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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

Factors in Fashion: Factor Analysis towards the Mode

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arXiv 2024年

作者： Sun, Zhe Tu, Yundong Guanghua School of Management Peking University China

The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of the distribution of the observables. Statistical inference is developed with the aid of mode estimation, where the modal factors and the loadings are estimated through maximizing a kernel-type objective function. An easy-to-implement alternating maximization algorithm is designed to obtain the estimators numerically. Two model selection criteria are further proposed to determine the number of factors. The asymptotic properties of the proposed estimators are established under some regularity conditions. Simulations demonstrate the nice finite sample performance of our proposed estimators, even in the presence of heavy-tailed and asymmetric idiosyncratic error distributions. Finally, the application to inflation forecasting illustrates the practical merits of modal factors. © 2024, CC BY-NC-ND.

关键词： expectation maximization algorithm

The Spectral Approach to Linear Rational expectations Models

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arXiv 2020年

作者： Al-Sadoon, Majid M. Durham University Business School United Kingdom

This paper considers linear rational expectations models in the frequency domain. The paper characterizes existence and uniqueness of solutions to particular as well as generic systems. The set of all solutions to a given system is shown to be a finite dimensional affine space in the frequency domain. It is demonstrated that solutions can be discontinuous with respect to the parameters of the models in the context of non-uniqueness, invalidating mainstream frequentist and Bayesian methods. The ill-posedness of the problem motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability *** Codes 91B84 Copyright © 2020, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Blind Channel Estimation and Joint Symbol Detection with Data-Driven Factor Graphs

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arXiv 2024年

作者： Schmid, Luca Raviv, Tomer Shlezinger, Nir Schmalen, Laurent Hertzstr. 16 Karlsruhe76187 Germany School of ECE Ben-Gurion University of the Negev Be’er-Sheva Israel

We investigate the application of the factor graph framework for blind joint channel estimation and symbol detection on time-variant linear inter-symbol interference channels. In particular, we consider the expectation maximization (EM) algorithm for maximum likelihood estimation, which typically suffers from high complexity as it requires the computation of the symbol-wise posterior distributions in every iteration. We address this issue by efficiently approximating the posteriors using the belief propagation (BP) algorithm on a suitable factor graph. By interweaving the iterations of BP and EM, the detection complexity can be further reduced to a single BP iteration per EM step. In addition, we propose a data-driven version of our algorithm that introduces momentum in the BP updates and learns a suitable EM parameter update schedule, thereby significantly improving the performance-complexity tradeoff with a few offline training samples. Our numerical experiments demonstrate the excellent performance of the proposed blind detector and show that it even outperforms coherent BP detection in high signal-to-noise scenarios. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

On the maximal correlation coefficient for the bivariate Marshall Olkin distribution

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arXiv 2024年

作者： Bücher, Axel Staud, Torben Ruhr-Universität Bochum Fakultät für Mathematik Austria

We prove a formula for the maximal correlation coefficient of the bivariate Marshall Olkin distribution that was conjectured in Lin, Lai, and Govindaraju (2016, Stat. Methodol., 29:1–9). The formula is applied to obtain a new proof for a variance inequality in extreme value statistics that links the disjoint and the sliding block maxima method. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression

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arXiv 2023年

作者： Zgodic, Anja Bai, Ray Zhang, Jiajia Wang, Yuan Rorden, Chris McLain, Alexander C. Department of Epidemiology and Biostatistics University of South Carolina South Carolina United States Department of Statistics University of South Carolina South Carolina United States Department of Psychology University of South Carolina South Carolina United States

Sparse linear regression methods for high-dimensional data commonly assume that residuals have constant variance, which can be violated in practice. For example, Aphasia Quotient (AQ) is a critical measure of language impairment and informs treatment decisions, but it is challenging to measure in stroke patients. It is of interest to use high-resolution T2 neuroimages of brain damage to predict AQ. However, sparse regression models show marked evidence of heteroscedastic error even after transformations are applied. This violation of the homoscedasticity assumption can lead to bias in estimated coefficients, prediction intervals (PI) with improper length, and increased type I errors. Bayesian heteroscedastic linear regression models relax the homoscedastic error assumption but can enforce restrictive prior assumptions on parameters, and many are computationally infeasible in the high-dimensional setting. This paper proposes estimating high-dimensional heteroscedastic linear regression models using a heteroscedastic partitioned empirical Bayes expectation Conditional maximization (H-PROBE) algorithm. H-PROBE is a computationally efficient maximum a posteriori estimation approach that requires minimal prior assumptions and can incorporate covariates hypothesized to impact heterogeneity. We apply this method by using high-dimensional neuroimages to predict and provide PIs for AQ that accurately quantify predictive uncertainty. Our analysis demonstrates that H-PROBE can provide narrower PI widths than standard methods without sacrificing coverage. Narrower PIs are clinically important for determining the risk of moderate to severe aphasia. Additionally, through extensive simulation studies, we exhibit that H-PROBE results in superior prediction, variable selection, and predictive inference compared to alternative methods. Copyright © 2023, The Authors. All rights reserved.

关键词： expectation maximization algorithm

Maximum Ideal Likelihood Estimator: An New Estimation and Inference Framework for Latent Variable Models

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arXiv 2024年

作者： Cai, Jake Yizhou Ma, Ting Fung Department of Statistics University of South Carolina 1523 Greene Street ColumbiaSC29208 United States

In this paper, a new estimation framework, Maximum Ideal Likelihood Estimator (MILE), is proposed for general parametric models with latent variables and missing values. Instead of focusing on the marginal likelihood of the observed data as in many traditional approaches, the MILE directly considers the joint distribution of the complete dataset by treating the latent variables as parameters (the ideal likelihood). The MILE framework remains valid, even when traditional methods are not applicable, e.g., non-finite conditional expectation of the marginal likelihood function, via different optimization techniques and algorithms. The statistical properties of the MILE, such as the asymptotic equivalence to the Maximum Likelihood Estimation (MLE), are proved under some mild conditions, which facilitate statistical inference and prediction. Simulation studies illustrate that MILE outperforms traditional approaches with computational feasibility and scalability using existing and our proposed algorithms. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm

MaxMin-RLHF: Alignment with Diverse Human Preferences

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arXiv 2024年

作者： Chakraborty, Souradip Qiu, Jiahao Yuan, Hui Koppel, Alec Manocha, Dinesh Huang, Furong Bedi, Amrit Singh Wang, Mengdi Department of Computer Science University of Maryland College ParkMD United States Department of Electrical and Computer Engineering Princeton University NJ United States JP Morgan Chase AI Research New York United States Department of Computer Science University of Central Florida FL United States

Reinforcement Learning from Human Feedback (RLHF) aligns language models to human preferences by employing a singular reward model derived from preference data. However, the single reward model overlooks the rich diversity of human preferences inherent in data collected from multiple users. In this work, we first derive an impossibility result of alignment with single reward RLHF, thereby highlighting its insufficiency in representing diverse human preferences. Next, we propose to learn a mixture of reward models via an expectation-maximization algorithm and solve a MaxMin alignment objective inspired by the Egalitarian principle in social choice theory to better honor diverse human preferences. We present comprehensive experimental results on small-scale (GPT-2) and large-scale language (with Tulu2-7B)) and show the efficacy of the proposed approach in the presence of diversity among human preferences. We remark that our findings in this work are not only limited to language models but also extend to reinforcement learning in general. Copyright © 2024, The Authors. All rights reserved.

关键词： expectation maximization algorithm