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Dual NUP Representations and Min-maximization in Factor Graphs

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arXiv 2025年

作者： Li, Yun-Peng Loeliger, Hans-Andrea Dept. of Information Technology and Electrical Engineering ETH Zürich Switzerland

Normals with unknown parameters (NUP) can be used to convert nontrivial model-based estimation problems into iterations of linear least-squares or Gaussian estimation problems. In this paper, we extend this approach by augmenting factor graphs with convex-dual variables and pertinent NUP representations. In particular, in a state space setting, we propose a new iterative forward-backward algorithm that is dual to a recently proposed backward-forward algorithm. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Optimal algorithms in Linear Regression under Covariate Shift: On the Importance of Precondition

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arXiv 2025年

作者： Liu, Yuanshi Zhang, Haihan Chen, Qian Fang, Cong Peking University China Huazhong University of Science and Technology China

A common pursuit in modern statistical learning is to attain satisfactory generalization out of the source data distribution (OOD). In theory, the challenge remains unsolved even under the canonical setting of covariate shift for the linear model. This paper studies the foundational (high-dimensional) linear regression where the ground truth variables are confined to an ellipse-shape constraint and addresses two fundamental questions in this regime: (i) given the target covariate matrix, what is the min-max optimal algorithm under covariate shift? (ii) for what kinds of target classes, the commonly-used SGD-type algorithms achieve optimality? Our analysis starts with establishing a tight lower generalization bound via a Bayesian Cramer-Rao inequality. For (i), we prove that the optimal estimator can be simply a certain linear transformation of the best estimator for the source distribution. Given the source and target matrices, we show that the transformation can be efficiently computed via a convex program. The min-max optimal analysis for SGD leverages the idea that we recognize both the accumulated updates of the applied algorithms and the ideal transformation as preconditions on the learning variables. We provide sufficient conditions when SGD with its acceleration variants attain optimality. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

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

Variations on the expectation Due to Changes in the Probability Measure

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arXiv 2025年

作者： Perlaza, Samir M. Bisson, Gaetan INRIA Centre Inria d’Université Côte d’Azur Sophia Antipolis France ECE Dept. Princeton University Princeton08544 NJ United States Laboratoire GAATI University of French Polynesia French Polynesia

Closed-form expressions are presented for the variation of the expectation of a given function due to changes in the probability measure used for the expectation. They unveil interesting connections with Gibbs probabi... 详细信息

关键词： expectation maximization algorithm

Identification of non-causal systems with random switching modes (Extended Version)

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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 consider the identification of non-causal systems with random switching modes (NCS-RSM), a class of models essential for describing typical power load management and department store inventory dynamics. The simultaneous identification of causal-and-anticausal subsystems, along with the presence of random switching sequences, however, make the overall identification problem particularly challenging. To this end, we develop an expectation-maximization (EM) based system identification technique, where the E-step proposes a modified Kalman filter (KF) to estimate the states and switching sequences of causal-and-anticausal subsystems, while the M-step consists in a switching least-squares algorithm to estimate the parameters of individual subsystems. We establish the main convergence features of the proposed identification procedure, also providing bounds on the parameter estimation errors under mild conditions. Finally, the effectiveness of our identification method is validated through two numerical simulations. Copyright © 2025, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Joint ML-Bayesian Approach to Adaptive Radar Detection in the presence of Gaussian Interference

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arXiv 2025年

作者： Yin, Chaoran Wang, Tianqi Yan, Linjie Hao, Chengpeng Farina, Alfonso Orlando, Danilo Institute of Acoustics Chinese Academy of Sciences Beijing100190 China Selex ES. Roma Italy Dipartimento di Ingegneria dell’Informazione Universita di Pisa Via Caruso 16 Pisa56122 Italy

This paper addresses the adaptive radar target detection problem in the presence of Gaussian interference with unknown statistical properties. To this end, the problem is first formulated as a binary hypothesis test, and then we derive a detection architecture grounded on the hybrid of Maximum Likelihood (ML) and Maximum A Posterior (MAP) approach. Specifically, we resort to the hidden discrete latent variables in conjunction with the expectation-maximization (EM) algorithms which cyclically updates the estimates of the unknowns. In this framework, the estimates of the a posteriori probabilities under each hypothesis are representative of the inherent nature of data and used to decide for the presence of a potential target. In addition, we prove that the developed detection scheme ensures the desired Constant False Alarm Rate property with respect to the unknown interference covariance matrix. Numerical examples obtained through synthetic and real recorded data corroborate the effectiveness of the proposed architecture and show that the MAP-based approach ensures evident improvement with respect to the conventional generalized likelihood ratio test at least for the considered scenarios and parameter setting. Copyright © 2025, The Authors. All rights reserved.

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

Fenchel-Young Variational Learning

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arXiv 2025年

作者： Sklaviadis, Sophia Agrawal, Sweta Farinhas, Antonio Martins, Andre Figueiredo, Mario Instituto de Telecomunicacoes Lisbon Portugal Instituto Superior Técnico Universidade de Lisboa Lisbon Portugal Unbabel Lisbon Portugal Lisbon Portugal

From a variational perspective, many statistical learning criteria involve seeking a distribution that balances empirical risk and regularization. In this paper, we broaden this perspective by introducing a new general class of variational methods based on Fenchel-Young (FY) losses, treated as divergences that generalize (and encompass) the familiar Kullback-Leibler divergence at the core of classical variational learning. Our proposed formulation—FY variational learning—includes as key ingredients new notions of FY free energy, FY evidence, FY evidence lower bound, and FY posterior. We derive alternating minimization and gradient backpropagation algorithms to compute (or lower bound) the FY evidence, which enables learning a wider class of models than previous variational formulations. This leads to generalized FY variants of classical algorithms, such as an FY expectation-maximization (FYEM) algorithm, and latent-variable models, such as an FY variational autoencoder (FYVAE). Our new methods are shown to be empirically competitive, often outperforming their classical counterparts, and most importantly, to have qualitatively novel features. For example, FYEM has an adaptively sparse E-step, while the FYVAE can support models with sparse observations and sparse posteriors. © 2025, CC BY.

关键词： expectation maximization algorithm