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arXiv 2024年

作者： Liu, Panfeng Qiu, Guoliang Tao, Biaoshuai Yang, Kuan Shanghai Jiao Tong University China

We study cascades in social networks with the independent cascade (IC) model and the Susceptible-Infected-recovered (SIR) model. The well-studied IC model fails to capture the feature of node recovery, and the SIR model is a variant of the IC model with the node recovery feature. In the SIR model, by computing the probability that a node successfully infects another before its recovery and viewing this probability as the corresponding IC parameter, the SIR model becomes an "out-going-edge-correlated" version of the IC model: the events of the infections along different out-going edges of a node become dependent in the SIR model, whereas these events are independent in the IC model. In this paper, we thoroughly compare the two models and examine the effect of this extra dependency in the SIR model. By a carefully designed coupling argument, we show that the seeds in the IC model have a stronger influence spread than their counterparts in the SIR model, and sometimes it can be significantly stronger. Specifically, we prove that, given the same network, the same seed sets, and the parameters of the two models being set based on the above-mentioned equivalence, the expected number of infected nodes at the end of the cascade for the IC model is weakly larger than that for the SIR model, and there are instances where this dominance is significant. We also study the influence maximization problem (the optimization problem of selecting a set of nodes as initial seeds in a social network to maximize their influence) with the SIR model. We show that the above-mentioned difference in the two models yields different seed-selection strategies, which motivates the design of influence maximization algorithms specifically for the SIR model. We design efficient approximation algorithms with theoretical guarantees by adapting the reverse-reachable-set-based algorithms, commonly used for the IC model, to the SIR model. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

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Learning Submodular Sequencing from Samples

arXiv

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arXiv 2024年

作者： Yuan, Jing Tang, Shaojie Department of Computer Science and Engineering The University of North Texas United States Department of Management Science and Systems University at Buffalo United States

This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility function, we assume that we are given only a set of samples. Each sample includes a random sequence of items and its associated utility. We present an algorithm that, given polynomially many samples drawn from a two-stage uniform distribution, achieves an approximation ratio dependent on the curvature of individual submodular functions. Our results apply in a wide variety of real-world scenarios, such as ranking products in online retail platforms, where complete knowledge of the utility function is often impossible to obtain. Our algorithm gives an empirically useful solution in such contexts, thus proving that limited data can be of great use in sequencing tasks. From a technical perspective, our results extend prior work on "optimization from samples" by generalizing from optimizing a set function to a sequence-dependent function. © 2024, CC BY.

关键词： expectation maximization algorithm

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Community Detection with Heterogeneous Block Covariance Model

arXiv

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arXiv 2024年

作者： Li, Xiang Zhao, Yunpeng Pan, Qing Hao, Ning Department of Statistics George Washington University United States Department of Statistics Colorado State University United States Department of Biostatistics and Bioinformatics George Washington University United States Department of Mathematics University of Arizona United States

Community detection is the task of clustering objects based on their pairwise relationships. Most of the model-based community detection methods, such as the stochastic block model and its variants, are designed for networks with binary (yes/no) edges. In many practical scenarios, edges often possess continuous weights, spanning positive and negative values, which reflect varying levels of connectivity. To address this challenge, we introduce the heterogeneous block covariance model (HBCM) that defines a community structure within the covariance matrix, where edges have signed and continuous weights. Furthermore, it takes into account the heterogeneity of objects when forming connections with other objects within a community. A novel variational expectation-maximization algorithm is proposed to estimate the group membership. The HBCM provides provable consistent estimates of memberships, and its promising performance is observed in numerical simulations with different setups. The model is applied to a single-cell RNA-seq dataset of a mouse embryo and a stock price dataset. Supplementary materials for this article are available online. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

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High-Dimensional Markov-switching Ordinary Differential Processes

arXiv

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arXiv 2024年

作者： Tsai, Katherine Kolar, Mladen Koyejo, Sanmi Department of Electrical and Computer Engineering University of Illinois Urbana-Champaign United States Marshall School of Business University of Southern California United States Department of Computer Science Stanford University United States

We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological systems, control systems, and other domains;however, limited research has been conducted on reconstructing the generating processes from observations. In contrast, many physical systems, such as human brains, cannot be directly experimented upon and rely on observations to infer the underlying systems. To address this gap, this manuscript presents a comprehensive study of the model, encompassing algorithm design, optimization guarantees, and quantification of statistical errors. Specifically, we develop a two-stage algorithm that first recovers the continuous sample path from discrete samples and then estimates the parameters of the processes. We provide novel theoretical insights into the statistical error and linear convergence guarantee when the processes are β-mixing. Our analysis is based on the truncation of the latent posterior processes and demonstrates that the truncated processes approximate the true processes under mixing conditions. We apply this model to investigate the differences in resting-state brain networks between the ADHD group and normal controls, revealing differences in the transition rate matrices of the two groups. © 2024, CC BY.

关键词： expectation maximization algorithm

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A Model-Based Clustering Approach for Bounded Data Using Transformation-Based Gaussian Mixture Models

arXiv

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arXiv 2024年

作者： Scrucca, Luca Department of Statistical Sciences University of Bologna Italy

The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data. Building on the transformation-based approach to Gaussian mixture density estimation introduced by Scrucca (2019), we extend this framework to develop a probabilistic clustering algorithm for data with bounded support that allows for accurate clustering while respecting the natural bounds of the variables. In our proposal, a flexible range-power transformation is employed to map the data from its bounded domain to the unrestricted real space, hence enabling the estimation of Gaussian mixture models in the transformed space. This approach leads to improved cluster recovery and interpretation, especially for complex distributions within bounded domains. The performance of the proposed method is evaluated through real-world data applications involving both fully and partially bounded data, in both univariate and multivariate settings. The results demonstrate the effectiveness and advantages of our approach over traditional and advanced model-based clustering techniques that employ distributions with bounded support. © 2024, CC BY.

关键词： expectation maximization algorithm

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A Robust Probability-based Joint Registration Method of Multiple Point Clouds Considering Local Consistency

arXiv

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arXiv 2024年

作者： Su, Ling-Jie Xu, Wei Zhao, Shu-Yang Cheng, Yu-Qi Li, Wen-Long The State Key Laboratory of Intelligent Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China

In robotic inspection, joint registration of multiple point clouds is an essential technique for estimating the transformation relationships between measured parts, such as multiple blades in a propeller. However, the presence of noise and outliers in the data can significantly impair the registration performance by affecting the correctness of correspondences. To address this issue, we incorporate local consistency property into the probability-based joint registration method. Specifically, each measured point set is treated as a sample from an unknown Gaussian Mixture Model (GMM), and the registration problem is framed as estimating the probability model. By incorporating local consistency into the optimization process, we enhance the robustness and accuracy of the posterior distributions, which represent the one-to-all correspondences that directly determine the registration results. Effective closed-form solution for transformation and probability parameters are derived with expectation-maximization (EM) algorithm. Extensive experiments demonstrate that our method outperforms the existing methods, achieving high accuracy and robustness with the existence of noise and outliers. The code will be available at https://***/sulingjie/JPRLC_registration. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

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Multi-objective Reinforcement Learning with Nonlinear Preferences: Provable Approximation for Maximizing Expected Scalarized Return

arXiv

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arXiv 2023年

作者： Peng, Nianli Tian, Muhang Fain, Brandon Harvard University CambridgeMA United States Duke University DurhamNC United States

We study multi-objective reinforcement learning with nonlinear preferences over trajectories. That is, we maximize the expected value of a nonlinear function over accumulated rewards (expected scalarized return or ESR) in a multi-objective Markov Decision Process (MOMDP). We derive an extended form of Bellman optimality for nonlinear optimization that explicitly considers time and current accumulated reward. Using this formulation, we describe an approximation algorithm for computing an approximately optimal non-stationary policy in pseudopolynomial time for smooth scalarization functions with a constant number of rewards. We prove the approximation analytically and demonstrate the algorithm experimentally, showing that there can be a substantial gap between the optimal policy computed by our algorithm and alternative baselines. © 2023, CC BY-NC-SA.

关键词： expectation maximization algorithm

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Block Coordinate DC Programming

arXiv

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arXiv 2024年

作者： Maskan, Hoomaan Halvachi, Paniz Sra, Suvrit Yurtsever, Alp Umeå University Sweden Massachusetts Institute of Technology United States Technical University of Munich Germany

We introduce an extension of the Difference of Convex algorithm (DCA) in the form of a block coordinate approach for problems with separable structure. For n coordinate-blocks and k iterations, our main result proves a non-asymptotic convergence rate of O(n/k) for the proposed method. Furthermore, leveraging the connection between DCA and expectation maximization (EM), we propose a block coordinate EM *** Codes 90C26 Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

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On an EM-based closed-form solution for 2 parameter IRT models

arXiv

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arXiv 2024年

作者： Stefano, Noventa Faleh, Roberto Kelava, Augustin Methods Center Universität Tübingen Germany

It is a well-known issue that in Item Response Theory models there is no closed-form for the maximum likelihood estimators of the item parameters. Parameter estimation is therefore typically achieved by means of numerical methods like gradient search. The present work has a two-fold aim: On the one hand, we revise the fundamental notions associated to the item parameter estimation in 2 parameter Item Response Theory models from the perspective of the complete-data likelihood. On the other hand, we argue that, within an expectation-maximization approach, a closed-form for discrimination and difficulty parameters can actually be obtained that simply corresponds to the Ordinary Least Square solution. © 2024, CC BY.

关键词： expectation maximization algorithm

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Adaptive maximization of social welfare

arXiv

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arXiv 2023年

作者： Cesa-Bianchi, Nicolò Colomboni, Roberto Kasy, Maximilian Università degli Studi di Milano Politecnico di Milano Italy Department of Economics University of Oxford United Kingdom

We consider the problem of repeatedly choosing policies to maximize social welfare. Welfare is a weighted sum of private utility and public revenue. Earlier outcomes inform later policies. Utility is not observed, but indirectly inferred. Response functions are learned through experimentation. We derive a lower bound on regret, and a matching adversarial upper bound for a variant of the Exp3 algorithm. Cumulative regret grows at a rate of T2/3. This implies that (i) welfare maximization is harder than the multi-armed bandit problem (with a rate of T1/2 for finite policy sets), and (ii) our algorithm achieves the optimal rate. For the stochastic setting, if social welfare is concave, we can achieve a rate of T1/2 (for continuous policy sets), using a dyadic search algorithm. We analyze an extension to nonlinear income taxation, and sketch an extension to commodity taxation. We compare our setting to monopoly pricing (which is easier), and price setting for bilateral trade (which is harder). © 2023, CC BY-NC-SA.

关键词： expectation maximization algorithm

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