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Likelihood-based Nonparametric Receiver Operating Characteristic Curve Analysis in the Presence of Imperfect Reference Standard

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arXiv 2025年

作者： Sun, Yifan Sang, Peijun Tian, Qinglong Li, Pengfei Department of Statistics and Actuarial Science University of Waterloo Canada

In diagnostic studies, researchers frequently encounter imperfect reference standards with some misclassified labels. Treating these as gold standards can bias receiver operating characteristic (ROC) curve analysis. To address this issue, we propose a novel likelihood-based method under a nonparametric density ratio model. This approach enables the reliable estimation of the ROC curve, area under the curve (AUC), partial AUC, and Youden’s index with favorable statistical properties. To implement the method, we develop an efficient expectation-maximization algorithm algorithm. Extensive simulations evaluate its finite-sample performance, showing smaller mean squared errors in estimating the ROC curve, partial AUC, and Youden’s index compared to existing methods. We apply the proposed approach to a malaria study. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Information maximization for a broad variety of multi-armed bandit games

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arXiv 2025年

作者： Barbier–Chebbah, Alex Vestergaard, Christian L. Masson, Jean-Baptiste Institut Pasteur Université Paris Cité CNRS UMR 3571 Decision and Bayesian Computation Paris75015 France Épimethée Inria Paris France

Information and free-energy maximization are physics principles that provide general rules for an agent to optimize actions in line with specific goals and policies. These principles are the building blocks for designing decision-making policies capable of efficient performance with only partial information. Notably, the information maximization principle has shown remarkable success in the classical bandit problem and has recently been shown to yield optimal algorithms for Gaussian and sub-Gaussian reward distributions. This article explores a broad extension of physics-based approaches to more complex and structured bandit problems. To this end, we cover three distinct types of bandit problems, where information maximization is adapted and leads to strong performances. Since the main challenge of information maximization lies in avoiding over-exploration, we highlight how information is tailored at various levels to mitigate this issue, paving the way for more efficient and robust decision-making strategies. Copyright © 2025, The Authors. All rights reserved.

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

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

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

Learning a Class of Mixed Linear Regressions: Global Convergence under General Data Conditions

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arXiv 2025年

作者： Liu, Yujing Liu, Zhixin Guo, Lei Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100192 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable efforts have been devoted to the learning problem of such systems, i.e., estimating data labels and identifying model parameters, most existing investigations employ the offline algorithm, impose the strict independent and identically distributed (i.i.d.) or persistent excitation (PE) conditions on the regressor data, and provide local convergence results only. In this paper, we investigate the recursive estimation and data clustering problems for a class of stochastic MLRs with two components. To address this inherently nonconvex optimization problem, we propose a novel two-step recursive identification algorithm to estimate the true parameters, where the direction vector and the scaling coefficient of the unknown parameters are estimated by the least squares and the expectation-maximization (EM) principles, respectively. Under a general data condition, which is much weaker than the traditional i.i.d. and PE conditions, we establish the global convergence and the convergence rate of the proposed identification algorithm for the first time. Furthermore, we prove that, without any excitation condition on the regressor data, the data clustering performance including the cumulative mis-classification error and the within-cluster error can be optimal asymptotically. Finally, we provide a numerical example to illustrate the performance of the proposed learning algorithm. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

DATA DENOISING WITH SELF CONSISTENCY, VARIANCE maximization, AND THE KANTOROVICH DOMINANCE

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arXiv 2025年

作者： Hiew, Joshua Zoen-Git Lim, Tongseok Pass, Brendan de Souza, Marcelo Cruz Department of Mathematical and Statistical Sciences University of Alberta EdmontonAB Canada Mitch Daniels School of Business Purdue University West LafayetteIN47907 United States Financial System Monitoring Department Central Bank of Brazil CE Fortaleza Brazil

We introduce a new framework for data denoising, partially inspired by martingale optimal transport. For a given noisy distribution (the data), our approach involves finding the closest distribution to it among all distributions which 1) have a particular prescribed structure (expressed by requiring they lie in a particular domain), and 2) are self-consistent with the data. We show that this amounts to maximizing the variance among measures in the domain which are dominated in convex order by the data. For particular choices of the domain, this problem and a relaxed version of it, in which the self-consistency condition is removed, are intimately related to various classical approaches to denoising. We prove that our general problem has certain desirable features: solutions exist under mild assumptions, have certain robustness properties, and, for very simple domains, coincide with solutions to the relaxed problem. We also introduce a novel relationship between distributions, termed Kantorovich dominance, which retains certain aspects of the convex order while being a weaker, more robust, and easier-to-verify condition. Building on this, we propose and analyze a new denoising problem by substituting the convex order in the previously described framework with Kantorovich dominance. We demonstrate that this revised problem shares some characteristics with the full convex order problem but offers enhanced stability, greater computational efficiency, and, in specific domains, more meaningful solutions. Finally, we present simple numerical examples illustrating solutions for both the full convex order problem and the Kantorovich dominance problem. © 2025, CC BY.

关键词： expectation maximization algorithm

Optimal investment and consumption under g- expected utility and general constraints in incomplete market

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arXiv 2025年

作者： Faidi, Wahid Department of Mathematics College of Science and Humanities Shaqra University Al Quwayiyah Saudi Arabia University of Tunis El Manar LAMSIN Tunis Tunisia

This article studies the problem of utility maximization in an incomplete market under a class of nonlinear expectations and general constraints on trading strategies. Using a g-martingale method, we provide an explicit solution to our optimization problem for different utility functions and characterize an optimal investment-consumption strategy through the solutions to quadratic BSDEs. Copyright © 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