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arXiv 2020年

作者： Noma, Hisashi Shinozaki, Tomohiro Iba, Katsuhiro Teramukai, Satoshi Furukawa, Toshi A. Department of Data Science The Institute of Statistical Mathematics Tokyo Japan Department of Information and Computer Technology Faculty of Engineering Tokyo University of Science Tokyo Japan Department of Statistical Science School of Multidisciplinary Sciences The Graduate University for Advanced Studies Tokyo Japan Office of Biostatistics Department of Biometrics Headquarters of Clinical Development Otsuka Pharmaceutical Co. Ltd. Tokyo Japan Department of Biostatistics Graduate School of Medical Science Kyoto Prefectural University of Medicine Kyoto Japan Department of Health Promotion and Human Behavior and of Clinical Epidemiology Kyoto University Graduate School of Medicine School of Public Health Kyoto Japan

In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction accuracy measures are corrected by adequate bootstrap-based correction methods, but their confidence intervals are not corrected, e.g., the DeLong's confidence interval is usually used for assessing the Cstatistic. These naïve methods do not adjust for the optimism bias and do not account for statistical variability in the estimation of parameters in the prediction models. Therefore, their coverage probabilities of the true value of the prediction accuracy measure can be seriously below the nominal level (e.g., 95%). In this article, we provide two generic bootstrap methods, namely (1) location-shifted bootstrap confidence intervals and (2) two-stage bootstrap confidence intervals, that can be generally applied to the bootstrap-based optimism correction methods, i.e., the Harrell's bias correction, 0.632, and 0.632+ methods. In addition, they can be widely applied to various methods for prediction model development involving modern shrinkage methods such as the ridge and lasso regressions. Through numerical evaluations by simulations, the proposed confidence intervals showed favourable coverage performances. Besides, the current standard practices based on the optimism-uncorrected methods showed serious undercoverage properties. To avoid erroneous results, the optimism-uncorrected confidence intervals should not be used in practice, and the adjusted methods are recommended instead. We also developed the R package predboot for implementing these methods (https://***/nomahi/predboot). The effectiveness of the proposed methods are illustrated via applications to the GUSTO-I clinical trial. Copyright © 2020, The Authors. All rights reserved.

关键词： Forecasting

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Market Basket Analysis Using Apriori and FP-Growth for Analysis Consumer Expenditure Patterns at Berkah Mart in Pekanbaru Riau

Market Basket Analysis Using Apriori and FP-Growth for Analy...

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2018 Workshop on Multidisciplinary and Its Applications: Applied Mathematics, computer science, Information Systems, and Information Technology, WMA-Mathcomtech 2018

作者： Mustakim Herianda, Della Maulina Ilham, Ahmad Daeng Gs, Achmad Laumal, Folkes E. Kurniasih, Nuning Iskandar, Akbar Manulangga, Gloria Indra Iswara, Ida Bagus Ary Rahim, Robbi Puzzle Research Data Technology UIN Sultan Syarif Kasim Riau Indonesia Department of Information System UIN Sultan Syarif Kasim Riau Indonesia Informatics Department Universitas Muhammadiyah Semarang Semarang Indonesia Department of Management University of 45 Surabaya Surabaya Indonesia Department of Electrical Engineering Politeknik Negeri Kupang Kupang Indonesia Faculty of Communication Sciences Library and Information Science Program Universitas Padjadjaran Bandung Indonesia Informatics Engineering STMIK AKBA Makassar Indonesia Informatics Department STMIK STIKOM Indonesia Denpasar Indonesia School of Computer and Communication Engineering Universiti Malaysia Perlis Kubang Gajah Malaysia

Berkah Mart is one of the new minimarkets in Pekanbaru city which began to develop as a retail business to meet the needs of the community. In his operation, Berkah Mart still uses the traditional store management perception that the placement of product layout on sale shelves has not been through sales analysis. Existing products have not been reviewed from the consumer's point of view, whereas the marketing economics concept provides a variety of product and consumer management methods for business management in Berkah Mart, including market bucket analysis techniques and various itemset search algorithms. In this research, Market Basket Basket Analysis with FP-Growth algorithm is proposed to determine the layout and planning of goods availability. The application of FP-Growth algorithm proved to be useful in generating many and informative association rules to find out the consumer spending pattern at Berkah Mart in Pekanbaru. Moreover, from the rules of the customer association can be segmented separately to meet the specific needs of customers with cost-effective by using some special promotions for the general group. The experimental results show that FP-Growth algorithm can analyze quickly and efficiently informing consumer shopping pattern at Berkah Mart and can increase Berkah Mart revenue. © Published under licence by IOP Publishing Ltd.

关键词： Sales

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A SHEAF-THEORETIC CONSTRUCTION OF SHAPE SPACE

arXiv

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arXiv 2022年

作者： Arya, Shreya Curry, Justin Mukherjee, Sayan Department of Mathematics Duke University DurhamNC United States Department of Mathematics and Statistics University at Albany SUNY AlbanyNY United States Department of Statistical Science Mathematics Computer Science Biostatistics & Bioinformatics Duke University DurhamNC United States Center for Scalable Data Analytics and Artificial Intelligence Universität Leipzig The Max Planck Institute for Mathematics in the Natural Sciences Leipzig Germany

We present a sheaf-theoretic construction of shape space-the space of all shapes. We do this by describing a homotopy sheaf on the poset category of constructible sets, where each set is mapped to its Persistent Homology Transforms (PHT). Recent results that build on fundamental work of Schapira have shown that this transform is injective, thus making the PHT a good summary object for each shape. Our homotopy sheaf result allows us to "glue" PHTs of different shapes together to build up the PHT of a larger shape. In the case where our shape is a polyhedron we prove a generalized nerve lemma for the PHT. Finally, by re-examining the sampling result of Smale-Niyogi-Weinberger, we show that we can reliably approximate the PHT of a manifold by a polyhedron up to arbitrary precision. © 2022, CC BY.

关键词： Geometry

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Unbiased Approximations for Stationary Distributions of McKean-Vlasov SDEs

arXiv

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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

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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

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Unbiased Estimation Using a Class of Diffusion Processes

SSRN

引用

SSRN 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas 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 Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (Rd,B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}t∈[0,1] on Rd, d ∈ N0. This latter process is constructed such that, starting at X0 = 0, one has X1 ∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 15] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(Ε2), for arbitrary Ε > 0, the associated cost is O(Ε−5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(Ε2), the associated cost is, with high probability, O(Ε−2|log(Ε)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse problems. © 2022, The Authors. All rights reserved.

关键词： Diffusion

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Sequential Markov Chain Monte Carlo for Lagrangian data Assimilation with Applications to Unknown data Locations

arXiv

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arXiv 2023年

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location

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CONCENTRATION INEQUALITIES AND OPTIMAL NUMBER OF LAYERS FOR STOCHASTIC DEEP NEURAL NETWORKS

arXiv

引用

arXiv 2022年

作者： Caprio, Michele Mukherjee, Sayan PRECISE Center Department of Computer and Information Science University of Pennsylvania 3330 Walnut Street PhiladelphiaPA19104 United States Center for Scalable Data Analytics and Artificial Intelligence Universität Leipzig Humboldtstraße 25 Leipzig04105 Germany The Max Planck Institute for Mathematics in the Sciences Inselstraße 22 Leipzig04103 Germany Departments of Statistical Science Mathematics Computer Science and Biostatistics & Bioinformatics Duke University DurhamNC27708 United States

We state concentration inequalities for the output of the hidden layers of a stochastic deep neural network (SDNN), as well as for the output of the whole SDNN. These results allow us to introduce an expected classifier (EC), and to give probabilistic upper bound for the classification error of the EC. We also state the optimal number of layers for the SDNN via an optimal stopping procedure. We apply our analysis to a stochastic version of a feedforward neural network with ReLU activation *** Codes Primary: 62M45, Secondary: 60G42 © 2022, CC BY.

关键词： Deep neural networks

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Asymptotics of Bayesian Uncertainty Estimation in Random Features Regression

arXiv

引用

arXiv 2023年

作者： Baek, Youngsoo Berchuck, Samuel I. Mukherjee, Sayan Department of Statistical Science Duke University DurhamNC27705 United States Department of Biostatistics & Bioinformatics Duke University DurhamNC27705 United States Center for Scalable Data Analysis and Artificial Intelligence Universität Leipzig Leipzig04105 Germany Deparments of Mathematics Computer Science Biostatistics & Bioinformatics Duke University NC United States Max Planck Institute for Mathematics in the Sciences Leipzig Germany

In this paper, we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori (MAP) estimator for the random features regression model in the overparameterized regime. We will focus on the variance of the posterior predictive distribution (Bayesian model average) and compare its asymptotics to that of the risk of the MAP estimator. In the regime where the model dimensions grow faster than any constant multiple of the number of samples, asymptotic agreement between these two quantities is governed by the phase transition in the signal-to-noise ratio. They also asymptotically agree with each other when the number of samples grows faster than any constant multiple of model dimensions. Numerical simulations illustrate finer distributional properties of the two quantities for finite dimensions. We conjecture they have Gaussian fluctuations and exhibit similar properties as found by previous authors in a Gaussian sequence model, which is of independent theoretical interest. © 2023, CC BY.

关键词： Signal to noise ratio

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Unbiased Estimation using a Class of Diffusion Processes

arXiv

引用

arXiv 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 KSA Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (d, B(d)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}tϵ[0,1]on d, d ϵ 0. This latter process is constructed such that, starting at X0= 0, one has X1∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 16] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(ϵ2), for arbitrary ϵ > 0, the associated cost is O(ϵ-5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(ϵ2), the associated cost (which is random) is, with high probability, O(ϵ-2| log(ϵ)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse *** Codes 60J60, 62D05, 65C40 © 2022, CC BY.

关键词： Diffusion

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