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Many Hands Make Light Work: Group Influence maximization in Evolving Social Networks

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IEEE Transactions on Big Data 2024年

作者： Ma, Yuliang Chen, Yu Wei, Peng Yuan, Ye Wang, Guoren Jiang, Zhong-Zhong Northeastern University College of Information Science and Engineering Shenyang110167 China Northeastern University College of Information Science and Engineering Shenyang110189 China Shandong Branch Industrial and Commercial Bank of China Jinan250001 China Beijing Institute of Technology School of Computer Science and Technology Beijing100081 China Northeastern University School of Business Administration The Institute of Behavioral and Service Operations Management Shenyang110167 China

As the adage 'many hands make light work' suggests, collaborative influence often surpasses individual influence. Inspired by this insight, we undertook a study on group influence maximization in evolving social networks, which is applicable to domains such as social media marketing and financial risk management. Our goal is to reveal how collaborative influence propagates in dynamic settings. Existing research concentrates predominantly on static networks and overlooks the dynamics of evolving social structures. Recognizing the limitations of current influence propagation models for our specific issue, we introduce an innovative model rooted in user behaviors. It considers temporal aspects, and we also suggest a methodology for assessing influence propagation probabilities based on both user behaviors and duration. We introduce an algorithm for extracting user groups using community search, improving efficiency through supergraph construction. Additionally, we present an influence maximization algorithm based on group dynamics with a 3-degree propagation framework. Recognizing diminishing influence, a 3-degree truncation strategy effectively enhances the group influence propagation efficiency. This approach efficiently captures the influence spread and accelerates convergence, boosting the search efficiency. Finally, we conducted comprehensive experiments on real-world and synthetic datasets. The results distinctly highlight the superiority of the proposed algorithms. © 2015 IEEE.

关键词： expectation maximization algorithm

High-dimensional variable clustering based on maxima of a weakly dependent random process

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arXiv 2023年

作者： Boulin, Alexis Di Bernardino, Elena Laloë, Thomas Toulemonde, Gwladys Université Côte d’Azur CNRS LJAD France Univ Montpellier CNRS Montpellier France Inria Lemon France

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random process among clusters. This class of models is identifiable, meaning that there exists a maximal element with a partial order between partitions, allowing for statistical inference. We also present an algorithm depending on a tuning parameter that recovers the clusters of variables without specifying the number of clusters a priori. Our work provides some theoretical insights into the consistency of our algorithm, demonstrating that under certain conditions it can effectively identify clusters in the data with a computational complexity that is polynomial in the dimension. A data-driven selection method for the tuning parameter is also proposed. To further illustrate the significance of our work, we applied our method to neuroscience and environmental real-datasets. These applications highlight the potential and versatility of the proposed *** Codes 60G70, 62H05, 62M99 © 2023, CC BY.

关键词： expectation maximization algorithm

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Geometric Sampling

arXiv 2023年

作者： Panahbehagh, Bardia Faculty of Mathematical Sciences and Computer Kharazmi University Tehran Iran

This paper introduces an innovative and intuitive finite population sampling method that have been developed using a unique geometric framework. In this approach, I represent first-order inclusion probabilities as bars on a two-dimensional graph. By manipulating the positions of these bars, researchers can create a wide range of different sampling designs. This geometric visualization of sampling designs not only leads to increased creativity for researchers to provide new efficient designs but also eliminates the need for complex mathematical algorithms. This novel approach holds significant promise for tackling complex challenges in sampling, such as maximizing entropy and achieving an optimal design. By applying a version of the greedy best-first search algorithm to this geometric approach for finding an optimal design, I have demonstrated the potential for integrating intelligent algorithms into finite population sampling. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Extending Cluster-Weighted Factor Analyzers for multivariate prediction and high-dimensional interpretability

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arXiv 2024年

作者： Qin, Xiaoke Martella, Francesca Subedi, Sanjeena School of Mathematics and Statistics Carleton University ON Canada Department of Statistical Sciences Sapienza University of Rome Italy

Cluster-weighted factor analyzers (CWFA) are a versatile class of mixture models designed to estimate the joint distribution of a random vector that includes a response variable along with a set of explanatory variables. They are particularly valuable in situations involving high dimensionality. This paper enhances CWFA models in two notable ways. First, it enables the prediction of multiple response variables while considering their potential interactions. Second, it identifies factors associated with disjoint groups of explanatory variables, thereby improving interpretability. This development leads to the introduction of the multivariate cluster-weighted disjoint factor analyzers (MCWDFA) model. An alternating expectation-conditional maximization algorithm is employed for parameter estimation. The effectiveness of the proposed model is assessed through an extensive simulation study that examines various scenarios. The proposal is applied to crime data from the United States, sourced from the UCI Machine Learning Repository, with the aim of capturing potential latent heterogeneity within communities and identifying groups of socioeconomic features that are similarly associated with factors predicting crime rates. Results provide valuable insights into the underlying structures influencing crime rates which may potentially be helpful for effective cluster-specific policymaking and social *** Codes 62H30 © 2024, CC BY.

关键词： expectation maximization algorithm

A novel family of beta mixture models for the differential analysis of DNA methylation data: an application to prostate cancer

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arXiv 2022年

作者： Majumdar, Koyel Silva, Romina Perry, Antoinette Sabrina Watson, Ronald William Rau, Andrea Jaffrezic, Florence Murphy, Thomas Brendan Gormley, Isobel Claire School of Mathematics and Statistics University College Dublin Ireland School of Medicine University College Dublin Ireland Conway Institute of Biomedical and Biomolecular Research University College Dublin Ireland School of Biology and Environmental Science University College Dublin Ireland INRAE UMR1313 AgroParisTech GABI Université Paris-Saclay France

Identifying differentially methylated cytosine-guanine dinucleotide (CpG) sites between benign and tumour samples can assist in understanding disease. However, differential analysis of bounded DNA methylation data often requires data transformation, reducing biological interpretability. To address this, a family of beta mixture models (BMMs) is proposed that (i) objectively infers methylation state thresholds and (ii) identifies differentially methylated CpG sites (DMCs) given untransformed, beta-valued methylation data. The BMMs achieve this through model-based clustering of CpG sites and by employing parameter constraints, facilitating application to different study settings. Inference proceeds via an expectation-maximisation algorithm, with an approximate maximization step providing tractability and computational feasibility. Performance of the BMMs is assessed through thorough simulation studies, and the BMMs are used for differential analyses of DNA methylation data from a prostate cancer study. Intuitive and biologically interpretable methylation state thresholds are inferred and DMCs are identified, including those related to genes such as GSTP1, RASSF1 and RARB, known for their role in prostate cancer development. Gene ontology analysis of the DMCs revealed significant enrichment in cancer-related pathways, demonstrating the utility of BMMs to reveal biologically relevant insights. An R package betaclust facilitates widespread use of BMMs. © 2022, CC BY.

关键词： expectation maximization algorithm

Non-linear Welfare-Aware Strategic Learning

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arXiv 2024年

作者： Xie, Tian Zhang, Xueru Department of Computer Science and Engineering The Ohio State University United States

This paper studies algorithmic decision-making in the presence of strategic individual behaviors, where an ML model is used to make decisions about human agents and the latter can adapt their behavior strategically to improve their future data. Existing results on strategic learning have largely focused on the linear setting where agents with linear labeling functions best respond to a (noisy) linear decision policy. Instead, this work focuses on general non-linear settings where agents respond to the decision policy with only "local information" of the policy. Moreover, we simultaneously consider objectives of maximizing decision-maker welfare (model prediction accuracy), social welfare (agent improvement caused by strategic behaviors), and agent welfare (the extent that ML underestimates the agents). We first generalize the agent best response model in previous works to the non-linear setting and then investigate the compatibility of welfare objectives. We show the three welfare can attain the optimum simultaneously only under restrictive conditions which are challenging to achieve in non-linear settings. The theoretical results imply that existing works solely maximizing the welfare of a subset of parties usually diminish the welfare of others. We thus claim the necessity of balancing the welfare of each party in non-linear settings and propose an irreducible optimization algorithm suitable for general strategic learning. Experiments on synthetic and real data validate the proposed algorithm. © 2024, CC BY.

关键词： expectation maximization algorithm

General Linear Threshold Models with Application to Influence maximization

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arXiv 2024年

作者： Kagan, Alexander Levina, Elizaveta Zhu, Ji Department of Statistics University of Michigan United States

A number of models have been developed for information spread through networks, often for solving the Influence maximization (IM) problem. IM is the task of choosing a fixed number of nodes to "seed" with information in order to maximize the spread of this information through the network, with applications in areas such as marketing and public health. Most methods for this problem rely heavily on the assumption of the known strength of connections between network members (edge weights), which is often unrealistic. In this paper, we develop a likelihood-based approach to estimate edge weights from the fully and partially observed information diffusion paths. We also introduce a broad class of information diffusion models, the general linear threshold (GLT) model, which generalizes the well-known linear threshold (LT) model by allowing arbitrary distributions of node activation thresholds. We then show our weight estimator is consistent under the GLT and some mild assumptions. For the special case of the standard LT model, we also present a much faster expectation-maximization approach for weight estimation. Finally, we prove that for the GLT models, the IM problem can be solved by a natural greedy algorithm with standard optimality guarantees if all node threshold distributions have concave cumulative distribution functions. Extensive experiments on synthetic and real-world networks demonstrate that the flexibility in the choice of threshold distribution combined with the estimation of edge weights significantly improves the quality of IM solutions, spread prediction, and the estimates of the node activation probabilities. © 2024, CC BY.

关键词： expectation maximization algorithm

The Generalization Error of Machine Learning algorithms

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arXiv 2024年

作者： Perlaza, Samir M. Zou, Xinying INRIA Centre Inria d’Université Côte d’Azur Sophia Antipolis06902 France The Department of Electrical and Computer Engineering Princeton University PrincetonNJ08544 United States The GAATI Mathematics Laboratory University of French Polynesia Faaa98702 French Polynesia

In this paper, the method of gaps, a technique for deriving closed-form expressions in terms of information measures for the generalization error of machine learning algorithms is introduced. The method relies on two central observations: (a) The generalization error is an average of the variation of the expected empirical risk with respect to changes on the probability measure (used for expectation);and (b) these variations, also referred to as gaps, exhibit closed-form expressions in terms of information measures. The expectation of the empirical risk can be either with respect to a measure on the models (with a fixed dataset) or with respect to a measure on the datasets (with a fixed model), which results in two variants of the method of gaps. The first variant, which focuses on the gaps of the expected empirical risk with respect to a measure on the models, appears to be the most general, as no assumptions are made on the distribution of the datasets. The second variant develops under the assumption that datasets are made of independent and identically distributed data points. All existing exact expressions for the generalization error of machine learning algorithms can be obtained with the proposed method. Also, this method allows obtaining numerous new exact expressions, which improves the understanding of the generalization error;establish connections with other areas in statistics, e.g., hypothesis testing;and potentially, might guide algorithm designs. © 2024, CC BY.

关键词： expectation maximization algorithm

Unsupervised Satellite Image Segmentation using a Bivariate Beta type-II Mixture Model

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Unsupervised Satellite Image Segmentation using a Bivariate ...

IEEE International Conference on Computational Cybernetics

作者： Taher Ben Arab Mourad Zribi Afif Masmoudi Laboratoire d'Informatique Signal et Image de la Cote d'Opale (LISIC-EA 4491) ULCO 50 Rue Ferdinand Buisson BP 719 62228 Calais Cedex France. Laboratoire de Probabilités et Statistique Faculté des Sciences de Sfax Université de Sfax. B. P. 1171 Sfax Laboratoire d'Informatique Signal et Image de la C?te d'Opale (LISIC-EA 4491) ULCO 50 Rue Ferdinand Buisson BP 719 62228 Calais Cedex France. Laboratoire de Probabilités et Statistique Faculté des Sciences de Sfax Université de Sfax. B. P. 1171 Sfax Tunisie.

ISBN: (纸本)9781479900626

This paper presents an unsupervised satellite color image segmentation approach based on Bivariate Beta type-II. Such a method could be considered as original since it uses a K-Means clustering algorithm in order to initialize the image class number. Moreover, it exploits a Bivariate Beta type-II for statistical distributions applying it for each class. Satellite image exploitation requires the use of different approaches, especially those based on the unsupervised statistical segmentation principle. Such approaches necessitate the definition of several parameters such as image class number, class variables estimation and mixture distributions. The use of statistical image attributes has allowed us to get convincing results, provided that we ensure under the condition of having an initialization step with appropriate statistical distributions. Bivariate Beta type-II associated with a K-means clustering algorithm and expectation-maximization (EM) algorithm could be adapted to such a problem. For each image class, Bivariate Beta type-II attributes a specific distribution type according to different parameters. Different adapted algorithms (namely K-Means clustering algorithm, EM algorithm and Bivariate Beta type-II algorithm) are then applied to the satellite image segmentation problem. The efficiency of those combined algorithms is validated with the Mean Squared Errors (MSE), Signal to Noise Ratio (SNR) and Maximum Distance (MD).

关键词： Bivariate Beta type-II expectation maximization algorithm K-means clustering algorithm Mean Squared Errors Unsupervised color image segmentation