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Improved Image Classification with Manifold Neural Networks

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Improved Image Classification with Manifold Neural Networks

International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Caio F. Deberaldini Netto Zhiyang Wang Luana Ruiz Department of Applied Mathematics and Statistics Mathematical Institute for Data Science (MINDS) Data Science and Artificial Intelligence Institute (DSAI) Johns Hopkins University Baltimore USA Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia USA

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting from GNNs’ message-passing framework. However, the potential of GNNs in more general data representations, especially in the image domain, remains underexplored. Leveraging the manifold hypothesis, which posits that high-dimensional data lies in a low-dimensional manifold, we explore GNNs’ potential in this context. We construct an image manifold using variational autoencoders, then sample the manifold to generate graphs where each node is an image. This approach reduces data dimensionality while preserving geometric information. We then train a GNN to predict node labels corresponding to the image labels in the classification task, and leverage convergence of GNNs to manifold neural networks to analyze GNN generalization. Experiments on MNIST and CIFAR10 datasets demonstrate that GNNs generalize effectively to unseen graphs, achieving competitive accuracy in classification tasks.

关键词： Manifolds Electric potential High dimensional data Autoencoders Transportation Signal processing Graph neural networks Molecular biology Speech processing Image classification

Analyzing Classroom Interaction data Using Prompt Engineering and Network Analysis

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arXiv 2025年

作者： Kim, Gwanghee Jin, Ick Hoon Jeon, Minjeong Department of Statistics and Data Science Yonsei University Korea Republic of Department of Applied Statistics Yonsei University Korea Republic of School of Education and Information Studies University of California Los Angeles United States

Classroom interactions play a vital role in developing critical thinking, collaborative problem-solving abilities, and enhanced learning outcomes. While analyzing these interactions is crucial for improving educational practices, the examination of classroom dialogues presents significant challenges due to the complexity and high-dimensionality of conversational data. This study presents an integrated framework that combines prompt engineering with network analysis to investigate classroom interactions comprehensively. Our approach automates utterance classification through prompt engineering, enabling efficient and scalable dialogue analysis without requiring pre-labeled datasets. The classified interactions are subsequently transformed into network representations, facilitating the analysis of classroom dynamics as structured social networks. To uncover complex interaction patterns and how underlying interaction structures relate to student learning, we utilize network mediation analysis. In this approach, latent interaction structures, derived from the additive and multiplicative effects network (AMEN) model that places students within a latent social space, act as mediators. In particular, we investigate how the gender gap in mathematics performance may be mediated by students’ classroom interaction structures. Copyright © 2025, The Authors. All rights reserved.

关键词： Students

ESTIMATING UNBOUNDED DENSITY RATIOS: APPLICATIONS IN ERROR CONTROL UNDER COVARIATE SHIFT

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arXiv 2025年

作者： Xu, Shuntuo Yu, Zhou Huang, Jian School of Statistics East China Normal University China Departments of Data Science and Artificial Intelligence Applied Mathematics The Hong Kong Polytechnic University Hong Kong

The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often depend on stringent regularity conditions, mainly focusing on density ratio functions with bounded domains and ranges. In this paper, we study density ratio estimators using loss functions based on least squares and logistic regression. We establish upper bounds on estimation errors with standard minimax optimal rates, up to logarithmic factors. Our results accommodate density ratio functions with unbounded domains and ranges. We apply our results to nonparametric regression and conditional flow models under covariate shift and identify the tail properties of the density ratio as crucial for error control across domains affected by covariate shift. We provide sufficient conditions under which loss correction is unnecessary and demonstrate effective generalization capabilities of a source estimator to any suitable target domain. Our simulation experiments support these theoretical findings, indicating that the source estimator can outperform those derived from loss correction methods, even when the true density ratio is *** Codes 62G05, 62G08, 68T07 © 2025, CC BY.

关键词： Deep neural networks

Modified least squares ratio estimator for autocorrelated data: Estimation and prediction

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Journal of Computational Mathematics and data science 2025年 14卷

作者： Poojari, Satyanarayana Acharya, Sachin Varun Kumar, S.G. Serrao, Vinitha Department of Applied Statistics and Data Science Prasanna School of Public Health Manipal Academy of Higher Education Manipal Karnataka 576104 India

Autocorrelated errors in regression models make ordinary least squares (OLS) estimators inefficient, potentially leading to the misinterpretation of test procedures. Generalized least squares (GLS) estimation is a more efficient approach than OLS in the presence of autocorrelated errors. The GLS estimators based on Cochrane–Orcutt (COR) and Hildreth–Lu (HU) methods are the most commonly used to estimate unknown model parameters. This study investigates the impact of autocorrelation on parameter estimation and prediction in regression models and introduces a novel approach to address the challenge possessed by autocorrelated errors. In this paper, two modified GLS estimators based on the least square ratio method are proposed namely the Least Square Ratio-Cochrane–Orcutt Estimator (LSRE-COR) estimator and the Least Square Ratio-Hildreth–Lu (LSRE-HU) estimator. A Monte Carlo simulation study is carried out to compare the performance of the proposed estimators with OLS, COR, HU, maximum likelihood estimator (MLE), and least square ratio estimator (LSRE) based on total mean square error (TMSE) and root mean square error (RMSE). The results show that the proposed LSRE-HU and LSRE-COR consistently outperform all other estimators across various levels of autocorrelation and numbers of regressors for moderately large samples. The effectiveness of these methods is illustrated through real-life applications. © 2025 The Author(s)

关键词： Autocorrelated error Cochrane–Orcutt Least square ratio estimator Linear regression model Prediction

Principal Graph Encoder Embedding and Principal Community Detection

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arXiv 2025年

作者： Shen, Cencheng Dong, Yuexiao Priebe, Carey E. Larson, Jonathan Trinh, Ha Park, Youngser Department of Applied Economics and Statistics University of Delaware United States Department of Statistics Operations and Data Science Temple University United States Microsoft Research at Redmond WA United States Johns Hopkins University United States

In this paper, we introduce the concept of principal communities and propose a principal graph encoder embedding method that concurrently detects these communities and achieves vertex embedding. Given a graph adjacency matrix with vertex labels, the method computes a sample community score for each community, ranking them to measure community importance and estimate a set of principal communities. The method then produces a vertex embedding by retaining only the dimensions corresponding to these principal communities. Theoretically, we define the population version of the encoder embedding and the community score based on a random Bernoulli graph distribution. We prove that the population principal graph encoder embedding preserves the conditional density of the vertex labels and that the population community score successfully distinguishes the principal communities. We conduct a variety of simulations to demonstrate the finite-sample accuracy in detecting ground-truth principal communities, as well as the advantages in embedding visualization and subsequent vertex classification. The method is further applied to a set of real-world graphs, showcasing its numerical advantages, including robustness to label noise and computational scalability. Copyright © 2025, The Authors. All rights reserved.

关键词： Graph embeddings

Local geometry of high-dimensional mixture models: Effective spectral theory and dynamical transitions

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arXiv 2025年

作者： Arous, Gerard Ben Gheissari, Reza Huang, Jiaoyang Jagannath, Aukosh Courant Institute New York University United States Department of Mathematics Northwestern University United States Department of Statistics and Data Science University of Pennsylvania United States Department of Statistics and Actuarial Science Department of Applied Mathematics Cheriton School of Computer Science University of Waterloo Canada

We study the local geometry of empirical risks in high dimensions via the spectral theory of their Hessian and information matrices. We focus on settings where the data, (Y)n=1 ∈ d, are i.i.d. draws of a k-component Gaussian mixture model, and the loss depends on the projection of the data into a fixed number of vectors, namely xY, where x ∈ d×C are the parameters, and C need not equal k. This setting captures a broad class of problems such as classification by one and two-layer networks and regression on multi-index models. We prove exact formulas for the limits of the empirical spectral distribution and outlier eigenvalues and eigenvectors of such matrices in the proportional asymptotics limit, where the number of samples and dimension n, d → ∞ and n/d = ∈ (0, ∞). These limits depend on the parameters x only through the summary statistic of the (C + k) × (C + k) Gram matrix of the parameters and class means, G = (x, µ)(x, µ). It is known that under general conditions, when x is trained by stochastic gradient descent, the evolution of these same summary statistics along training converges to the solution of an autonomous system of ODEs, called the effective dynamics. This enables us to connect the spectral theory to the training dynamics. We demonstrate our general results by analyzing the effective spectrum along the effective dynamics in the case of multi-class logistic regression. In this setting, the empirical Hessian and information matrices have substantially different spectra, each with their own static and even dynamical spectral transitions. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

Advancements on multi-fidelity random Fourier neural networks: application to hurricane modeling for offshore wind energy

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Advancements on multi-fidelity random Fourier neural network...

AIAA science and Technology Forum and Exposition, AIAA SciTech Forum 2025

作者： Davis, Owen Geraci, Gianluca Wentz, Jacqueline M. King, Ryan N. Cortiella, Alexandre Rybchuk, Alex Gomez, Miguel Sanchez Deskos, Georgios Motamed, Mohammad Optimization and Uncertainty Quantification Sandia National Laboratories AlbuquerqueNM United States Computational Data Science Sandia National Laboratories LivermoreCA United States National Wind Technology Center National Renewable Energy Laboratory GoldenCO United States Department of Applied Mathematics and Statistics University of New Mexico AlbuquerqueNM United States

ISBN: (数字)9781624107238

ISBN: (纸本)9781624107238

Multi-fidelity approaches are emerging as effective strategies in computational science to handle otherwise intractable tasks like Uncertainty Quantification (UQ), training of Machine Learning (ML) models, and optimization, for expensive high-fidelity applications in which the amount of available simulations or data is limited. The main idea is simple: large datasets generated for low-fidelity approximations of the problem at hand are fused with a much sparser dataset for the target (high-fidelity) system. In this paper, we build on our recent success in designing random Fourier Neural Networks (rFNNs) [1] to target problems arising in wind energy applications and in particular problems of interest for hurricane modeling. In this context, data for the high-fidelity models are limited and lower fidelity alternatives are needed. In this work, we introduce a novel multi-fidelity training approach for our rFNNs and demonstrate its use on a simple verification problem and on a hurricane modeling problem in which high-fidelity data are generated via Large-Eddy Simulations (LES), while low-fidelity data are given by a mesoscale model. Initial results demonstrate how the multi-fidelity training approach can improve the quality of the resulting surrogate. © 2025, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

关键词： Large eddy simulation

Conditional Independence Test Based on Transport Maps

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arXiv 2025年

作者： He, Chenxuan Gao, Yuan Zhu, Liping Huang, Jian Institute of Statistics and Big Data Renmin University of China Beijing China Department of Data Science and AI The Hong Kong Polytechnic University Hong Kong Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong

Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We propose a novel framework for testing conditional independence using transport maps. At the population level, we show that two well-defined transport maps can transform the conditional independence test into an unconditional independence test, this substantially simplifies the problem. These transport maps are estimated from data using conditional continuous normalizing flow models. Within this framework, we derive a test statistic and prove its consistency under both the null and alternative hypotheses. A permutation-based procedure is employed to evaluate the significance of the test. We validate the proposed method through extensive simulations and real-data analysis. Our numerical studies demonstrate the practical effectiveness of the proposed method for conditional independence *** Codes 62G05, 62G08, 68T07 © 2025, CC BY.

关键词： Population statistics

Identifying Critical Tokens for Accurate Predictions in Transformer-based Medical Imaging Models

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arXiv 2025年

作者： Kang, Solha Vankerschaver, Joris Ozbulak, Utku Center for Biosystems and Biotech Data Science Ghent University Global Campus Korea Republic of Department of Applied Mathematics Computer Science and Statistics Ghent University Belgium Department of Electronics and Information Systems Ghent University Belgium

With the advancements in self-supervised learning (SSL), transformer-based computer vision models have recently demonstrated superior results compared to convolutional neural networks (CNNs) and are poised to dominate the field of artificial intelligence (AI)-based medical imaging in the upcoming years. Nevertheless, similar to CNNs, unveiling the decision-making process of transformer-based models remains a challenge. In this work, we take a step towards demystifying the decision-making process of transformer-based medical imaging models and propose "Token Insight", a novel method that identifies the critical tokens that contribute to the prediction made by the model. Our method relies on the principled approach of token discarding native to transformer-based models, requires no additional module, and can be applied to any transformer model. Using the proposed approach, we quantify the importance of each token based on its contribution to the prediction and enable a more nuanced understanding of the model’s decisions. Our experimental results which are showcased on the problem of colonic polyp identification using both supervised and self-supervised pretrained vision transformers indicate that Token Insight contributes to a more transparent and interpretable transformer-based medical imaging model, fostering trust and facilitating broader adoption in clinical settings. Copyright © 2025, The Authors. All rights reserved.

关键词： Self-supervised learning