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DTSFormer: Decoupled temporal-spatial diffusion transformer for enhanced long-term time series forecasting

KNOWLEDGE-BASED SYSTEMS 2025年 309卷

作者： Zhu, Jiaming Liu, Dezhi Chen, Huayou Liu, Jinpei Tao, Zhifu Anhui Univ Sch Internet Hefei 230039 Anhui Peoples R China Natl Engn Res Ctr Agroecol Big Data Anal & Applica Hefei 230601 Anhui Peoples R China Anhui Univ Sch Big Data & Stat Hefei 230601 Anhui Peoples R China Anhui Univ Sch Business Hefei 230601 Anhui Peoples R China

Transformer-based models have significantly advanced long-term time series forecasting by leveraging self- attention mechanisms to capture long-term dependencies. However, these models face high computational costs, slow inference speeds, and limitations in utilizing information from longer lookback windows. Additionally, existing methods often neglect implicit spatial dependencies between variables, and struggle with semantic misalignment and insufficient diffusion of spatial information. To address these challenges, we propose DTSFormer, a D ecoupled T emporal-Spatial Diffusion Transformer designed specifically for long-term time series forecasting: (1) DTSFormer effectively integrates temporal features with implicit spatial attributes, ensuring comprehensive utilization of both temporal and spatial information. (2) DTSFormer introduce a Mix- hop Diffusion layer to effectively propagate and aggregate spatial information while preserving the original graph structure, significantly improving the accuracy of spatial information dissemination. (3) we develop a cross-diffusion attention mechanism based on the expectation-maximization algorithm, which integrates graph structure information with varying semantics under a seasonal trend decomposition framework. This approach enhances the fusion of semantic information from different graph structures and reduces computational complexity. Our extensive experiments on multiple benchmark datasets across different domains demonstrate that DTSFormer consistently achieves state-of-the-art performance in both accuracy and efficiency. These results validate DTSFormer as a robust and scalable solution for advanced long-term time series forecasting tasks.

关键词： Long-term series forecasting Transformer-based model expectation-maximization algorithm Diffusion Temporal-Spatial features

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On Classical Inference of a Flexible Semi-Parametric Class of Distributions Under a Joint Balanced Progressive Censoring Scheme

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2025年第1期41卷

作者： Bhattacharyya, Dhrubasish Kundu, Debasis Rajiv Gandhi Inst Petr Technol Dept Math Sci Amethi India Indian Inst Technol Kanpur Dept Math & Stat Kanpur India

The paper deals with the estimation procedures for the proportional hazard class of distributions under a two-sample balanced joint progressive censoring scheme. The baseline hazard function is assumed to be piecewise constant, instead of any specific form. This adds flexibility to the proposed model, and the shape of the underlying hazard function is completely data-driven. Since the complicated form of the likelihood function does not yield closed-form estimators, we propose a variant of the expectation-maximization algorithm, known as the expectation Conditional maximization (ECM) algorithm, for obtaining maximum likelihood estimates of the model parameters. This leads to explicit expressions for the iterative constrained maximization steps of the algorithm. An extension to the case when the cut points are unknown has also been considered for dealing with problems involving real data. Simulation results and illustrations using real data have also been presented.

关键词： bootstrap confidence interval expectation conditional maximization algorithm expectation-maximization algorithm maximum likelihood estimators

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Restoration after deterioration in interdependent infrastructure networks: A two-stage hybrid method with minimum network performance loss

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INFORMATION SCIENCES 2025年 693卷

作者： Li, Yulong Su, Han Yang, Baisong Lin, Jie Shen, Yinghua Wu, Guobin Cent Univ Finance & Econ Sch Management Sci & Engn Beijing 100081 Peoples R China Chongqing Univ Sch Econ & Business Adm Chongqing 400044 Peoples R China

Restoration of interdependent infrastructure networks (IINs) relies on the information from deterioration, which is of great significance because IINs support the normal functioning of social productivity and life. However, existing research has not fully addressed the restoration after deterioration in IINs, which is not conducive to the timely elimination of the adverse effects of infrastructure deterioration. First, a unified model for IINs is innovatively devised by considering both functional and operational interdependencies between infrastructures. Second, a two-stage hybrid method that generates the optimal restoration strategies after deterioration in IINs is proposed. Specifically, in the first stage, a hidden Markov chain model for deterioration prediction is constructed, which is solved by the expectation-maximization (EM) algorithm. In the second stage, an objective programming model with minimum network performance loss for restoration optimization is developed, and the optimal strategy is obtained by the ant colony algorithm. Finally, a real-world case is used to validate the feasibility and effectiveness of the proposed method. The results show that this method is efficient and effective in finding optimal restoration strategy after deterioration in IINs. We also investigate the effects of initial restoration time and restoration resource grouping, which provide helpful decision guidance for real cases.

关键词： Interdependent infrastructure networks Deterioration prediction Restoration optimization expectation-maximization algorithm Ant colony algorithm

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Classification of PolSAR data with the Complex Riesz distribution

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2025年

作者： Kammoun, Rayhan Kessentini, Sameh Zine, Raoudha Univ Sfax Fac Sci Sfax Lab Probabil & Stat BP 1171 Sfax 3000 Tunisia

This article deals with unsupervised classification strategies applied to polarimetric synthetic aperture radar (PolSAR) images. We discuss the performance of the Complex Riesz distribution, which is used for the first time to classify PolSAR images. Hence, we extend the maximum likelihood (ML) and expectation-maximization (EM) algorithms to the Complex Riesz distribution. Furthermore, we derive the analytic expression of five stochastic distances (Kullback-Leibler, Bhattacharyya, R & eacute;nyi, Hellinger, and Chi-square) between Complex Riesz distributions. We assess the accuracy of the Complex Riesz EM algorithm on synthetic data generated by an extension of the Bartlett decomposition. Then, comparing the Complex Wishart and the Complex Riesz distributions on PolSAR data reveals that the latter performs better than the former. Finally, the EM algorithm for the Complex Riesz distribution serves to classify the actual data, and the discrimination potential of the five stochastic distances is discussed. These results in both experimental, ML, and EM algorithms suggest that most stochastic distances are significant, and mainly the 0. 7-order R & eacute;nyi.

关键词： Complex Riesz distribution expectation-maximization algorithm Hermitian random matrix maximum likelihood algorithm PolSAR classification stochastic distances

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DS-Net: A model driven network framework for lesion segmentation on fundus image

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KNOWLEDGE-BASED SYSTEMS 2025年 315卷

作者： Tan, Feiyu Wang, Yuhan Xie, Qi Fu, Jiahong Wang, Renzhen Meng, Deyu Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Xi An Jiao Tong Univ Key Lab Intelligent Networks & Network Secur Minist Educ Xian 710049 Shaanxi Peoples R China Zhejiang Lab Res Inst Interdisciplinary Innovat Res Ctr Intelligent Robot Hangzhou 311100 Peoples R China Macau Univ Sci & Technol Macao Inst Syst Engn Taipa 999078 Macao Peoples R China

Diabetic retinopathy (DR) is a leading cause of vision loss in working-age adults, and analyzing retinal fundus plays a crucial role in early DR screening. However, multi-lesion segmentation of fundus images remains a challenging task due to the highly diverse shape, size, position, and brightness of lesions. In this paper, we propose an interpretable network framework for multi-lesion segmentation by integrating the prior knowledge of retinal fundus images into it. Specifically, we propose a probabilistic model for retinal fundus images, which is in a foreground-background decomposition manner, and both the characteristics of the foreground (lesions) and background (non-lesion fundus images) are taken into consideration. Then, we exploit the expectation- maximization (EM) algorithm to solve the proposed model and design a novel network architecture under the guidance of the calculation flow of the algorithm, called Decomposition-Segmentation Network (DS-Net). The components of the network consist of two subnetworks: S-Net and D-Net, corresponding to the E step and M step of the EM algorithm, respectively. D-Net aims to decompose the background and foreground compositions of the fundus image and S-Net takes the foreground as input and executes segmentation task. Similar to the EM algorithm, the two subnetworks separate the original segmentation task into two much easier but interpretable sub-tasks. This not only helps enhance the performance, but also greatly facilitates a deeper analysis of the network. Moreover, the proposed DS-Net framework can be easily integrated with current lesion segmentation networks in a plug-and-play manner, by setting current segmentation networks as S-Net in the framework, and lead to general performance improvements. Experiments on benchmark datasets substantiate the superiority of DS-Net quantitatively and visually. The code of our method is available at https://***/tanfy929/DS-Net.

关键词： Multi-class segmentation Prior knowledge of retinal fundus images expectation-maximization algorithm Interpretable network Deep learning

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Majorization ordering of dependent aggregate claims clustered by statistical machine learning

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 277卷

作者： Nevruz, Ezgi Yildirak, Kasirga Sengupta, Ashis Hacettepe Univ Dept Actuarial Sci Ankara Turkiye MCG Augusta Univ Dept Populat Hlth Sci Augusta GA USA Indian Inst Technol Dept Math Kharagpur India Middle East Tech Univ Dept Stat Ankara Turkiye

The primary driver of decision-making is prioritization or ordering of risks, which plays a vital role optimizing risk management strategies. This paper focuses on ordering aggregate claim vectors across various risk clusters utilizing agricultural insurance data. The data was sourced from the Turkish Agricultural Insurance Pool (TARS & Idot;M), the sole entity responsible for compiling agricultural insurance claim datasets. We consider the spatial and temporal features of claims, supposing that individual claims subject to similar environmental risks are dependent. We cluster risks based on meteorological values related to the location and time the reported crop-hail insurance claims, estimated using an extended spatiotemporal interpolation method that we proposed. Bayesian regularization enhanced the performance of the statistical machine learning approach. Having clustered the risk regions, we order the aggregate claim vectors by using majorization relation and Schur-convex risk measures, which are more flexible for multivariate actuarial risks. Moreover, a contribution to the literature, we modify the definition of majorization to fulfill the criteria for continuous random variables. The findings of this study indicate that the risk clusters, when ordered according to the modified majorization conditions and the Schur-convex risk measure, exhibit consistency. These results further demonstrate the compatibility of the climate-based, probabilistic clustering method with the modified majorization relation.

关键词： Agricultural insurance expectation-maximization algorithm Multivariate actuarial risk Partial order theory Schur-convexity

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The dynamic expectation-conditional maximization either' algorithm

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 2012年第2期74卷 313-336页

作者： He, Yunxiao Liu, Chuanhai Purdue Univ Dept Stat W Lafayette IN 47907 USA Yale Univ New Haven CT USA

. The expectationconditional maximization either (ECME) algorithm has proven to be an effective way of accelerating the expectationmaximization algorithm for many problems. Recognizing the limitation of using prefixed acceleration subspaces in the ECME algorithm, we propose a dynamic ECME (DECME) algorithm which allows the acceleration subspaces to be chosen dynamically. The simplest DECME implementation is what we call DECME-1, which uses the line that is determined by the two most recent estimates as the acceleration subspace. The investigation of DECME-1 leads to an efficient, simple, stable and widely applicable DECME implementation, which uses two-dimensional acceleration subspaces and is referred to as DECME-2. The fast convergence of DECME-2 is established by the theoretical result that, in a small neighbourhood of the maximum likelihood estimate, it is equivalent to a conjugate direction method. The remarkable accelerating effect of DECME-2 and its variant is also demonstrated with several numerical examples.

关键词： Conjugate direction expectation-conditional maximization algorithm expectation-conditional maximization either algorithm expectation-maximization algorithm Square iterative methods Successive over-relaxation

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Modelling the size distribution and bioaccumulation of gold nanoparticles under mixture exposure

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AQUATIC TOXICOLOGY 2025年 280卷 107286页

作者： Li, Yao Wang, Xiangrui Liang, Dingyuan Zhao, Xiaoli Dong, Zhaomin Bai, Yingchen Wang, Wen-Xiong Peijnenburg, Willie J. G. M. Wang, Ying Fan, Wenhong Beihang Univ Sch Mat Sci & Engn Beijing 100191 Peoples R China Chinese Res Inst Environm Sci State Key Lab Environm Criteria & Risk Assessment Beijing 100012 Peoples R China City Univ Hong Kong Sch Energy & Environm Kowloon Hong Kong Peoples R China City Univ Hong Kong State Key Lab Marine Pollut Kowloon Hong Kong Peoples R China Leiden Univ Inst Environm Sci CML NL-2300 RA Leiden Netherlands Natl Inst Publ Hlth & Environm RIVM Ctr Safety Subst & Prod NL-3720 BA Bilthoven Netherlands

To assess the bioaccumulation and toxicity of nanoparticles (NPs), analyzing and modelling the relationship between the size distribution of NPs in organisms and the exposure particle size distribution represents an important challenge. Previous studies mostly focused on the NPs with single size. However, the size distribution of NPs is wide and variable in the natural environment. There is a lack of research on the NPs with mixed sizes. This study investigated the size distribution of three gold (Au) NPs with different sizes and their mixtures within a ciliate Tetrahymena thermophila under the same number concentration of particles. Results revealed that smaller particles tended to aggregate and bioaccumulate more in cells. Using expectation-maximization algorithm, a particle size distribution model of NPs in cells was established. This model effectively simulated the size distribution of NPs with mixed sizes in cells, demonstrating high accuracy with a mean absolute error of < 0.001, a root mean squared error of < 0.001, and a correlation coefficient exceeding 0.98. Experimental results further verified that the model reliably predicted the size distribution of NPs with mixed sizes in cells, and smaller particles accounted for a larger proportion of the size distribution and bioaccumulation. These results demonstrated the importance of particle size and size distribution of NPs in their environmental effects. Models developed here can provide guidance for future evaluation of the environmental risks of NPs mixtures.

关键词： Nanoparticles Single-particle ICP-MS Size distribution expectation-maximization algorithm Tetrahymena thermophila

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An improved EM algorithm for variable selection with missing data in spatial error models

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2025年第6期95卷 1141-1164页

作者： Wang, Yuanfeng Song, Yunquan China Univ Petr Coll Sci Qingdao 266580 Peoples R China

In the field of spatial economics, choosing the right variables for spatial error models (SEM) with missing data is of utmost importance. Many excellent approaches are proposed to select variables for regression models with missing data. However, little literature addresses this problem in the SEM model. To address this issue, we have developed an observed-data penalized quasi-maximum likelihood estimation method called OPQMLE, which simultaneously performs variable selection and parameter estimation in the presence of a missing response. This method employs the Smoothly Clipped Absolute Deviation (SCAD) penalty to select variables for SEM models. Under certain assumptions, we have established the method's theoretical properties, including consistency and asymptotic normality. Furthermore, we have provided an improved expectation-maximization algorithm for optimizing the penalized quasi-likelihood function. We have conducted a simulation and real data analysis to evaluate the proposed method's performance.

关键词： Spatial error models observed penalized quasi-likelihood function expectation-maximization algorithm missing data variable selection

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On a class of finite mixture models that includes hidden Markov models

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JOURNAL OF MULTIVARIATE ANALYSIS 2025年 208卷

作者： Bartolucci, Francesco Pandolfi, Silvia Pennoni, Fulvia Univ Perugia Dipartimento Econ Via A Pascoli 20 I-06123 Perugia Italy Univ Milano Bicocca Dipartimento Stat & Metodi Quantitat Via Bicocca Arcimboldi 8 I-20126 Milan Italy

In the context of longitudinal data, we introduce a class of finite mixture (FM) models that generalizes that of hidden Markov (HM) models, and derive conditions under which the two classes are equivalent. On the basis of this result, we develop a likelihood ratio (LR) misspecification test for assessing the latent structure of an HM model, along with a multiple version of this test that may be used in the presence of many latent states or time occasions. This testing procedure requires the maximum likelihood estimation of the two models under comparison, that is, the assumed HM model and the more general FM model, which is performed by suitable versions of the expectation-maximization algorithm. The approach is validated through a simulation study, aimed at assessing the performance of the proposed tests under different circumstances, and by an application using data derived from the SCImago Journal & Country Rank database.

关键词： expectation-maximization algorithm Likelihood ratio test Model selection Multiple testing SCImago Journal & Country Rank

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