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Jingru Zhang

Publications and source records attributed to Jingru Zhang.

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The Bichromatic Two-Center Problem on Graphs

In this paper, we study the (weighted) bichromatic two-center problem on graphs. The input consists of a graph $G$ of $n$ (weighted) vertices and $m$ edges, and a set $\mathcal{P}$ of pairs of distinct vertices, where no vertex appears in more than one pair. The problem aims to find two points (i.e., centers) on $G$ by assigning vertices of each pair to different centers so as to minimize the maximum (weighted) distance of vertices to their assigned centers (so that the graph can be bi-colored with this goal). To the best of our knowledge, this problem has not been studied on graphs, including tree graphs. In this paper, we propose an $O(m^2n\log n\log mn)$ algorithm for solving the problem on an undirected graph provided with the distance matrix, an $O(n\log n)$-time algorithm for the problem on trees, and a linear-time approach for the unweighted tree version.

cs.DS

Change-Point Detection With Multivariate Repeated Measures

Graph-based methods have shown particular strengths in change-point detection (CPD) tasks for high-dimensional nonparametric settings. However, existing CPD research has rarely addressed data with repeated measurements or local group structures. A common treatment is to average repeated measurements, which can result in the loss of important within-individual information. In this paper, we propose a new graph-based method for detecting change-points in data with repeated measurements or local structures by incorporating both within-individual and between-individual information. Analytical approximations to the significance of the proposed statistics are derived, enabling efficient computation of p-values for the combined test statistic. We also establish consistency of the proposed test and the estimated change-point location. The proposed method effectively detects change-points across a wide range of alternatives, particularly when within-individual differences are present. The new method is illustrated through an analysis of the New York City taxi dataset.

stat.ME

Externally Validated Breast Ultrasound Segmentation via Multi-task Learning with BI-RADS-Consistent Morphological Priors

External validation of breast ultrasound segmentation models remains limited because internal train--test splits do not capture domain shifts across imaging systems, acquisition protocols, and patient populations. We introduce a novel multi-task framework for breast ultrasound segmentation and malignancy classification. Its central methodological advance is a differentiable morphology-to-malignancy bridge: lesion area, boundary roughness, compactness, and texture are computed from the predicted soft segmentation mask, aggregated with learned weights into a morphology-based malignancy score, and constrained to agree with the image-level classifier. To our knowledge, this is the first breast ultrasound framework to use BI-RADS-inspired morphology derived from its own soft segmentation output as an end-to-end consistency target for malignancy classification. It is also the first 2D B-mode multi-task study to report every directed external transfer among four independent datasets: training on each dataset and testing on the other three yields 12 source--target pairs, assessed with single models and five-fold ensembles. In matched comparisons across all pairs, the proposed single-model configuration outperforms dedicated single-task baselines in segmentation (DC: 0.764 vs. 0.740) and malignancy classification (AUC: 0.818 vs. 0.791). The ensemble achieves a mean external DC of 0.786 and is competitive with SAM-based segmentation methods using an EfficientNet-B7 encoder while also predicting malignancy. The learned morphology weights retain the same ordering across all four datasets, with boundary roughness receiving the greatest weight. These results establish the first complete four-dataset directed benchmark for joint 2D breast ultrasound segmentation and malignancy classification and demonstrate that clinically grounded morphological consistency improves both tasks under domain shift.

cs.CV

The k-Center Problem of Uncertain Points on Graphs

In this paper, we study the $k$-center problem of uncertain points on a graph. Given are an undirected graph $G = (V, E)$ and a set $\mathcal{P}$ of $n$ uncertain points where each uncertain point with a non-negative weight has $m$ possible locations on $G$ each associated with a probability. The problem aims to find $k$ centers (points) on $G$ so as to minimize the maximum weighted expected distance of uncertain points to their expected closest centers. No previous work exist for the $k$-center problem of uncertain points on undirected graphs. We propose exact algorithms that solve respectively the case of $k=2$ in $O(|E|^2m^2n\log |E|mn\log mn )$ time and the problem with $k\geq 3$ in $O(\min\{|E|^km^kn^{k+1}k\log |E|mn\log m, |E|^kn^\frac{k}{2}m^\frac{k^2}{2}\log |E|mn\})$ time, provided with the distance matrix of $G$. In addition, an $O(|E|mn\log mn)$-time algorithmic approach is given for the one-center case.

cs.DS

A Generalized Fréchet Test for Object Data with Unequal Repeated Measurements

Advancements in data collection have led to increasingly common repeated observations with complex structures in biomedical studies. Treating these observations as random objects, rather than summarizing features as vectors, avoids feature extraction and better reflects the data's nature. Examples include repeatedly measured activity intensity distributions in physical activity analysis and brain networks in neuroimaging. Testing whether these repeated random objects differ across groups is fundamentally important; however, traditional statistical tests often face challenges due to the non-Euclidean nature of metric spaces, dependencies from repeated measurements, and the unequal number of repeated measures. By defining within-subject variability using pairwise distances between repeated measures and extending Fréchet analysis of variance, we develop a generalized Fréchet test for exchangeable repeated random objects, applicable to general metric space-valued data with unequal numbers of repeated measures. The proposed test can simultaneously detect differences in location, scale, and within-subject variability. We derive the asymptotic distribution of the test statistic, which follows a weighted chi-squared distribution. Simulations demonstrate that the proposed test performs well across different types of random objects. We illustrate its effectiveness through applications to physical activity data and resting-state functional magnetic resonance imaging data.

stat.ME

The Two-Center Problem of Uncertain Points on Cactus Graphs

We study the two-center problem on cactus graphs in facility locations, which aims to place two facilities on the graph network to serve customers in order to minimize the maximum transportation cost. In our problem, the location of each customer is uncertain and may appear at $O(m)$ points on the network with probabilities. More specifically, given are a cactus graph $G$ and a set $\calP$ of $n$ (weighted) uncertain points where every uncertain point has $O(m)$ possible locations on $G$ each associated with a probability and is of a non-negative weight. The problem aims to compute two centers (points) on $G$ so that the maximum (weighted) expected distance of the $n$ uncertain points to their own expected closest center is minimized. No previous algorithms are known for this problem. In this paper, we present the first algorithm for this problem and it solves the problem in $O(|G|+ m^{2}n^{2}\log mn)$ time.

cs.DS

The Connected k-Vertex One-Center Problem on Graphs

We consider a generalized version of the (weighted) one-center problem on graphs. Given an undirected graph $G$ of $n$ vertices and $m$ edges and a positive integer $k\leq n$, the problem aims to find a point in $G$ so that the maximum (weighted) distance from it to $k$ connected vertices in its shortest path tree(s) is minimized. No previous work has been proposed for this problem except for the case $k=n$, that is, the classical graph one-center problem. In this paper, an $O(mn\log n\log mn + m^2\log n\log mn)$-time algorithm is proposed for the weighted case, and an $O(mn\log n)$-time algorithm is presented for the unweighted case, provided that the distance matrix for $G$ is given. When $G$ is a tree graph, we propose an algorithm that solves the weighted case in $O(n\log^2 n\log k)$ time with no given distance matrix, and improve it to $O(n\log^2 n)$ for the unweighted case.

cs.DS

The Two-Center Problem of Uncertain Points on Trees

In this paper, we consider the (weighted) two-center problem of uncertain points on a tree. Given are a tree $T$ and a set $\calP$ of $n$ (weighted) uncertain points each of which has $m$ possible locations on $T$ associated with probabilities. The goal is to compute two points on $T$, i.e., two centers with respect to $\calP$, so that the maximum (weighted) expected distance of $n$ uncertain points to their own expected closest center is minimized. This problem can be solved in $O(|T|+ n^{2}\log n\log mn + mn\log^2 mn \log n)$ time by the algorithm for the general $k$-center problem. In this paper, we give a more efficient and simple algorithm that solves this problem in $O(|T| + mn\log mn)$ time.

cs.DS

Computing the Center of Uncertain Points on Cactus Graphs

In this paper, we consider the (weighted) one-center problem of uncertain points on a cactus graph. Given are a cactus graph $G$ and a set of $n$ uncertain points. Each uncertain point has $m$ possible locations on $G$ with probabilities and a non-negative weight. The (weighted) one-center problem aims to compute a point (the center) $x^*$ on $G$ to minimize the maximum (weighted) expected distance from $x^*$ to all uncertain points. No previous algorithm is known for this problem. In this paper, we propose an $O(|G| + mn\log mn)$-time algorithm for solving it. Since the input is $O(|G|+mn)$, our algorithm is almost optimal.

cs.DS

EarCough: Enabling Continuous Subject Cough Event Detection on Hearables

Cough monitoring can enable new individual pulmonary health applications. Subject cough event detection is the foundation for continuous cough monitoring. Recently, the rapid growth in smart hearables has opened new opportunities for such needs. This paper proposes EarCough, which enables continuous subject cough event detection on edge computing hearables by leveraging the always-on active noise cancellation (ANC) microphones. Specifically, we proposed a lightweight end-to-end neural network model -- EarCoughNet. To evaluate the effectiveness of our method, we constructed a synchronous motion and audio dataset through a user study. Results show that EarCough achieved an accuracy of 95.4% and an F1-score of 92.9% with a space requirement of only 385 kB. We envision EarCough as a low-cost add-on for future hearables to enable continuous subject cough event detection.

cs.SD

Mediation analysis with densities as mediators with an application to iCOMPARE trial

Physical activity has long been shown to be associated with biological and physiological performance and risk of diseases. It is of great interest to assess whether the effect of an exposure or intervention on an outcome is mediated through physical activity measured by modern wearable devices such as actigraphy. However, existing methods for mediation analysis focus almost exclusively on mediation variable that is in the Euclidean space, which cannot be applied directly to the actigraphy data of physical activity. Such data is best summarized in the form of an histogram or density. In this paper, we extend the structural equation models (SEMs) to the settings where a density is treated as the mediator to study the indirect mediation effect of physical activity on an outcome. We provide sufficient conditions for identifying the average causal effects of density mediator and present methods for estimating the direct and mediating effects of density on an outcome. We apply our method to the data set from the iCOMPARE trial that compares flexible duty-hour policies and standard duty-hour policies on interns' sleep related outcomes to explore the mediation effect of physical activity on the causal path between flexible duty-hour policies and sleep related outcomes.

stat.AP

Principal component analysis for high-dimensional compositional data

Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables are latent and rarely observed, and standard techniques of principal component analysis are inadequate for compositional data because of the simplex constraint. To address the challenging problem, we relate the principal subspace of the centered log-ratio compositional covariance to that of the basis covariance, and prove that the latter is approximately identifiable with the diverging dimensionality under some subspace sparsity assumption. The interesting blessing-of-dimensionality phenomenon enables us to propose the principal subspace estimation methods by using the sample centered log-ratio covariance. We also derive nonasymptotic error bounds for the subspace estimators, which exhibits a tradeoff between identification and estimation. Moreover, we develop efficient proximal alternating direction method of multipliers algorithms to solve the nonconvex and nonsmooth optimization problems. Simulation results demonstrate that the proposed methods perform as well as the oracle methods with known basis. Their usefulness is illustrated through an analysis of word usage pattern for statisticians.

stat.ME

Two-sample tests for repeated measurements of histogram objects with applications to wearable device data

Repeated observations have become increasingly common in biomedical research and longitudinal studies. For instance, wearable sensor devices are deployed to continuously track physiological and biological signals from each individual over multiple days. It remains of great interest to appropriately evaluate how the daily distribution of biosignals might differ across disease groups and demographics. Hence these data could be formulated as multivariate complex object data such as probability densities, histograms, and observations on a tree. Traditional statistical methods would often fail to apply as they are sampled from an arbitrary non-Euclidean metric space. In this paper, we propose novel non-parametric graph-based two-sample tests for object data with repeated measures. A set of test statistics are proposed to capture various possible alternatives. We derive their asymptotic null distributions under the permutation null. These tests exhibit substantial power improvements over the existing methods while controlling the type I errors under finite samples as shown through simulation studies. The proposed tests are demonstrated to provide additional insights on the location, inter- and intra-individual variability of the daily physical activity distributions in a sample of studies for mood disorders.

stat.AP

A new non-parametric test for multivariate paired data from pair matching or paired designs

In observational studies, achieving covariate balance in pair matching between treatment and control groups or exposed and unexposed groups is essential. This balance enables testing treatment effects or examining {associations between exposures and} multivariate response variables in pair-matched data. Paired design studies involve taking multiple measurements for the same subjects under different conditions. All these call for an effective test for multivariate paired data. However, current methods for assessing covariate balance in matched observational studies often ignore the paired structure, leading to reduced performance in some cases. The multivariate paired Hotelling's $T^2$ test can be used for paired data, but its power decreases rapidly as dimensions increase. To address these issues, we propose a new non-parametric test for paired data, significantly improving power across various scenarios. We also derive the test's asymptotic distribution, making it user-friendly for practical applications. Our proposed test's effectiveness is demonstrated through an analysis of real data on Alzheimer's disease research.

stat.ME

Graph-Based Two-Sample Tests for Data with Repeated Observations

In the regime of two-sample comparison, tests based on a graph constructed on observations by utilizing similarity information among them is gaining attention due to their flexibility and good performances for high-dimensional/non-Euclidean data. However, when there are repeated observations, these graph-based tests could be problematic as they are versatile to the choice of the similarity graph. We propose extended graph-based test statistics to resolve this problem. The analytic p-value approximations to these extended graph-based tests are derived to facilitate the application of these tests to large datasets. The new tests are illustrated in the analysis of a phone-call network dataset. All tests are implemented in an R package gTests.

stat.ME

An $O(n\log n)$-Time Algorithm for the k-Center Problem in Trees

We consider a classical k-center problem in trees. Let T be a tree of n vertices and every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to their closest centers is minimized. Megiddo and Tamir (SIAM J. Comput., 1983) gave an algorithm that can solve the problem in $O(n\log^2 n)$ time by using Cole's parametric search. Since then it has been open for over three decades whether the problem can be solved in $O(n\log n)$ time. In this paper, we present an $O(n\log n)$ time algorithm for the problem and thus settle the open problem affirmatively.

cs.DS

Covering Uncertain Points in a Tree

In this paper, we consider a coverage problem for uncertain points in a tree. Let T be a tree containing a set P of n (weighted) demand points, and the location of each demand point P_i\in P is uncertain but is known to appear in one of m_i points on T each associated with a probability. Given a covering range λ, the problem is to find a minimum number of points (called centers) on T to build facilities for serving (or covering) these demand points in the sense that for each uncertain point P_i\in P, the expected distance from P_i to at least one center is no more than $λ$. The problem has not been studied before. We present an O(|T|+M\log^2 M) time algorithm for the problem, where |T| is the number of vertices of T and M is the total number of locations of all uncertain points of P, i.e., M=\sum_{P_i\in P}m_i. In addition, by using this algorithm, we solve a k-center problem on T for the uncertain points of P.

cs.CG

Computing the Rectilinear Center of Uncertain Points in the Plane

In this paper, we consider the rectilinear one-center problem on uncertain points in the plane. In this problem, we are given a set $P$ of $n$ (weighted) uncertain points in the plane and each uncertain point has $m$ possible locations each associated with a probability for the point appearing at that location. The goal is to find a point $q^*$ in the plane which minimizes the maximum expected rectilinear distance from $q^*$ to all uncertain points of $P$, and $q^*$ is called a rectilinear center. We present an algorithm that solves the problem in $O(mn)$ time. Since the input size of the problem is $Θ(mn)$, our algorithm is optimal.

cs.CG