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Optimality Gap of Decentralized Submodular maximization under Probabilistic Communication

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arXiv 2024年

作者： Vendrell, Joan Kia, Solmaz The Mechanical and Aerospace Engineering Department of University of California Irvie IrvineCA United States

This paper considers the problem of decentralized submodular maximization subject to partition matroid constraint using a sequential greedy algorithm with probabilistic inter-agent message-passing. We propose a communication-aware framework where the probability of successful communication between connected devices is considered. Our analysis introduces the notion of the probabilistic optimality gap, highlighting its potential influence on determining the message-passing sequence based on the agent's broadcast reliability and strategic decisions regarding agents that can broadcast their messages multiple times in a resource-limited environment. This work not only contributes theoretical insights but also has practical implications for designing and analyzing decentralized systems in uncertain communication environments. A numerical example demonstrates the impact of our results. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm

Ensemble Prediction via Covariate-dependent Stacking

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arXiv 2024年

作者： Wakayama, Tomoya Sugasawa, Shonosuke Graduate School of Economics The University of Tokyo Japan Faculty of Economics Keio University Japan

This paper presents a novel approach to ensemble prediction called "Covariate-dependent Stacking" (CDST). Unlike traditional stacking methods, CDST allows model weights to vary flexibly as a function of covariates, thereby enhancing predictive performance in complex scenarios. We formulate the covariate-dependent weights through combinations of basis functions, estimate them by optimizing cross-validation, and develop an expectation-maximization algorithm, ensuring computational efficiency. To analyze the theoretical properties, we establish an oracle inequality regarding the expected loss to be minimized for estimating model weights. Through comprehensive simulation studies and an application to large-scale land price prediction, we demonstrate that CDST consistently outperforms conventional model averaging methods, particularly on datasets where some models fail to capture the underlying complexity. Our findings suggest that CDST is especially valuable for, but not limited to, spatio-temporal prediction problems, offering a powerful tool for researchers and practitioners in various fields of data analysis. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Modeling sparsity in count-weighted networks

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arXiv 2024年

作者： Cerqueira, Andressa Costa, Laila L.S. Department of Statistics Universidade Federal de São Carlos Brazil

Community detection methods have been extensively studied to recover communities structures in network data. While many models and methods focus on binary data, real-world networks also present the strength of connections, which could be considered in the network analysis. We propose a probabilistic model for generating weighted networks that allows us to control network sparsity and incorporates degree corrections for each node. We propose a community detection method based on the Variational expectation-maximization (VEM) algorithm. We show that the proposed method works well in practice for simulated networks. We analyze the Brazilian airport network to compare the community structures before and during the COVID-19 *** Codes 62Fxx Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Deep Out-of-Distribution Uncertainty Quantification via Weight Entropy maximization

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arXiv 2023年

作者： de Mathelin, Antoine Deheeger, François Mougeot, Mathilde Vayatis, Nicolas Manufacture Française des pneumatiques Michelin Clermont-Ferrand63000 France Centre Borelli Université Paris-Saclay CNRS ENS Paris-Saclay Gif-sur-Yvette91190 France

This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. It proposes a practical solution to the lack of prediction diversity observed recently for standard approaches when used out-of-distribution (Ovadia et al., 2019;Liu et al., 2021). Considering that this issue is mainly related to a lack of weight diversity, we claim that standard methods sample in "over-restricted" regions of the weight space due to the use of "over-regularization" processes, such as weight decay and zero-mean centered Gaussian priors. We propose to solve the problem by adopting the maximum entropy principle for the weight distribution, with the underlying idea to maximize the weight diversity. Under this paradigm, the epistemic uncertainty is described by the weight distribution of maximal entropy that produces neural networks "consistent" with the training observations. Considering stochastic neural networks, a practical optimization is derived to build such a distribution, defined as a trade-off between the average empirical risk and the weight distribution entropy. We provide both theoretical and numerical results to assess the efficiency of the approach. In particular, the proposed algorithm appears in the top three best methods in all configurations of an extensive out-of-distribution detection benchmark including more than thirty competitors. © 2023, CC BY.

关键词： expectation maximization algorithm

A Low-dose CT Reconstruction Network Based on TV-regularized OSEM algorithm

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arXiv 2024年

作者： An, Ran Zhang, Yinghui Chen, Xi Li, Lemeng Chen, Ke Li, Hongwei The School of Mathematical Sciences Capital Normal University Beijing100048 China The Centre for Mathematical Imaging Techniques University of Liverpool LiverpoolL69 7ZL United Kingdom The LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Department of Mathematics and Statistics University of Strathclyde GlasgowG1 1XQ United Kingdom

Low-dose computed tomography (LDCT) offers significant advantages in reducing the potential harm to human bodies. However, reducing the X-ray dose in CT scanning often leads to severe noise and artifacts in the reconstructed images, which might adversely affect diagnosis. By utilizing the expectation maximization (EM) algorithm, statistical priors could be combined with artificial priors to improve LDCT reconstruction quality. However, conventional EM-based regularization methods adopt an alternating solving strategy, i.e. full reconstruction followed by image-regularization, resulting in over-smoothing and slow convergence. In this paper, we propose to integrate TV regularization into the "M"-step of the EM algorithm, thus achieving effective and efficient regularization. Besides, by employing the Chambolle-Pock (CP) algorithm and the ordered subset (OS) strategy, we propose the OSEM-CP algorithm for LDCT reconstruction, in which both reconstruction and regularization are conducted view-by-view. Furthermore, by unrolling OSEM-CP, we propose an end-to-end reconstruction neural network (NN), named OSEM-CPNN, with remarkable performance and efficiency that achieves high-quality reconstructions in just one full-view iteration. Experiments on different models and datasets demonstrate our methods' outstanding performance compared to traditional and state-of-the-art deep-learning methods. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Outlier Detection algorithm Based on Gaussian Mixture Model

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Outlier Detection Algorithm Based on Gaussian Mixture Model

IEEE International Conference on Power, Intelligent Computing and Systems

作者： Wenbo Liu Delong Cui Zhiping Peng Jihai Zhong Faulty of Computer Science Guangdong University of Technology Department of Computer and Electronic Information Guangdong University of Petrochemical Technology

ISBN: (纸本)9781728137216

Outlier detection is an important aspect in the field of data mining. In order to solve the problem of outlier detection in high-dimensional datasets, an outlier detection algorithm based on Gaussian mixture model is proposed. First of all, for the data set to be tested, the global optimization expectation maximization algorithm is used to fit a Gaussian mixture model, and then the three-time standard deviation principle is introduced on each Gaussian component, the outlier is the data point outside the range of the mean deviation of the mean value of three times the standard deviation. Through the experiments on the simulation dataset and the real data set, the effectiveness of the algorithm on the outlier detection of high-dimensional data sets is verified.

关键词： Data mining Outlier detection Gaussian mixture model expectation maximization algorithm The principle of three times standard deviation expectation-maximisation algorithm data mining Mixture models outliers Detection algorithms Dataset Mean deviation mean value

SPO: Sequential Monte Carlo Policy Optimisation

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arXiv 2024年

作者： Macfarlane, Matthew V. Toledo, Edan Byrne, Donal Duckworth, Paul Laterre, Alexandre University of Amsterdam Netherlands InstaDeep

Leveraging planning during learning and decision-making is central to the long-term development of intelligent agents. Recent works have successfully combined tree-based search methods and self-play learning mechanisms to this end. However, these methods typically face scaling challenges due to the sequential nature of their search. While practical engineering solutions can partly overcome this, they often result in a negative impact on performance. In this paper, we introduce SPO: Sequential Monte Carlo Policy Optimisation, a model-based reinforcement learning algorithm grounded within the expectation Maximisation (EM) framework. We show that SPO provides robust policy improvement and efficient scaling properties. The sample-based search makes it directly applicable to both discrete and continuous action spaces without modifications. We demonstrate statistically significant improvements in performance relative to model-free and model-based baselines across both continuous and discrete environments. Furthermore, the parallel nature of SPO’s search enables effective utilisation of hardware accelerators, yielding favourable scaling laws. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Enhancing parameter estimation in finite mixture of generalized normal distributions

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arXiv 2024年

作者： Duttilo, Pierdomenico Gattone, Stefano Antonio Department of Statistical Sciences University of Padova Padova Italy DiSEGS University "G. d’Annunzio" of Chieti-Pescara Pescara Italy

Mixtures of generalized normal distributions (MGND) have gained popularity for modelling datasets with complex statistical behaviours. However, the estimation of the shape parameter within the maximum likelihood framework is quite complex, presenting the risk of numerical and degeneracy issues. This study introduced an expectation conditional maximization algorithm that includes an adaptive step size function within Newton-Raphson updates of the shape parameter and a modified criterion for stopping the EM iterations. Through extensive simulations, the effectiveness of the proposed algorithm in overcoming the limitations of existing approaches, especially in scenarios with high shape parameter values, high parameters overalp and low sample sizes, is shown. A detailed comparative analysis with a mixture of normals and Student-t distributions revealed that the MGND model exhibited superior goodness-of-fit performance when used to fit the density of the returns of 50 stocks belonging to the Euro Stoxx index. © 2024, CC BY.

关键词： expectation maximization algorithm

A Generalized Mixture Cure Model Incorporating Known Cured Individuals

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arXiv 2024年

作者： Karakatsoulis, Georgios Institute of Applied Biosciences Centre for Research and Technology Hellas Thessaloniki Greece

The Mixture Cure (MC) models constitute an appropriate and easily interpretable method when studying a time-to-event variable in a population comprised of both susceptible and cured individuals. In literature, those models usually assume that the latter are unobservable. However, there are cases in which a cured individual may be identified. For example, when studying the distant metastasis during the lifetime or the miscarriage during pregnancy, individuals that have died without a metastasis or have given birth are certainly non-susceptible. The same also holds when studying the x-year overall survival or the death during hospital stay. Common MC models ignore this information and consider them all censored, thus yielding in risk of assigning low immune probabilities to cured individuals. In this study, we consider a MC model that incorporates known information on cured individuals, with the time to cure identification being either deterministic or stochastic. We use the expectation-maximization algorithm to derive the maximum likelihood estimators. Furthermore, we compare different strategies that account for cure information such as (1) assigning infinite times to event for known cured cases and adjusting the traditional model and (2) considering only the probability of cure identification but ignoring the time until that happens. Theoretical results and simulations demonstrate the value of the proposed model especially when the time to cure identification is stochastic, increasing precision and decreasing the mean squared error. On the other hand, the traditional models that ignore the known cured information perform well when the curation is achieved after a known cutoff point. Moreover, through simulations the comparisons of the different strategies are examined, as possible alternatives to the complete-information model. © 2024, CC BY.

关键词： expectation maximization algorithm