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

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Journal of Computational Mathematics and Data Science

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

Proposing a Genetic Algorithms-Based data Selection Method for Imbalanced Medical datasets 15th

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Proposing a Genetic Algorithms-Based Data Selection Method ...

15th International Conference on Soft Computing and Pattern Recognition, SoCPaR 2023 and 14th World Congress on Nature and Biologically Inspired Computing, NaBIC 2023

作者： Salmi, Mabrouka Atif, Dalia Abraham, Ajith Ventura, Sebastian Laboratory of Applied Statistics (LASAP) National Higher School of Statistics and Applied Economics Tipaza Algeria Andalusian Research Institute in Data Science and Computational Intelligence (DaSCI) University of Cordoba Cordoba Spain University Center Tipaza Algeria School of Artificial Intelligence Sai University Chennai India

ISBN: (纸本)9783031810794

The class imbalance issue is evident in medical datasets, posing a hurdle for accurate predictive modeling. Maintaining the natural characteristics of medical data while mitigating this issue is paramount in ensuring the success of clinical decision support systems. Therefore, this study proposes a genetic algorithm-based data selection method (GA-DS) for imbalanced medical data reserving its distribution and characteristics. It optimizes the assignment of samples into train and test sets by improving the recognition of rare samples on test data. We presented three versions of the GA-DS, one unconstrained and two constrained (train-set >=50%, train-set = 70%) to ensure the reliability of the results. Evaluation of the GA-DS methods on three commonly used imbalanced medical datasets and comparison with SMOTE, random oversampling, and stratified random sampling demonstrated the superior performance of GA-DS by improving the sensitivity score on test data. Future work will investigate its performance on large and highly imbalanced data. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Class imbalance data distribution data selection genetic algorithms

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

Self-supervised Benchmark Lottery on ImageNet: Do Marginal Improvements Translate to Improvements on Similar datasets?

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arXiv 2025年

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

Machine learning (ML) research strongly relies on benchmarks in order to determine the relative effectiveness of newly proposed models. Recently, a number of prominent research effort argued that a number of models that improve the state-of-the-art by a small margin tend to do so by winning what they call a "benchmark lottery". An important benchmark in the field of machine learning and computer vision is the ImageNet where newly proposed models are often showcased based on their performance on this dataset. Given the large number of self-supervised learning (SSL) frameworks that has been proposed in the past couple of years each coming with marginal improvements on the ImageNet dataset, in this work, we evaluate whether those marginal improvements on ImageNet translate to improvements on similar datasets or not. To do so, we investigate twelve popular SSL frameworks on five ImageNet variants and discover that models that seem to perform well on ImageNet may experience significant performance declines on similar datasets. Specifically, state-of-the-art frameworks such as DINO and Swav, which are praised for their performance, exhibit substantial drops in performance while MoCo and Barlow Twins displays comparatively good results. As a result, we argue that otherwise good and desirable properties of models remain hidden when benchmarking is only performed on the ImageNet validation set, making us call for more adequate benchmarking. To avoid the "benchmark lottery" on ImageNet and to ensure a fair benchmarking process, we investigate the usage of a unified metric that takes into account the performance of models on other ImageNet variant datasets. Copyright © 2025, The Authors. All rights reserved.

关键词： Self-supervised learning

Lung Cancer Diagnosis Based on Object Detection Technology 14th

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Lung Cancer Diagnosis Based on Object Detection Technology

14th International Conference on Frontier Computing, FC 2024

作者： Xu, Jia-Lang Wang, Pei-Yun Huang, Tzu-Hsuan Hsu, Ying-Lin Huang, Kuo-Yang Chen, Mu-Yen Artificial Intelligence Development Center Changhua Christian Hospital Changhua Taiwan Doctoral Program in Data Science and Industrial Analytics National Chung Hsing University Taichung Taiwan Department of Applied Mathematics and Institute of Statistics National Chung Hsing University Taichung Taiwan Division of Chest Medicine Department of Internal Medicine Changhua Christian Hospital Changhua Taiwan Department of Engineering Science National Cheng Kung University Tainan Taiwan

ISBN: (纸本)9789819623945

With the rise of artificial intelligence, many people nowadays use artificial intelligence to help solve some problems in life, and the medical field is also with the rise of artificial intelligence, many people are slowly applying artificial intelligence to medical images to assist in decision-making, this study proposes a Yolov8 algorithm for object tracking of CT images of lung cancer, which can quickly tell the doctor where the cancer is and what the type of cancer is. The results of this study show that the Box_Loss, Cls_Loss, and Dfl_loss of the Yolov8 algorithm in detecting the location of lung cancer are 1.3689, 0.4552, and 1.5569 in the validation data, respectively, and thus this study suggests that this method can help physicians know the location of the tumor and what kind of tumor it belongs to. Therefore, this study suggests that this method can help physicians know the location of the tumor and the type of tumor. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Lung cancer