arXiv subjects

Yan Zhuang

Publications and source records attributed to Yan Zhuang.

At least 55 records · Page 3Linked to original sources

arXiv2024

Optimizing Student Ability Assessment: A Hierarchy Constraint-Aware Cognitive Diagnosis Framework for Educational Contexts

Cognitive diagnosis (CD) aims to reveal students' proficiency in specific knowledge concepts. With the increasing adoption of intelligent education applications, accurately assessing students' knowledge mastery has become an urgent challenge. Although existing cognitive diagnosis frameworks enhance diagnostic accuracy by analyzing students' explicit response records, they primarily focus on individual knowledge state, failing to adequately reflect the relative ability performance of students within hierarchies. To address this, we propose the Hierarchy Constraint-Aware Cognitive Diagnosis Framework (HCD), designed to more accurately represent student ability performance within real educational contexts. Specifically, the framework introduces a hierarchy mapping layer to identify students' levels. It then employs a hierarchy convolution-enhanced attention layer for in-depth analysis of knowledge concepts performance among students at the same level, uncovering nuanced differences. A hierarchy inter-sampling attention layer captures performance differences across hierarchies, offering a comprehensive understanding of the relationships among students' knowledge state. Finally, through personalized diagnostic enhancement, the framework integrates hierarchy constraint perception features with existing models, improving the representation of both individual and group characteristics. This approach enables precise inference of students' knowledge state. Research shows that this framework not only reasonably constrains changes in students' knowledge states to align with real educational settings, but also supports the scientific rigor and fairness of educational assessments, thereby advancing the field of cognitive diagnosis.

cs.CY↗

arXiv2024

Two-sided permutation statistics via symmetric functions

Given a permutation statistic $\operatorname{st}$, define its inverse statistic $\operatorname{ist}$ by $\operatorname{ist}(π):=\operatorname{st}(π^{-1})$. We give a general approach, based on the theory of symmetric functions, for finding the joint distribution of $\operatorname{st}_{1}$ and $\operatorname{st}_{2}$ whenever $\operatorname{st}_{1}$ and $\operatorname{st}_{2}$ are descent statistics: permutation statistics that depend only on the descent composition. We apply this method to a number of descent statistics, including the descent number, the peak number, the left peak number, the number of up-down runs, and the major index. Perhaps surprisingly, in many cases the polynomial giving the joint distribution of $\operatorname{st}_{1}$ and $\operatorname{ist}_{2}$ can be expressed as a simple sum involving products of the polynomials giving the (individual) distributions of $\operatorname{st}_{1}$ and $\operatorname{st}_{2}$. Our work leads to a rederivation of Stanley's generating function for doubly alternating permutations, as well as several conjectures concerning real-rootedness and $γ$-positivity.

math.CO↗

arXiv2024

PertEval: Unveiling Real Knowledge Capacity of LLMs with Knowledge-Invariant Perturbations

Expert-designed close-ended benchmarks are indispensable in assessing the knowledge capacity of large language models (LLMs). Despite their widespread use, concerns have mounted regarding their reliability due to limited test scenarios and an unavoidable risk of data contamination. To rectify this, we present PertEval, a toolkit devised for in-depth probing of LLMs' knowledge capacity through \textbf{knowledge-invariant perturbations}. These perturbations employ human-like restatement techniques to generate on-the-fly test samples from static benchmarks, meticulously retaining knowledge-critical content while altering irrelevant details. Our toolkit further includes a suite of \textbf{response consistency analyses} that compare performance on raw vs. perturbed test sets to precisely assess LLMs' genuine knowledge capacity. Six representative LLMs are re-evaluated using PertEval. Results reveal significantly inflated performance of the LLMs on raw benchmarks, including an absolute 25.8% overestimation for GPT-4. Additionally, through a nuanced response pattern analysis, we discover that PertEval retains LLMs' uncertainty to specious knowledge, and reveals their potential rote memorization to correct options which leads to overestimated performance. We also find that the detailed response consistency analyses by PertEval could illuminate various weaknesses in existing LLMs' knowledge mastery and guide the development of refinement. Our findings provide insights for advancing more robust and genuinely knowledgeable LLMs. Our code is available at \url{https://github.com/aigc-apps/PertEval}.

cs.CL↗

arXiv2024

Zig-zag Eulerian polynomials

For any finite partially ordered set $P$, the $P$-Eulerian polynomial is the generating function for the descent number over the set of linear extensions of $P$, and is closely related to the order polynomial of $P$ arising in the theory of $P$-partitions. Here we study the $P$-Eulerian polynomial where $P$ is a naturally labeled zig-zag poset; we call these zig-zag Eulerian polynomials. A result of Brändén implies that these polynomials are gamma-nonnegative, and hence their coefficients are symmetric and unimodal. The zig-zag Eulerian polynomials and the associated order polynomials have appeared fleetingly in the literature in a wide variety of contexts$\unicode{x2014}$e.g., in the study of polytopes, magic labelings of graphs, and Kekulé structures$\unicode{x2014}$but they do not appear to have been studied systematically. In this paper, we use a "relaxed" version of $P$-partitions to both survey and unify results. Our technique shows that the zig-zag Eulerian polynomials also capture the distribution of "big returns" over the set of (up-down) alternating permutations, as first observed by Coons and Sullivant. We develop recurrences for refined versions of the relevant generating functions, which evoke similarities to recurrences for the classical Eulerian polynomials. We conclude with a literature survey and open questions.

math.CO↗

arXiv2024

Counting pattern-avoiding permutations by big descents

A descent $k$ of a permutation $π=π_{1}π_{2}\dotsπ_{n}$ is called a big descent if $π_{k}>π_{k+1}+1$; denote the number of big descents of $π$ by $\operatorname{bdes}(π)$. We study the distribution of the $\operatorname{bdes}$ statistic over permutations avoiding prescribed sets of length-three patterns. Specifically, we classify all pattern sets $Π\subseteq\mathfrak{S}_{3}$ of size 1 and 2 into $\operatorname{bdes}$-Wilf equivalence classes, and we derive a formula for the distribution of big descents for each of these classes. Our methods include generating function techniques along with various bijections involving objects such as Dyck paths and binary words. Several future directions of research are proposed, including conjectures concerning real-rootedness, log-concavity, and Schur positivity.

math.CO↗

arXiv2024

MRISegmentator-Abdomen: A Fully Automated Multi-Organ and Structure Segmentation Tool for T1-weighted Abdominal MRI

Background: Segmentation of organs and structures in abdominal MRI is useful for many clinical applications, such as disease diagnosis and radiotherapy. Current approaches have focused on delineating a limited set of abdominal structures (13 types). To date, there is no publicly available abdominal MRI dataset with voxel-level annotations of multiple organs and structures. Consequently, a segmentation tool for multi-structure segmentation is also unavailable. Methods: We curated a T1-weighted abdominal MRI dataset consisting of 195 patients who underwent imaging at National Institutes of Health (NIH) Clinical Center. The dataset comprises of axial pre-contrast T1, arterial, venous, and delayed phases for each patient, thereby amounting to a total of 780 series (69,248 2D slices). Each series contains voxel-level annotations of 62 abdominal organs and structures. A 3D nnUNet model, dubbed as MRISegmentator-Abdomen (MRISegmentator in short), was trained on this dataset, and evaluation was conducted on an internal test set and two large external datasets: AMOS22 and Duke Liver. The predicted segmentations were compared against the ground-truth using the Dice Similarity Coefficient (DSC) and Normalized Surface Distance (NSD). Findings: MRISegmentator achieved an average DSC of 0.861$\pm$0.170 and a NSD of 0.924$\pm$0.163 in the internal test set. On the AMOS22 dataset, MRISegmentator attained an average DSC of 0.829$\pm$0.133 and a NSD of 0.908$\pm$0.067. For the Duke Liver dataset, an average DSC of 0.933$\pm$0.015 and a NSD of 0.929$\pm$0.021 was obtained. Interpretation: The proposed MRISegmentator provides automatic, accurate, and robust segmentations of 62 organs and structures in T1-weighted abdominal MRI sequences. The tool has the potential to accelerate research on various clinical topics, such as abnormality detection, radiotherapy, disease classification among others.

eess.IV↗

arXiv2024

On kernels of descent statistics

The kernel $\mathcal{K}^{\operatorname{st}}$ of a descent statistic $\operatorname{st}$, introduced by Grinberg, is a subspace of the algebra $\operatorname{QSym}$ of quasisymmetric functions defined in terms of $\operatorname{st}$-equivalent compositions, and is an ideal of $\operatorname{QSym}$ if and only if $\operatorname{st}$ is shuffle-compatible. This paper continues the study of kernels of descent statistics, with emphasis on the peak set $\operatorname{Pk}$ and the peak number $\operatorname{pk}$. The kernel $\mathcal{K}^{\operatorname{Pk}}$ in particular is precisely the kernel of the canonical projection from $\operatorname{QSym}$ to Stembridge's algebra of peak quasisymmetric functions, and is the orthogonal complement of Nyman's peak algebra. We prove necessary and sufficient conditions for obtaining spanning sets and linear bases for the kernel $\mathcal{K}^{\operatorname{st}}$ of any descent statistic $\operatorname{st}$ in terms of fundamental quasisymmetric functions, and give characterizations of $\mathcal{K}^{\operatorname{Pk}}$ and $\mathcal{K}^{\operatorname{pk}}$ in terms of the fundamental basis and the monomial basis of $\operatorname{QSym}$. Our results imply that the peak set and peak number statistics are $M$-binomial, confirming a conjecture of Grinberg.

math.CO↗

arXiv2024

A Systematic Survey of Blockchained Federated Learning

With the technological advances in machine learning, effective ways are available to process the huge amount of data generated in real life. However, issues of privacy and scalability will constrain the development of machine learning. Federated learning (FL) can prevent privacy leakage by assigning training tasks to multiple clients, thus separating the central server from the local devices. However, FL still suffers from shortcomings such as single-point-failure and malicious data. The emergence of blockchain provides a secure and efficient solution for the deployment of FL. In this paper, we conduct a comprehensive survey of the literature on blockchained FL (BCFL). First, we investigate how blockchain can be applied to federal learning from the perspective of system composition. Then, we analyze the concrete functions of BCFL from the perspective of mechanism design and illustrate what problems blockchain addresses specifically for FL. We also survey the applications of BCFL in reality. Finally, we discuss some challenges and future research directions.

cs.CR↗

arXiv2024

Linear optimal transport subspaces for point set classification

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set classification under spatial deformations. Here we propose a framework for classifying point sets experiencing certain types of spatial deformations, with a particular emphasis on datasets featuring affine deformations. Our approach employs the Linear Optimal Transport (LOT) transform to obtain a linear embedding of set-structured data. Utilizing the mathematical properties of the LOT transform, we demonstrate its capacity to accommodate variations in point sets by constructing a convex data space, effectively simplifying point set classification problems. Our method, which employs a nearest-subspace algorithm in the LOT space, demonstrates label efficiency, non-iterative behavior, and requires no hyper-parameter tuning. It achieves competitive accuracies compared to state-of-the-art methods across various point set classification tasks. Furthermore, our approach exhibits robustness in out-of-distribution scenarios where training and test distributions vary in terms of deformation magnitudes.

cs.CV↗

arXiv2024

On the $\operatorname{rix}$ statistic and valley-hopping

This paper studies the relationship between the modified Foata$\unicode{x2013}$Strehl action (a.k.a. valley-hopping)$\unicode{x2014}$a group action on permutations used to demonstrate the $γ$-positivity of the Eulerian polynomials$\unicode{x2014}$and the number of rixed points $\operatorname{rix}$$\unicode{x2014}$a recursively-defined permutation statistic introduced by Lin in the context of an equidistribution problem. We give a linear-time iterative algorithm for computing the set of rixed points, and prove that the $\operatorname{rix}$ statistic is homomesic under valley-hopping. We also demonstrate that a bijection $Φ$ introduced by Lin and Zeng in the study of the $\operatorname{rix}$ statistic sends orbits of the valley-hopping action to orbits of a cyclic version of valley-hopping, which implies that the number of fixed points $\operatorname{fix}$ is homomesic under cyclic valley-hopping.

math.CO↗

arXiv2024

A subfamily of skew Dyck paths related to $k$-ary trees

We introduce a subfamily of skew Dyck paths called box paths and show that they are in bijection with pairs of ternary trees, confirming an observation stated previously on the On-Line Encyclopedia of Integer Sequences. More generally, we define $k$-box paths, which are in bijection with $(k+1)$-tuples of $(k+2)$-ary trees. A bijection is given between $k$-box paths and a subfamily of $k_{t}$-Dyck paths, as well as a bijection with a subfamily of $(k,\ell)$-threshold sequences. We also study the refined enumeration of $k$-box paths by the number of returns and the number of long ascents. Notably, the distribution of long ascents over $k$-box paths generalizes the Narayana distribution on Dyck paths, and we find that $(k-3)$-box paths with exactly two long ascents provide a combinatorial model for the second $k$-gonal numbers.

math.CO↗

arXiv2023

Semantic Image Synthesis for Abdominal CT

As a new emerging and promising type of generative models, diffusion models have proven to outperform Generative Adversarial Networks (GANs) in multiple tasks, including image synthesis. In this work, we explore semantic image synthesis for abdominal CT using conditional diffusion models, which can be used for downstream applications such as data augmentation. We systematically evaluated the performance of three diffusion models, as well as to other state-of-the-art GAN-based approaches, and studied the different conditioning scenarios for the semantic mask. Experimental results demonstrated that diffusion models were able to synthesize abdominal CT images with better quality. Additionally, encoding the mask and the input separately is more effective than naïve concatenating.

cs.CV↗

arXiv2023

ECLM: Efficient Edge-Cloud Collaborative Learning with Continuous Environment Adaptation

Pervasive mobile AI applications primarily employ one of the two learning paradigms: cloud-based learning (with powerful large models) or on-device learning (with lightweight small models). Despite their own advantages, neither paradigm can effectively handle dynamic edge environments with frequent data distribution shifts and on-device resource fluctuations, inevitably suffering from performance degradation. In this paper, we propose ECLM, an edge-cloud collaborative learning framework for rapid model adaptation for dynamic edge environments. We first propose a novel block-level model decomposition design to decompose the original large cloud model into multiple combinable modules. By flexibly combining a subset of the modules, this design enables the derivation of compact, task-specific sub-models for heterogeneous edge devices from the large cloud model, and the seamless integration of new knowledge learned on these devices into the cloud model periodically. As such, ECLM ensures that the cloud model always provides up-to-date sub-models for edge devices. We further propose an end-to-end learning framework that incorporates the modular model design into an efficient model adaptation pipeline including an offline on-cloud model prototyping and training stage, and an online edge-cloud collaborative adaptation stage. Extensive experiments over various datasets demonstrate that ECLM significantly improves model performance (e.g., 18.89% accuracy increase) and resource efficiency (e.g., 7.12x communication cost reduction) in adapting models to dynamic edge environments by efficiently collaborating the edge and the cloud models.

cs.LG↗

arXiv2023

A Sequential Learning Procedure with Applications to Online Sales Examination

In this paper, we consider the problem of estimating parameters in a linear regression model. We propose a sequential learning procedure to determine the sample size for achieving a given small estimation risk, under the widely used Gauss-Markov setup with independent normal errors. The procedure is proven to enjoy the second-order efficiency and risk-efficiency properties, which are validated through Monte Carlo simulation studies. Using e-commerce data, we implement the procedure to examine the influential factors of online sales.

stat.ME↗

arXiv2023

Cyclic shuffle-compatibility via cyclic shuffle algebras

A permutation statistic $\operatorname{st}$ is said to be shuffle-compatible if the distribution of $\operatorname{st}$ over the set of shuffles of two disjoint permutations $π$ and $σ$ depends only on $\operatorname{st}π$, $\operatorname{st}σ$, and the lengths of $π$ and $σ$. Shuffle-compatibility is implicit in Stanley's early work on $P$-partitions, and was first explicitly studied by Gessel and Zhuang, who developed an algebraic framework for shuffle-compatibility centered around their notion of the shuffle algebra of a shuffle-compatible statistic. For a family of statistics called descent statistics, these shuffle algebras are isomorphic to quotients of the algebra of quasisymmetric functions. Recently, Domagalski, Liang, Minnich, Sagan, Schmidt, and Sietsema defined a version of shuffle-compatibility for statistics on cyclic permutations, and studied cyclic shuffle-compatibility through purely combinatorial means. In this paper, we define the cyclic shuffle algebra of a cyclic shuffle-compatible statistic, and develop an algebraic framework for cyclic shuffle-compatibility in which the role of quasisymmetric functions is replaced by the cyclic quasisymmetric functions recently introduced by Adin, Gessel, Reiner, and Roichman. We use our theory to provide explicit descriptions for the cyclic shuffle algebras of various cyclic permutation statistics, which in turn gives algebraic proofs for their cyclic shuffle-compatibility.

math.CO↗

arXiv2023

A Survey of Deep Graph Clustering: Taxonomy, Challenge, Application, and Open Resource

Graph clustering, which aims to divide nodes in the graph into several distinct clusters, is a fundamental yet challenging task. Benefiting from the powerful representation capability of deep learning, deep graph clustering methods have achieved great success in recent years. However, the corresponding survey paper is relatively scarce, and it is imminent to make a summary of this field. From this motivation, we conduct a comprehensive survey of deep graph clustering. Firstly, we introduce formulaic definition, evaluation, and development in this field. Secondly, the taxonomy of deep graph clustering methods is presented based on four different criteria, including graph type, network architecture, learning paradigm, and clustering method. Thirdly, we carefully analyze the existing methods via extensive experiments and summarize the challenges and opportunities from five perspectives, including graph data quality, stability, scalability, discriminative capability, and unknown cluster number. Besides, the applications of deep graph clustering methods in six domains, including computer vision, natural language processing, recommendation systems, social network analyses, bioinformatics, and medical science, are presented. Last but not least, this paper provides open resource supports, including 1) a collection (\url{https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering}) of state-of-the-art deep graph clustering methods (papers, codes, and datasets) and 2) a unified framework (\url{https://github.com/Marigoldwu/A-Unified-Framework-for-Deep-Attribute-Graph-Clustering}) of deep graph clustering. We hope this work can serve as a quick guide and help researchers overcome challenges in this vibrant field.

cs.LG↗

arXiv2023

From Sparse to Precise: A Practical Editing Approach for Intracardiac Echocardiography Segmentation

Accurate and safe catheter ablation procedures for patients with atrial fibrillation require precise segmentation of cardiac structures in Intracardiac Echocardiography (ICE) imaging. Prior studies have suggested methods that employ 3D geometry information from the ICE transducer to create a sparse ICE volume by placing 2D frames in a 3D grid, enabling training of 3D segmentation models. However, the resulting 3D masks from these models can be inaccurate and may lead to serious clinical complications due to the sparse sampling in ICE data, frames misalignment, and cardiac motion. To address this issue, we propose an interactive editing framework that allows users to edit segmentation output by drawing scribbles on a 2D frame. The user interaction is mapped to the 3D grid and utilized to execute an editing step that modifies the segmentation in the vicinity of the interaction while preserving the previous segmentation away from the interaction. Furthermore, our framework accommodates multiple edits to the segmentation output in a sequential manner without compromising previous edits. This paper presents a novel loss function and a novel evaluation metric specifically designed for editing. Results from cross-validation and testing indicate that our proposed loss function outperforms standard losses and training strategies in terms of segmentation quality and following user input. Additionally, we show quantitatively and qualitatively that subsequent edits do not compromise previous edits when using our method, as opposed to standard segmentation losses. Overall, our approach enhances the accuracy of the segmentation while avoiding undesired changes away from user interactions and without compromising the quality of previously edited regions, leading to better patient outcomes.

cs.CV↗

arXiv2023

Statistics on clusters and $r$-Stirling permutations

The Goulden$\unicode{x2013}$Jackson cluster method, adapted to permutations by Elizalde and Noy, reduces the problem of counting permutations by occurrences of a prescribed consecutive pattern to that of counting clusters, which are special permutations with a lot of structure. Recently, Zhuang found a generalization of the cluster method which specializes to refinements by additional permutation statistics, namely the inverse descent number $\operatorname{ides}$, the inverse peak number $\operatorname{ipk}$, and the inverse left peak number $\operatorname{ilpk}$. Continuing this line of work, we study the enumeration of $2134\cdots m$-clusters by $\operatorname{ides}$, $\operatorname{ipk}$, and $\operatorname{ilpk}$, which allows us to derive formulas for counting permutations by occurrences of the consecutive pattern $2134\cdots m$ jointly with each of these statistics. Analogous results for the pattern $12\cdots (m-2)m(m-1)$ are obtained via symmetry arguments. Along the way, we discover that $2134\cdots (r+1)$-clusters are equinumerous with $r$-Stirling permutations introduced by Gessel and Stanley, and we establish some joint equidistributions between these two families of permutations.

math.CO↗