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Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm

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arXiv 2019年

作者： Barigozzi, Matteo Luciani, Matteo Università di Bologna Italy Federal Reserve Board United States

We study estimation of large Dynamic Factor models implemented through the expectation maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both the cross-sectional dimension, n, and the sample size, T, diverge to infinity: (i) the estimated loadings are √T-consistent, asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates;(ii) the estimated factors are √nconsistent, asymptotically normal and equivalent to their Weighted Least Squares estimates. Moreover, the estimated loadings are asymptotically as efficient as those obtained by Principal Components analysis, while the estimated factors are more efficient if the idiosyncratic covariance is sparse enough. © 2019, CC BY.

关键词： expectation maximization algorithm

Aligning Explanations for Recommendation with Rating and Feature via Maximizing Mutual Information

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arXiv 2024年

作者： Zhao, Yurou Jiang, Fei Lin, Wei Sun, Yiding Guan, Lu Ma, Weizhi Han, Ruidong Li, Xiang Mao, Jiaxin Gaoling School of Artificial Intelligence Renmin University of China Beijing China Tsinghua University Beijing China Meituan Beijing China

Providing natural language-based explanations to justify recommendations helps to improve users’ satisfaction and gain users’ trust. However, as current explanation generation methods are commonly trained with an objective to mimic existing user reviews, the generated explanations are often not aligned with the predicted ratings or some important features of the recommended items, and thus, are suboptimal in helping users make informed decision on the recommendation platform. To tackle this problem, we propose a flexible model-agnostic method named MMI (Maximizing Mutual Information) framework to enhance the alignment between the generated natural language explanations and the predicted rating/important item features. Specifically, we propose to use mutual information (MI) as a measure for the alignment and train a neural MI estimator. Then, we treat a well-trained explanation generation model as the backbone model and further fine-tune it through reinforcement learning with guidance from the MI estimator, which rewards a generated explanation that is more aligned with the predicted rating or a pre-defined feature of the recommended item. Experiments on three datasets demonstrate that our MMI framework can boost different backbone models, enabling them to outperform existing baselines in terms of alignment with Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Robust Attitude Estimation with Quaternion Left-Invariant EKF and Noise Covariance Tuning

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arXiv 2024年

作者： Pandey, Yash Bhattacharyya, Rahul Singh, Yatindra Nath Department of Electronics Engineering Harcourt Butler Technical University Kanpur India Department of Electrical Engineering Indian Institute of Technology Kanpur Kanpur India

Accurate estimation of noise parameters is critical for optimal filter performance, especially in systems where true noise parameter values are unknown or time-varying. This article presents a quaternion left-invariant extended Kalman filter (LI-EKF) for attitude estimation, integrated with an adaptive noise covariance estimation algorithm. By employing an iterative expectation-maximization (EM) approach, the filter can effectively estimate both process and measurement noise covariances. Extensive simulations demonstrate the superiority of the proposed method in terms of attitude estimation accuracy and robustness to initial parameter misspecification. The adaptive LI-EKF’s ability to adapt to time-varying noise characteristics makes it a promising solution for various applications requiring reliable attitude estimation, such as aerospace, robotics, and autonomous systems. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm

CENSORED BELIEFS AND WISHFUL THINKING

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arXiv 2024年

作者： Burgh, Jarrod Melo, Emerson Department of Economics Indiana University BloomingtonIN47408 United States

We present a model elucidating wishful thinking, which comprehensively incorporates both the costs and benefits associated with biased beliefs. Our findings reveal that wishful thinking behavior can be characterized as equivalent to superquantile-utility maximization within the domain of threshold beliefs distortion cost functions. By leveraging this equivalence, we establish WT as driving decision-makers to exhibit a preference for choices characterized by skewness and increased risk. Furthermore, we discuss how our framework facilitates the study of optimistic stochastic choice and optimistic risk aversion. © 2024, CC BY.

关键词： expectation maximization algorithm

Robust Emax Model Fitting: Addressing Nonignorable Missing Binary Outcome in Dose-Response Analysis

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arXiv 2024年

作者： Zhang, Jiangshan Pradhan, Vivek Zhao, Yuxi Department of Statistics University of California DavisCA95616 United States Global Biometrics and Data Management Immunology and Inflammation Pfizer Inc. 1 Portland Street CambridgeMA02139 United States

The Binary Emax model is widely employed in dose-response analysis during drug development, where missing data often pose significant challenges. Addressing nonignorable missing binary responses—where the likelihood of missing data is related to unobserved outcomes—is particularly important, yet existing methods often lead to biased estimates. This issue is compounded when using the regulatory-recommended ‘imputing as treatment failure’ approach, known as non-responder imputation (NRI). Moreover, the problem of separation, where a predictor perfectly distinguishes between outcome classes, can further complicate likelihood maximization. In this paper, we introduce a penalized likelihood-based method that integrates a modified expectation-maximization (EM) algorithm in the spirit of Ibrahim and Lipsitz (Ibrahim and Lipsitz, 1996) to effectively manage both nonignorable missing data and separation issues. Our approach applies a noninformative Jeffreys’ prior to the likelihood, reducing bias in parameter estimation. Simulation studies demonstrate that our method outperforms existing methods, such as NRI, and the superiority is further supported by its application to data from a Phase II clinical trial. Additionally, we have developed an R package, ememax, to facilitate the implementation of the proposed method. © 2024, CC BY.

关键词： expectation maximization algorithm

Sparse high-dimensional linear mixed modeling with a partitioned empirical Bayes ECM algorithm

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arXiv 2023年

作者： Zgodic, Anja Bai, Ray Zhang, Jiajia Olejua, Peter McLain, Alexander C. Department of Epidemiology and Biostatistics University of South Carolina United States Department of Statistics University of South Carolina United States

High-dimensional longitudinal data is increasingly used in a wide range of scientific studies. To properly account for dependence between longitudinal observations, statistical methods for high-dimensional linear mixed models (LMMs) have been developed. However, few packages implementing these high-dimensional LMMs are available in the statistical software R. Additionally, some packages suffer from scalability issues. This work presents an efficient and accurate Bayesian framework for high-dimensional LMMs. We use empirical Bayes estimators of hyperparameters for increased flexibility and an expectation-Conditional-Minimization (ECM) algorithm for computationally efficient maximum a posteriori probability (MAP) estimation of parameters. The novelty of the approach lies in its partitioning and parameter expansion as well as its fast and scalable computation. We illustrate Linear Mixed Modeling with PaRtitiOned empirical Bayes ECM (LMM-PROBE) in simulation studies evaluating fixed and random effects estimation along with computation time. A real-world example is provided using data from a study of lupus in children, where we identify genes and clinical factors associated with a new lupus biomarker and predict the biomarker over time. Supplementary materials are available online. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Reward maximization for Pure Exploration: Minimax Optimal Good Arm Identification for Nonparametric Multi-Armed Bandits

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arXiv 2024年

作者： Cho, Brian Meier, Dominik Gan, Kyra Kallus, Nathan Cornell Tech United States

In multi-armed bandits, the tasks of reward maximization and pure exploration are often at odds with each other. The former focuses on exploiting arms with the highest means, while the latter may require constant exploration across all arms. In this work, we focus on good arm identification (GAI), a practical bandit inference objective that aims to label arms with means above a threshold as quickly as possible. We show that GAI can be efficiently solved by combining a reward-maximizing sampling algorithm with a novel nonparametric anytime-valid sequential test for labeling arm means. We first establish that our sequential test maintains error control under highly nonparametric assumptions and asymptotically achieves the minimax optimal e-power, a notion of power for anytime-valid tests. Next, by pairing regret-minimizing sampling schemes with our sequential test, we provide an approach that achieves minimax optimal stopping times for labeling arms with means above a threshold, under an error probability constraint δ. Our empirical results validate our approach beyond the minimax setting, reducing the expected number of samples for all stopping times by at least 50% across both synthetic and real-world settings. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Quantum distinguishability measures: projectors vs. states maximization

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arXiv 2024年

作者： Budini, Adrián A. de Matos Filho, Ruynet L. Santos, Marcelo F. Centro Atómico Bariloche Avenida E. Bustillo Km 9.5 Bariloche8400 Argentina Fanny Newbery 111 Bariloche8400 Argentina Instituto de Física Universidade Federal do Rio de Janeiro Caixa Postal 68528 Rio de Janeiro21941-972 Brazil

The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition of distinguishability which, instead of projectors, is based on maximization over normalized states (density matrices). It is shown that this procedure leads to a distance (between two states) that, in contrast to the usual approach based on a 1-norm, is based on an infinite-norm. Properties such as convexity, monotonicity, and invariance under unitary transformations are fulfilled. Equivalent operational implementations based on maximization over classical probabilities and hypothesis testing scenarios are also established. When considering the action of completely positive transformations contractivity is only granted for unital maps. This feature allows us to introduce a measure of the quantumness of non-unital maps that can be written in terms of the proposed distinguishability measure and corresponds to the maximal possible deviation from contractivity. Particular examples sustain the main results and conclusions. © 2024, CC BY.

关键词： expectation maximization algorithm

A Signal Processing Technique for Compensating Random Drift of MEMS Gyros

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A Signal Processing Technique for Compensating Random Drift ...

2014中国制导、导航与控制学术会议

作者： Jieyu Liu Qiang Shen Weiwei Qin Department of Automatic Control Xi''an Research Institute of High-techXi''anShannxi Province710025China

ISBN: (纸本)9781479946983

In this paper,we present a prediction and compensation method for Micro-Electro-Mechanical System (MEMS) gyroscope random drift,which is based on relevance vector *** relevance vector machine (RVM) model is established based on the feature of MEMS gyroscope random drift and the parameters are trained by the expectation maximization (EM) *** phase space reconstruction,the time sequence of random drift is accessed in the *** final experimental results indicate that our proposed methodology can achieve both the least complexity of structure and goodness of fit to data,and also can predict the gyroscope random drift ***,by compensating random drift using the predicting result,the precision of gyroscopes application could be improved well.

关键词： compensation expectation-maximisation algorithm gyroscopes learning (artificial intelligence) microsensors signal processing EM algorithm MEMS gyroscope RVM model compensation method expectation maximization algorithm microelectromechanical systems phase space reconstruction prediction method random drift compensation relevance vector machine signal processing technique Bayes methods Gyroscopes Kernel Micromechanical devices Prediction algorithms Support vector machines Vectors