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

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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

Estimation of finite population proportions for small areas – a statistical data integration approach

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arXiv 2023年

作者： Sen, Aditi Lahiri, Partha University of Maryland College Park United States The Joint Program in Survey Methodology Department of Mathematics University of Maryland College ParkMD20742 United States

Empirical best prediction (EBP) is a well-known method for producing reliable proportion estimates when the primary data source provides only small or no sample from finite populations. There are potential challenges in implementing existing EBP methodology such as limited auxiliary variables in the frame (not adequate for building a reasonable working predictive model) or unable to accurately link the sample to the finite population frame due to absence of identifiers. In this paper, we propose a new data linkage approach where the finite population frame is replaced by a big probability sample, having a large set of auxiliary variables but not the outcome binary variable of interest. We fit an assumed model on the small probability sample and then impute the outcome variable for all units of the big sample to obtain standard weighted proportions. We develop a new adjusted maximum likelihood (ML) method so that the estimate of model variance doesn’t fall on the boundary, which is otherwise encountered in commonly used ML method. We also propose an estimator of the mean squared prediction error using a parametric bootstrap method and address computational issues by developing an efficient expectation maximization algorithm. The proposed methodology is illustrated in the context of election projection for small areas. © 2023, CC BY.

关键词： expectation maximization algorithm

Block Coordinate DC Programming

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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

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

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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

Adaptive maximization of social welfare

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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

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

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

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