretability of diagnoses by highlighting the histopathological correlations of local (pixel-level) image features to morphological characteristics of endometrial tissue. In the ten-fold cross-validation process, the CADx approach, HIENet, achieved a 76.91 $\pm$ 1.17% (mean $\pm$ s. d.) classification accuracy for four classes of endometrial tissue, namely normal endometrium, endometrial polyp, endometrial hyperplasia, and endometrial adenocarcinoma. Also, HIENet achieved an area-under-the-curve (AUC) of 0.9579 $\pm$ 0.0103 with an 81.04 $\pm$ 3.87% sensitivity and 94.78 $\pm$ 0.87% specificity in a binary classification task that detected endometrioid adenocarcinoma (Malignant). Besides, in the external validation process, HIENet achieved an 84.50% accuracy in the four-class classification task, and it achieved an AUC of 0.9829 with a 77.97% (95% CI, 65.27%-87.71%) sensitivity and 100% (95% CI, 97.42%-100.00%) specificity. In summary, the proposed CADx approach, HIENet, outperformed three human experts and four end-to-end CNN-based classifiers on this small-scale dataset composed of 3,500 hematoxylin and eosin (H&E) images regarding overall classification performance.
Objective: Ultrahigh-resolution optical coherence microscopy (OCM) has recently demonstrated its potential for accurate diagnosis of human cervical diseases. One major challenge for clinical adoption, however, is the steep learning curve clinicians need to overcome to interpret OCM images. Developing an intelligent technique for computer-aided diagnosis (CADx) to accurately interpret OCM images will facilitate clinical adoption of the technology and improve patient care. Methods: 497 high-resolution 3-D OCM volumes (600 cross-sectional images each) were collected from 159 ex vivo specimens of 92 female patients. OCM image features were extracted using a convolutional neural network (CNN) model, concatenated with patient information (e.g., age, HPV results), and classified using a support vector machine classifier. Ten-fold cross-validations were utilized to test the performance of the CADx method in a five-class classification task and a binary classification task. Results: An 88.3 plus or minus 4.9% classification accuracy was achieved for five fine-grained classes of cervical tissue, namely normal, ectropion, low-grade and high-grade squamous intraepithelial lesions (LSIL and HSIL), and cancer. In the binary classification task (low-risk [normal, ectropion and LSIL] vs. high-risk [HSIL and cancer]), the CADx method achieved an area-under-the-curve (AUC) value of 0.959 with an 86.7 plus or minus 11.4% sensitivity and 93.5 plus or minus 3.8% specificity. Conclusion: The proposed deep-learning based CADx method outperformed three human experts. It was also able to identify morphological characteristics in OCM images that were consistent with histopathological interpretations. Significance: Label-free OCM imaging, combined with deep-learning based CADx methods, hold a great promise to be used in clinical settings for the effective screening and diagnosis of cervical diseases.
Convolutional neural networks are powerful tools for image segmentation and classification. Here, we use this method to identify and mark the heart region of Drosophila at different developmental stages in the cross-sectional images acquired by a custom optical coherence microscopy (OCM) system. With our well-trained convolutional neural network model, the heart regions through multiple heartbeat cycles can be marked with an intersection over union (IOU) of ~86%. Various morphological and dynamical cardiac parameters can be quantified accurately with automatically segmented heart regions. This study demonstrates an efficient heart segmentation method to analyze OCM images of the beating heart in Drosophila.
Let $λ$ and $μ$ be beta-Jacobi and beta-Laguerre ensembles with joint density function $f_{β, m, a_1, a_2}$ and $f_{β, m, a_1}$, respectively. Here $β>0$ and $a_1, a_2$ and $m$ satisfying . $a_1, a_2>\fracβ{2}(m-1).$ In this paper, we consider the distance between $2(a_1+a_2)λ$ and $μ$ in terms of total variation distance and Kullback-Leibler distance. Following the idea in \cite{JM2017}, we are able to prove that both the two distances go to zero once $a_1m=o(a_2)$ and not so if $\lim_{a_2\to\infty}a_1m/a_2=σ>0.$
Let $Γ_n$ be an $n\times n$ Haar-invariant orthogonal matrix. Let $ Z_n$ be the $p\times q$ upper-left submatrix of $Γ_n,$ where $p=p_n$ and $q=q_n$ are two positive integers. Let $G_n$ be a $p\times q$ matrix whose $pq$ entries are independent standard normals. In this paper we consider the distance between $\sqrt{n} Z_n$ and $ G_n$ in terms of the total variation distance, the Kullback-Leibler distance, the Hellinger distance and the Euclidean distance. We prove that each of the first three distances goes to zero as long as $pq/n$ goes to zero, and not so this rate is sharp in the sense that each distance does not go to zero if $(p, q)$ sits on the curve $pq=σn$, where $σ$ is a constant. However, it is different for the Euclidean distance, which goes to zero provided $pq^2/n$ goes to zero, and not so if $(p,q)$ sits on the curve $pq^2=σn.$ A previous work by Jiang \cite{Jiang06} shows that the total variation distance goes to zero if both $p/\sqrt{n}$ and $q/\sqrt{n}$ go to zero, and it is not true provided $p=c\sqrt{n}$ and $q=d\sqrt{n}$ with $c$ and $d$ being constants. One of the above results confirms a conjecture that the total variation distance goes to zero as long as $pq/n\to 0$ and the distance does not go to zero if $pq=σn$ for some constant $σ$.
Collaborative activities among knowledge workers such as software developers underlie the development of modern society, but the in-depth understanding of their behavioral patterns in open online communities is very challenging. The availability of large volumes of data in open-source software (OSS) repositories (e.g. bug tracking data, emails, and comments) enables us to investigate this issue in a quantitative way. In this paper, we conduct an empirical analysis of online collaborative activities closely related to assure software quality in two well-known OSS communities, namely Eclipse and Mozilla. Our main findings include two aspects: (1) developers exhibit two diametrically opposite behavioral patterns in spatial and temporal scale when they work under two different states (i.e. normal and overload), and (2) the processing times (including bug fixing times and bug tossing times) follow a stretched exponential distribution instead of the common power law distribution. Our work reveals regular patterns in human dynamics beyond online collaborative activities among skilled developers who work under different task-driven load conditions, and it could be an important supplementary to the current work on human dynamics.