arXiv subjects

Jiaye Chen

Publications and source records attributed to Jiaye Chen.

4 recordsLinked to original sources

arXiv2026

Marginal Coordinate Test for Fr\'echet Regression with Random Objects

We develop a marginal coordinate test for regression with Euclidean predictors and a random-object response in a separable metric space. The goal is to test whether a predictor provides additional information about the response conditional on the remaining predictors. In a semi-supervised design, an unlabeled sample is used to estimate predictor conditional means, while an independent labeled sample is reserved for inference. The resulting residuals are combined with a product-space kernel to form a kernel conditional mean dependence (KCMD) U-statistic without requiring a response residual. The primary identity-based test targets a necessary conditional mean restriction, while a multiple-transformation extension probes broader alternatives. We establish a weighted centered chi-square null limit, wild bootstrap validity, consistency against fixed detectable alternatives, and local power under mean-element alternatives. For simultaneous inference, truncated p-to-e calibration combined with e-BH provides asymptotic false discovery rate control under general dependence. Simulations with Euclidean and non-Euclidean responses, together with a New York City taxi-flow analysis, illustrate the method.

stat.ME↗

arXiv2026

DRBA: Dynamic Robotic Balance Assistant -- An assist-as-needed gait and balance rehabilitation robot for versatile training

The decline of human balance control due to aging and pathological conditions increases fall risk, a major concern in geriatric care and rehabilitation. Gait training is essential for balance recovery, enhancing walking ability and postural control. However, existing overground robotic gait trainers have limitations: body weight support systems are bulky and impractical for daily use, while end-effector-based systems often compromise transparency, altering natural gait dynamics. This paper presents the Dynamic Robotic Balance Assistant (DRBA), a novel gait trainer providing assist-as-needed body weight and balance support for various training scenarios. DRBA integrates a 3-degree-of-freedom (3-DoF) robotic arm for pelvic support with flexible motion, a compact sit-to-stand assistance module, and user-following and fall detection algorithms to ensure minimal interference and responsive support. Experimental results demonstrated high transparency, with minimal impact on natural gait dynamics. A patient trial with nine elderly patients with varying medical conditions and balance impairments (ranging from severe to mild) further validated DRBA's effectiveness. The results showed that DRBA-assisted training increased step length and walking speed compared to therapist-assisted gait training. Additionally, DRBA enabled users to perform tasks beyond their unaided ability, expanding rehabilitation possibilities. These findings highlight DRBA's potential to enhance rehabilitation outcomes by facilitating higher training intensity and enabling task-oriented exercises.

cs.RO↗

arXiv2025

Abstract questionnaires and FS-decision digraphs

A questionnaire is a sequence of multiple choice questions aiming to collect data on a population. We define an abstract questionnaire as an ordered pair $(N,{\cal M})$, where $N$ is a positive integer and ${\cal M}=(m_0,m_1,\ldots,m_{N-1})$ is an $N$-tuple of positive integers, with $m_i$, for $i \in \{0, 1, \ldots, N-1 \}$, as the number of possible answers to question $i$. An abstract questionnaire may be endowed with a skip-list (which tells us which questions to skip based on the sequence of answers to the earlier questions) and a flag-set (which tells us which sequences of answers are of special interest). An FS-decision tree is a decision tree of an abstract questionnaire that also incorporates the information contained in the skip-list and flag-set. The main objective of this paper is to represent the abstract questionnaire using a directed graph, which we call an FS-decision digraph, that contains the full information of an FS-decision tree, but is in general much more concise. We present an algorithm for constructing a fully reduced FS-decision digraph, and develop the theory that supports it. In addition, we show how to generate all possible orderings of the questions in an abstract questionnaire that respect a given precedence relation.

math.CO↗

arXiv2012

Clustering to Maximize the Ratio of Split to Diameter

Given a weighted and complete graph G = (V, E), V denotes the set of n objects to be clustered, and the weight d(u, v) associated with an edge (u, v) belonging to E denotes the dissimilarity between objects u and v. The diameter of a cluster is the maximum dissimilarity between pairs of objects in the cluster, and the split of a cluster is the minimum dissimilarity between objects within the cluster and objects outside the cluster. In this paper, we propose a new criterion for measuring the goodness of clusters: the ratio of the minimum split to the maximum diameter, and the objective is to maximize the ratio. For k = 2, we present an exact algorithm. For k >= 3, we prove that the problem is NP-hard and present a factor of 2 approximation algorithm on the precondition that the weights associated with E satisfy the triangle inequality. The worst-case runtime of both algorithms is O(n^3). We compare the proposed algorithms with the Normalized Cut by applying them to image segmentation. The experimental results on both natural and synthetic images demonstrate the effectiveness of the proposed algorithms.

cs.DS↗