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A right-truncated Poisson mixture model for analyzing count data

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arXiv 2025年

作者： Koladjo, Babagnidé François Donte, Ricardo Anderson Sodjinou, Epiphane Ecole Nationale de Statistique de Planification et de Démographie ENSPD Université de Parakou Parakou Benin Université de Parakou Parakou Benin Faculté d’Agronomie Université de Parakou Parakou Benin

In this paper, we investigate right-truncated count data models incorporating covariates into the parameters. A regression method is proposed to model right-truncated count data exhibiting high heterogeneity. The study encompasses the formulation of the proposed model, parameter estimation using an expectation Maximisation (EM) algorithm, and the properties of these estimators. We also discuss model selection procedures for the proposed method. Furthermore, a Monte Carlo simulation study is presented to assess the performance of the proposed method and the model selection process. Results express accuracy under regularity conditions of the model. The method is used to analyze the determinants of the degree of adherence to preventive measures during the COVID-19 pandemic in northern Benin. The results show that a right-truncated Poisson mixture model is adequate to analyze these data. Using this model, we conclude that age, education level, and household size determine an individual’s degree of adherence to preventive measures during COVID-19 in this region. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Estimation and Inference for Unbalanced Panel Data Models with Interactive Fixed Effects

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SSRN

SSRN 2025年

作者： Su, Liangjun Wang, Fa Wang, Yiren School of Economics and Management Tsinghua University China Department of Finance School of Economics Peking University China College of Finance and Statistics Hunan University China

This paper establishes the inferential theory for unbalanced panel data models with interactive fixed effects. We propose a two-step estimation algorithm with the first step obtaining an initial consistent estimator followed by an alternating maximization procedure. We prove that the alternating maximization procedure is a contractionary mapping and the final estimator is asymptotically normal, as long as the initial estimator is consistent. We also develop analytical bias corrections according to the derived asymptotic bias expressions and the observed missing pattern. Our results cover important missing patterns such as completely exogenous missing, selection on regressors/factors/loadings and block/staggered missing, and we also show that our results can be readily extended to cases with a Heckman correction term or more general settings. An empirical analysis of the U.S. state-level tax rates from 1951 to 2000 with missing data reveals persistence in tax rates, while state income influences different taxes in varying ways. © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Regularized Parameter Estimation in Mixed Model Trace Regression

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arXiv 2025年

作者： Hultman, Ian Srivastava, Sanvesh Department of Statistics and Actuarial Science University of Iowa United States

We introduce mixed model trace regression (MMTR), a mixed model linear regression extension for scalar responses and high-dimensional matrix-valued covariates. MMTR’s fixed effects component is equivalent to trace regression, with an element-wise lasso penalty imposed on the regression coefficients matrix to facilitate the estimation of a sparse mean parameter. MMTR’s key innovation lies in modeling the covariance structure of matrix-variate random effects as a Kronecker product of low-rank row and column covariance matrices, enabling sparse estimation of the covariance parameter through low-rank constraints. We establish identifiability conditions for the estimation of row and column covariance matrices and use them for rank selection by applying group lasso regularization on the columns of their respective Cholesky factors. We develop an expectation-maximization (EM) algorithm extension for numerically stable parameter estimation in high-dimensional applications. MMTR achieves estimation accuracy comparable to leading regularized quasi-likelihood competitors across diverse simulation studies and attains the lowest mean square prediction error compared to its competitors on a publicly available image dataset. © 2025, CC BY.

关键词： expectation maximization algorithm

Bound-Constrained expectation maximization for Weibull Competing-Risks Device Reliability

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IEEE TRANSACTIONS ON DEVICE AND MATERIALS RELIABILITY 2024年第4期24卷 556-570页

作者： Chakraborty, Uttara Boning, Duane S. Thompson, Carl V. MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA MIT Dept Elect Engn & Comp Sci Microsyst Technol Labs Cambridge MA 02139 USA MIT Dept Mat Sci & Engn Mat Res Lab Cambridge MA 02139 USA

Estimating the reliability of electronic devices involves identification of failure mechanisms and prediction of lifetimes. For parameter estimation and failure mode identification in Weibull competing-risks models, a differential-evolution-based global optimization approach has recently been developed, with the superiority of that approach demonstrated over the best-known local methods for the problem. In an effort to design a method faster than differential evolution for this problem, the present paper develops a new type of expectation maximization (EM) algorithm that is capable of handling bound constraints while optimizing the parameters of the Weibull component distributions. The differential-evolution-based approach guarantees a feasible, but not necessarily high-quality, solution in every run, while the proposed method offers no such guarantee. Despite this lack of guarantee, the proposed method is seen to produce results of a quality highly competitive with differential evolution. Numerical results on ten test cases, based on three real test datasets and two synthetic datasets, show that in terms of solution quality, the proposed method is competitive with differential evolution, while offering an average savings of about 64% in the computation time. Comparative performance analyses with the standard EM algorithm and the best-known local method L-BFGS-B are also provided. The numerical results are statistically validated. A new approach to model improvement via selective failure analysis is demonstrated as an application of the proposed algorithm. The proposed algorithm has the potential to be used for general-purpose likelihood maximization involving latent variables in diverse domains.

关键词： Failure analysis Shape Stress Maximum likelihood estimation Materials reliability Data models Random variables Competing-risks model electronic packaging expectation maximization algorithm maximum likelihood estimation reliability

Quasi maximum likelihood estimation of high-dimensional approximate dynamic matrix factor models via the EM algorithm

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arXiv 2025年

作者： Barigozzi, Matteo Trapin, Luca Department of Economics University of Bologna Piazza Scaravilli 2 Bologna Italy Department of Statistical Sciences University of Bologna Via Belle Arti 41 Bologna Italy

This paper considers an approximate dynamic matrix factor model that accounts for the time series nature of the data by explicitly modelling the time evolution of the factors. We study Quasi Maximum Likelihood estimation of the model parameters based on the expectation maximization (EM) algorithm, implemented jointly with the Kalman smoother which gives estimates of the factors. This approach allows to easily handle arbitrary patterns of missing data. We establish the consistency of the estimated loadings and factor matrices as the sample size T and the matrix dimensions p1 and p2 diverge to infinity. The finite sample properties of the estimators are assessed through a large simulation study and an application to a financial dataset of volatility proxies. © 2025, CC BY.

关键词： expectation maximization algorithm

Probabilistic Formulations for System Identification of Linear Dynamics with Bilinear Observation Models

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arXiv 2025年

作者： Liu, Diyou Khosravi, Mohammad Delft Center for Systems and Control Delft University of Technology Delft Netherlands

In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate the identification problem as the estimation of the parameters defining the mathematical model of the system using the observed input-output data. To this end, we propose two probabilistic frameworks. The first framework employs the Maximum Likelihood (ML) approach, which accurately finds the optimal parameter estimates by maximizing a likelihood function. Subsequently, we develop a tractable first-order method to solve the optimization problem corresponding to the proposed ML approach. Additionally, to further improve tractability and computational efficiency of the estimation of the parameters, we introduce an alternative framework based on the expectation–maximization (EM) approach, which estimates the parameters using an appropriately designed cost function. We show that the EM cost function is invex, which ensures the existence and uniqueness of the optimal solution. Furthermore, we derive the closed-form solution for the optimal parameters and also prove the recursive feasibility of the EM procedure. Through extensive numerical experiments, the practical implementation of the proposed approaches is demonstrated, and their estimation efficacy is verified and compared, highlighting the effectiveness of the methods to accurately estimate the system parameters and their potential for real-world applications in scenarios involving bilinear observation structures. © 2025, CC BY.

关键词： expectation maximization algorithm

Sublinear Variational Optimization of Gaussian Mixture Models with Millions to Billions of Parameters

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arXiv 2025年

作者： Salwig, Sebastian Kahlke, Till Hirschberger, Florian Forster, Dennis Lücke, Jörg Carl von Ossietzky University Oldenburg Faculty VI Machine Learning Oldenburg Germany Frankfurt University of Applied Sciences Faculty 3 Data Analytics and AI Frankfurt am Main Germany

Gaussian Mixture Models (GMMs) range among the most frequently used machine learning models. However, training large, general GMMs becomes computationally prohibitive for datasets with many data points N of high-dimensionality D. For GMMs with arbitrary covariances, we here derive a highly efficient variational approximation, which is integrated with mixtures of factor analyzers (MFAs). For GMMs with C components, our proposed algorithm significantly reduces runtime complexity per iteration from O(NCD2) to a complexity scaling linearly with D and remaining constant w.r.t. C. Numerical validation of this theoretical complexity reduction then shows the following: the distance evaluations required for the entire GMM optimization process scale sublinearly with NC. On large-scale benchmarks, this sublinearity results in speed-ups of an order-of-magnitude compared to the state-of-the-art. As a proof of concept, we train GMMs with over 10 billion parameters on about 100 million images, and observe training times of approximately nine hours on a single state-of-the-art CPU. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Estimating the Percentage of GBS Advantage in Gaussian expectation Problems

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arXiv 2025年

作者： Andersen, Jørgen Ellegaard Shan, Shan Center for Quantum Mathematics University of Southern Denmark Denmark Danish Institute of Advanced Study University of Southern Denmark Denmark

Gaussian Boson Sampling (GBS), which can be realized with a photonic quantum computing model, perform some special kind of sampling tasks. In [4], we introduced algorithms that use GBS samples to approximate Gaussian expectation problems. We found a non-empty open subset of the problem space where these algorithms achieve exponential speedup over the standard Monte Carlo (MC) method. This speedup is defined in terms of the guaranteed sample size to reach the same accuracy ϵ and success probability δ under the (ϵ, δ) multiplicative error approximation scheme. In this paper, we enhance our original approach by optimizing the average photon number in the GBS distribution to match the specific Gaussian expectation problem. We provide updated estimates of the guaranteed sample size for these improved algorithms and quantify the proportion of problem space where they outperform MC. Numerical results indicate that the proportion of the problem space where our improved algorithms have an advantage is substantial, and the advantage gained is significant. Notably, for certain special cases, our methods consistently outperform MC across nearly 100% of the problem space. © 2025, CC BY.

关键词： expectation maximization algorithm

Neural network-based identification of state-space switching nonlinear systems

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arXiv 2025年

作者： Zhang, Yanxin Yu, Chengpu Fabiani, Filippo School of Automation Beijing Institute of Technology Beijing100081 China IMT School for Advanced Studies Lucca Piazza San Francesco 19 Lucca55100 Italy

We design specific neural networks (NNs) for the identification of switching nonlinear systems in the state-space form, which explicitly model the switching behavior and address the inherent coupling between system parameters and switching modes. This coupling is specifically addressed by leveraging the expectation-maximization (EM) framework. In particular, our technique will combine a moving window approach in the E-step to efficiently estimate the switching sequence, together with an extended Kalman filter (EKF) in the M-step to train the NNs with a quadratic convergence rate. Extensive numerical simulations, involving both academic examples and a battery charge management system case study, illustrate that our technique outperforms available ones in terms of parameter estimation accuracy, model fitting, and switching sequence identification. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm