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Unbiased Parameter Estimation for Bayesian Inverse Problems

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

Unbiased Approximations for Stationary Distributions of McKean-Vlasov SDEs

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arXiv 2024年

作者： Awadelkarim, Elsiddig Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Mathematics City University of Hong Kong Hong Kong School of Data Science The Chinese University of Hong Kong Shenzhen Shenzhen China

We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications such as mathematical finance, biology and opinion dynamics. Typically the stationary distribution is unknown and indeed one cannot simulate such processes exactly. As a result one commonly requires a time-discretization scheme which results in a discretization bias and a bias from not being able to simulate the associated stationary distribution. To overcome this bias, we present a new unbiased estimator taking motivation from the literature on unbiased Monte Carlo. We prove the unbiasedness of our estimator, under assumptions. In order to prove this we require developing ergodicity results of various discrete time processes, through an appropriate discretization scheme, towards the invariant measure. Numerous numerical experiments are provided, on a range of MVSDEs, to demonstrate the effectiveness of our unbiased estimator. Such examples include the Currie-Weiss model, a 3D neuroscience model and a parameter estimation problem. © 2024, CC BY-NC-SA.

关键词： Stochastic systems

Structural phase transitions between layered Indium Selenide for integrated photonic memory

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arXiv 2025年

作者： Li, Tiantian Wang, Yong Li, Wei Mao, Dun Benmore, Chris J. Evangelista, Igor Xing, Huadan Li, Qiu Wang, Feifan Sivaraman, Ganesh Janotti, Anderson Law, Stephanie Gu, Tingyi Department of Electrical and Computer Engineering University of Delaware NewarkDE19716 United States Department of Materials Science and Engineering University of Delaware NewarkDE19716 United States Los Alamos National Laboratory Computer Computational and Statistical Sciences Division Los AlamosNM87545 United States X-ray Science Division Argonne National Laboratory LemontIL60439 United States Data Science and Learning Division Argonne National Laboratory LemontIL60439 United States

The primary mechanism of optical memoristive devices relies on the phase transitions between amorphous-crystalline states. The slow or energy hungry amorphous-crystalline transitions in optical phase-change materials are detrimental to the devices’ scalability and performance. Leveraging the integrated photonic platform, we demonstrate a single nanosecond pulse triggered nonvolatile and reversible switching between two layered structures of indium selenide (In2Se3). High resolution pair distribution function reveals the detailed atomistic transition pathways between the layered structures. With inter-layer ‘shear glide’ and isosymmetric phase transition, the switching between α- and β-structural states contain low re-configurational entropy, allowing reversible switching between layered structures. Broadband refractive index contrast, optical transparency, and volumetric effect in the crystalline-crystalline phase transition are experimentally characterized in molecular beam epitaxy-grown thin films and compared to ab-initial calculations. The nonlinear resonator transmission spectra measure incremental linear loss rate of 3.3 GHz introduced by 1.5 µm long In2Se3 covered layer, resulting from the combinations of material absorption and scattering. © 2025, CC BY.

关键词： Molecular beam epitaxy

Artificial intelligence for geoscience:Progress,challenges,and perspectives

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The Innovation 2024年第5期5卷 136-160,135页

作者： Tianjie Zhao Sheng Wang Chaojun Ouyang Min Chen Chenying Liu Jin Zhang Long Yu Fei Wang Yong Xie Jun Li Fang Wang Sabine Grunwald Bryan MWong Fan Zhang Zhen Qian Yongjun Xu Chengqing Yu Wei Han Tao Sun Zezhi Shao Tangwen Qian Zhao Chen Jiangyuan Zeng Huai Zhang Husi Letu Bing Zhang Li Wang Lei Luo Chong Shi Hongjun Su Hongsheng Zhang Shuai Yin Ni Huang Wei Zhao Nan Li Chaolei Zheng Yang Zhou Changping Huang Defeng Feng Qingsong Xu Yan Wu Danfeng Hong Zhenyu Wang Yinyi Lin Tangtang Zhang Prashant Kumar Antonio Plaza Jocelyn Chanussot Jiabao Zhang Jiancheng Shi Lizhe Wang Aerospace Information Research Institute Chinese Academy of SciencesBeijing 100094China School of Computer Science China University of GeosciencesWuhan 430078China State Key Laboratory of Mountain Hazards and Engineering Resilience Institute of Mountain Hazards and EnvironmentChinese Academy of SciencesChengdu 610299China Key Laboratory of Virtual Geographic Environment(Ministry of Education of PRC) Nanjing Normal UniversityNanjing 210023China Data Science in Earth Observation Technical University of Munich80333 MunichGermany The National Key Laboratory of Water Disaster Prevention Yangtze Institute for Conservation and DevelopmentHohai UniversityNanjing 210098China Institute of Computing Technology Chinese Academy of SciencesBeijing 100190China School of Geographical Sciences Nanjing University of Information Science and TechnologyNanjing 210044China State Key Laboratory of Soil and Sustainable Agriculture Institute of Soil ScienceChinese Academy of SciencesNanjing 210008China Soil Water and Ecosystem Sciences DepartmentUniversity of FloridaPO Box 110290GainesvilleFLUSA Materials Science Engineering Program Cooperating Faculty Member in the Department of Chemistry and Department of Physics Astronomy University of CaliforniaCaliforniaRiversideCA 92521USA Institute of Remote Sensing and Geographical Information System School of Earth and Space SciencesPeking UniversityBeijing 100871China Key Laboratory of Computational Geodynamics University of Chinese Academy of SciencesBeijing 100049China International Research Center of Big Data for Sustainable Development Goals Beijing 100094China College of Geography and Remote Sensing Hohai UniversityNanjing 211100China Department of Geography The University of Hong KongHong Kong 999077SARChina Jiangsu Key Laboratory of Atmospheric Environment Monitoring and Pollution Control Nanjing 210044China School of Environmental Science and Engineering Nanjing University of Information Science&TechnologyNanjing 210044China Collaborative Inno

This paper explores the evolution of geoscientific inquiry,tracing the progression from traditional physics-based models to modern data-driven approaches facilitated by significant advancements in artificial intelligence(AI)and data collection *** models,which are grounded in physical and numerical frameworks,provide robust explanations by explicitly reconstructing underlying physical ***,their limitations in comprehensively capturing Earth’s complexities and uncertainties pose challenges in optimization and real-world *** contrast,contemporary data-driven models,particularly those utilizing machine learning(ML)and deep learning(DL),leverage extensive geoscience data to glean insights without requiring exhaustive theoretical *** techniques have shown promise in addressing Earth science-related ***,challenges such as data scarcity,computational demands,data privacy concerns,and the“black-box”nature of AI models hinder their seamless integration into *** integration of physics-based and data-driven methodologies into hybrid models presents an alternative *** models,which incorporate domain knowledge to guide AI methodologies,demonstrate enhanced efficiency and performance with reduced training data *** review provides a comprehensive overview of geoscientific research paradigms,emphasizing untapped opportunities at the intersection of advanced AI techniques and *** examines major methodologies,showcases advances in large-scale models,and discusses the challenges and prospects that will shape the future landscape of AI in *** paper outlines a dynamic field ripe with possibilities,poised to unlock new understandings of Earth’s complexities and further advance geoscience exploration.

关键词： Earth utilizing landscape

A linearization for stable and fast geographically weighted Poisson regression

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arXiv 2023年

作者： Murakami, Daisuke Tsutsumida, Narumasa Yoshida, Takahiro Nakaya, Tomoki Lu, Binbin Harris, Paul Department of Data Statistical Science Institute of Statistical Mathematics Tachikawa Japan Department of Information and Computer Sciences Graduate School of Science and Engineering Saitama University Saitama Japan Department of Urban Engineering School of Engineering The University of Tokyo Tokyo Japan Department of Frontier Science for Advanced Environment The Graduate School of Environmental Studies Tohoku University Sendai Japan School of Remote Sensing and Information Engineering Wuhan University Wuhan China Net Zero and Resilient Farming Rothamsted Research North Wyke United Kingdom

Although geographically weighted Poisson regression (GWPR) is a popular regression for spatially indexed count data, its development is relatively limited compared to that found for linear geographically weighted regression (GWR), where many extensions (e.g., multiscale GWR, scalable GWR) have been proposed. The weak development of GWPR can be attributed to the computational cost and identification problem in the underpinning Poisson regression model. This study proposes linearized GWPR (L-GWPR) by introducing a log-linear approximation into the GWPR model to overcome these bottlenecks. Because the L-GWPR model is identical to the Gaussian GWR model, it is free from the identification problem, easily implemented, computationally efficient, and offers similar potential for extension. Specifically, L-GWPR does not require a double-loop algorithm, which makes GWPR slow for large samples. Furthermore, we extended L-GWPR by introducing ridge regularization to enhance its stability (regularized L-GWPR). The results of the Monte Carlo experiments confirmed that regularized L-GWPR estimates local coefficients accurately and computationally efficiently. Finally, we compared GWPR and regularized L-GWPR through a crime analysis in Tokyo. Copyright © 2023, The Authors. All rights reserved.

关键词： Linearization

Learner Action Patterns in the Problem-Solving Process Related to program Code Composition Based on Tracking System Activities 7

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Learner Action Patterns in the Problem-Solving Process Relat...

7th International Conference on Informatics and Computing, ICIC 2022

作者： Syahidi, Aulia Akhrian Supianto, Ahmad Afif Hirashima, Tsukasa Watanobe, Yutaka Politeknik Negeri Banjarmasin Smart City Information System Applied Undergraduate Program Banjarmasin City Indonesia Research Center for Data and Information Sciences Bandung City Indonesia Graduate School of Advanced Science and Engineering Hiroshima University Kagamiyama Learning Engineering Laboratory Higashihiroshima Japan University of Aizu Division of Information Systems Department of Computer Science and Engineering Fukushima AizuWakamatsu Japan

ISBN: (纸本)9798350345711

Learning activities are an indicator of the learner's desire to learn during the learning process. The pattern of learner action is related to learning activities. In this case, in extracting the learning process, it is necessary to collect a lot of data through analysis of the learning process. The purpose of this study is to recommend and report the performance of an activity tracking system equipped with visual artifacts as an educational data mining approach to analyze action patterns when learners complete the arrangement of program code lines in each programming problem. In this study, data were taken from activity recordings when learners used interactive learning media for a basic programming subject called TOLSYASUPI-EduMed which had problem-solving learning models embedded in their interactions. Learning Analytics is used as a method of this research and data relationships from learner actions during the learning process using the 'if-then' rule. Log data is used for recording and detecting activities carried out by learners. We confirm that the results of the study are based on the findings of the data relationship that if the lines of program code are too long (more than five lines) then almost all learners experience a bottleneck condition. The completion time of each question and the number of iterations in completing the program code lines for each question have also been recorded and have a pattern of connection between the data. The information that has been obtained is then forwarded to teachers or stakeholders as key information to make appropriate feedback to learners based on the results as a means of analyzing and evaluating the programming learning process. © 2022 IEEE.

关键词： data mining

Improved LSTM hyperparameters alongside sentiment walk-forward validation for time series prediction

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Journal of Open Innovation: Technology, Market, and Complexity 2025年第1期11卷

作者： Wahyuddin, Eko Putra Caraka, Rezzy Eko Kurniawan, Robert Caesarendra, Wahyu Gio, Prana Ugiana Pardamean, Bens Department of Statistical Computing Politeknik Statistika STIS Jakarta 13330 Indonesia Statistics Indonesia (BPS) Jl. Dr Sutomo 6-8 Jakarta Indonesia School of Economics and Business Telkom University Bandung 40257 Indonesia Research Center for Data and Information Sciences Research Organization for Electronics and Informatics National Research and Innovation Agency (BRIN) Bandung 40135 Indonesia Faculty of Integrated Technologies Universiti Brunei Darussalam Gadong BE1410 Brunei Darussalam Department of Mathematics Universitas Sumatera Utara Medan 20155 Indonesia Bioinformatics and Data Science Research Centre Bina Nusantara University DKI Jakarta 11480 Indonesia Computer Science Department BINUS Graduate Program Master of Computer Science Program Bina Nusantara University DKI Jakarta 11480 Indonesia

This study aims to address the common issue of biased estimation errors in time series modeling by analyzing the error in locating ideal hyperparameters and defining appropriate validation methods. Specifically, it focuses on predicting the stock price of Bank Rakyat Indonesia using a combination of historical stock prices, technical indicators, exchange rates, and news sentiment data, while determining the optimal variables for deep learning models. Employing a deep learning-based Long-Short Term Memory (LSTM) model, the study optimizes hyperparameters alongside walk-forward validation for time series prediction. It explores different combinations of variables and adapts the sliding window approach to the context of the data. The results highlight the importance of optimizing hyperparameters and utilizing walk-forward validation for accurate time series prediction. The model incorporating historical stock prices and sentiment scores outperforms others, achieving an RMSE of 96.61 and MAE of 86.97. Incorporating sentiment scores reduces RMSE by 39.55 % compared to models using only historical stock prices, while adding technical indicators does not yield improvement. This study contributes to the field by addressing the issue of biased estimation errors in time series modeling, offering insights into the optimization of hyperparameters and validation methods for accurate predictions. It also underscores the significance of incorporating sentiment analysis alongside historical stock prices for improved forecasting accuracy. © 2024 The Authors

关键词： LSTM Sentiment analysis Stock price prediction Time series modeling Validation methods

Minimum Φ-distance estimators for finite mixing measures

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arXiv 2023年

作者： Wei, Yun Mukherjee, Sayan Nguyen, XuanLong Department of Statistical Science Duke University NC United States Departments of Mathematics Computer Science Biostatistics & Bioinformatics Duke University NC United States Center for Scalable Data Analytics and Artificial Intelligence Universität Leipzig Germany Max Planck Institute for Mathematics in the Sciences Leipzig Germany Department of Statistics University of Michigan Ann ArborMI United States

Finite mixture models have long been used across a variety of fields in engineering and sciences. Recently there has been a great deal of interest in quantifying the convergence behavior of the mixing measure, a fundamental object that encapsulates all unknown parameters in a mixture distribution. In this paper we propose a general framework for estimating the mixing measure arising in finite mixture models, which we term minimum Φ-distance estimators. We establish a general theory for the minimum Φ-distance estimator, where sharp probability bounds are obtained on the estimation error for the mixing measures in terms of the suprema of the associated empirical processes for a suitably chosen function class Φ. Our framework includes several existing and seemingly distinct estimation methods as special cases but also motivates new estimators. For instance, it extends the minimum Kolmogorov-Smirnov distance estimator to the multivariate setting, and it extends the method of moments to cover a broader family of probability kernels beyond the Gaussian. Moreover, it also includes methods that are applicable to complex (e.g., non-Euclidean) observation domains, using tools from reproducing kernel Hilbert spaces. It will be shown that under general conditions the methods achieve optimal rates of estimation under Wasserstein metrics in either minimax or pointwise sense of convergence;the latter case can be achieved when no upper bound on the finite number of components is *** Codes Primary 62H30, 62C20, Secondary 62F12 © 2023, CC BY-NC-ND.

关键词： Method of moments

Optimized Security Mechanism for publicly Secret Key Sharing over Cloud using Blockchain

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Optimized Security Mechanism for publicly Secret Key Sharing...

2024 International Symposium on Securing Next Generation Systems Using Future Artificial Intelligence Technologies, SNSFAIT 2024

作者： Byeon, Haewon Quraishi, Aadam Thuniki, Praveen Keshta, Ismail Soni, Mukesh Shabaz, Mohammad Department of AI and Software Inje University Gimhae50834 Korea Republic of Inje University Medical Big Data Research Center Gimhae50834 Korea Republic of Intervention Treatment Institute HoustonTX United States Sr Program Analyst Georgia CummingGA30040 United States Computer Science and Information Systems Department College of Applied Sciences Al Maarefa University Riyadh Saudi Arabia Dr. D. Y. Patii Vidyapeeth Pune Dr. D. Y. Patii School of Science & Technology Tathawade Pune India Model Institute of Engineering and Technology J&K Jammu India

A publicly verifiable key sharing mechanism based on threshold key sharing is provided to explore the security of users' private keys on the blockchain. Participating nodes check the key fragment after receiving it, effectively preventing it from being abused. The crucial sections of the nodes that participated in the critical splicing are made public during the critical recovery stage to prevent them from performing harmful things during the critical recovery stage. Add IDs to the nodes that participated in the crucial splicing during the key distribution stage;a dynamic threshold system is intended to track and update the status of malicious nodes in real time. When the node that possesses the crucial component fails, the owner of the critical component and the main node relocate a key element to the new participating nodes. To safeguard sensitive information. The experimental results show that this system has a key recovery rate of 80% and threshold qualities such as traceability, enforceability, and recoverability. © 2024 Copyright for this paper by its authors.

关键词： Blockchain Encryption Key sharing mechanism Privacy Secret key Security