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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

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

Nested expectations with Kernel Quadrature

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arXiv 2025年

作者： Chen, Zonghao Naslidnyk, Masha Briol, François-Xavier Department of Computer Science University College London United Kingdom Department of Statistical Science University College London United Kingdom

This paper considers the challenging computational task of estimating nested expectations. Existing algorithms, such as nested Monte Carlo or multilevel Monte Carlo, are known to be consistent but require a large number of samples at both inner and outer levels to converge. Instead, we propose a novel estimator consisting of nested kernel quadrature estimators and we prove that it has a faster convergence rate than all baseline methods when the integrands have sufficient smoothness. We then demonstrate empirically that our proposed method does indeed require fewer samples to estimate nested expectations on real-world applications including Bayesian optimisation, option pricing, and health economics. 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

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