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learning gradients by a gradient descent algorithm

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2008年第2期341卷 1018-1027页

作者： Dong, Xuemei Zhou, Ding-Xuan City Univ Hong Kong Dept Math Kowloon Hong Kong Peoples R China Beijing Univ Aeronaut & Astronaut Dept Math Beijing 100083 Peoples R China

We propose a stochastic gradient descent algorithm for learning the gradient of a regression function from random samples of function values. This is a learning algorithm involving Mercer kernels. By a detailed analysis in reproducing kernel Hilbert spaces, we provide some error bounds to show that the gradient estimated by the algorithm converges to the true gradient, under some natural conditions on the regression function and suitable choices of the step size and regularization parameters. (C) 2007 Elsevier Inc. All rights reserved.

关键词： learning algorithm stochastic gradient descent variable selection reproducing kernel Hilbert space error analysis

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Neural network learning algorithms for tracking minor subspace in high-dimensional data stream

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2005年第3期16卷 513-521页

作者： Feng, DZ Zheng, WX Jia, Y Xidian Univ Natl Lab Radar Signaling Proc Xian 710071 Peoples R China Univ Western Sydney Sch QMMS Penrith NSW 1797 Australia Intel China Res Ctr Beijing 100080 Peoples R China

A novel random-gradient-based algorithm is developed for online tracking the minor component (MC) associated with the smallest eigenvalue of the autocorrelation matrix of the input vector sequence. The five available learning algorithms for tracking one MC are extended to those for tracking multiple MCs or the minor subspace (MS). In order to overcome the dynamical divergence properties of some available random-gradient-based algorithms, we propose a modification of the Oja-type algorithms, called OJAm, which can work satisfactorily. The averaging differential equation and the energy function associated with the OJAm are given. It is shown that the averaging differential equation will globally asymptotically converge to an invariance set. The corresponding energy or Lyapunov functions exhibit a unique global minimum attained if and only if its state matrices span the MS of the autocorrelation matrix of a vector data stream. The other stationary points are saddle (unstable) points. The globally convergence of OJAm is also studied. The OJAm provides an efficient online learning for tracking the MS. It can track an orthonormal basis of the MS while the other five available algorithms cannot track any orthonormal basis of the MS. The performances of the relative algorithms are shown via computer simulations.

关键词： convergence eigenvalue decomposition (EVD) energy function invariance set learning algorithm Lyapunov function minor subspace (MS) neural network stationary point stability

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A general kernelization framework for learning algorithms based on kernel PCA

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NEUROCOMPUTING 2010年第4-6期73卷 959-967页

作者： Zhang, Changshui Nie, Feiping Xiang, Shiming Tsinghua Univ State Key Lab Intelligent Technol & Syst TNList Dept Automat Beijing 100084 Peoples R China

In this paper, a general kernelization framework for learning algorithms is proposed via a two-stage procedure, i.e., transforming data by kernel principal component analysis (KPCA), and then directly performing the learning algorithm with the transformed data. It is worth noting that although a very few learning algorithms were also kernelized by this procedure before, why and under what condition this procedure is feasible have not been further studied. In this paper, we explicitly present this kernelization framework, and give a rigorous justification to reveal that under some mild conditions, the kernelization under this framework is equivalent to traditional kernel method. We show that these mild conditions are usually satisfied in most of learning algorithms. Therefore, most of learning algorithms can be kernelized under this framework without having to reformulate it into inner product form, which is a common yet vital step in traditional kernel methods. Enlightened by this framework, we also propose a novel kernel method based on the low-rank KPCA, which could be used to remove the noise in the feature space, speed up the kernel algorithm and improve the numerical stability for the kernel algorithm. Experiments are presented to verify the validity and effectiveness of the proposed methods. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Kernel method learning algorithm Kernel PCA Two-stage framework

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Machine learning facilitated business intelligence (Part I) Neural networks learning algorithms and applications

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INDUSTRIAL MANAGEMENT & DATA SYSTEMS 2019年第1期120卷 164-195页

作者： Khan, Waqar Ahmed Chung, S. H. Awan, Muhammad Usman Wen, Xin Hong Kong Polytech Univ Dept Ind & Syst Engn Kowloon Hong Kong Peoples R China Univ Punjab Inst Qual & Technol Management Lahore Pakistan

Purpose The purpose of this paper is to conduct a comprehensive review of the noteworthy contributions made in the area of the Feedforward neural network (FNN) to improve its generalization performance and convergence rate (learning speed);to identify new research directions that will help researchers to design new, simple and efficient algorithms and users to implement optimal designed FNNs for solving complex problems;and to explore the wide applications of the reviewed FNN algorithms in solving real-world management, engineering and health sciences problems and demonstrate the advantages of these algorithms in enhancing decision making for practical operations. Design/methodology/approach The FNN has gained much popularity during the last three decades. Therefore, the authors have focused on algorithms proposed during the last three decades. The selected databases were searched with popular keywords: "generalization performance," "learning rate," "overfitting" and "fixed and cascade architecture." Combinations of the keywords were also used to get more relevant results. Duplicated articles in the databases, non-English language, and matched keywords but out of scope, were discarded. Findings The authors studied a total of 80 articles and classified them into six categories according to the nature of the algorithms proposed in these articles which aimed at improving the generalization performance and convergence rate of FNNs. To review and discuss all the six categories would result in the paper being too long. Therefore, the authors further divided the six categories into two parts (i.e. Part I and Part II). The current paper, Part I, investigates two categories that focus on learning algorithms (i.e. gradient learning algorithms for network training and gradient-free learning algorithms). Furthermore, the remaining four categories which mainly explore optimization techniques are reviewed in Part II (i.e. optimization algorithms for learning rate, bias and varian

关键词： Data analytics Machine learning learning algorithm Feedforward neural network Industrial management

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A comparison of artificial neural networks learning algorithms in predicting tendency for suicide

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NEURAL COMPUTING & APPLICATIONS 2013年第5期23卷 1381-1386页

作者： Ayat, Saeed Farahani, Hojjat A. Aghamohamadi, Mehdi Alian, Mahmood Aghamohamadi, Somayeh Kazemi, Zeynab Payame Noor Univ Dept Comp Engn & Informat Technol Tehran Iran Univ Tehran Dept Psychol Tehran Iran Payame Noor Univ Dept Comp Engn & Informat Technol Najafabad Iran Islamic Azad Univ Dept Comp Engn Najafabad Branch Najafabad Iran Esfahan Univ Fac Educ Sci & Psychol Dept Psychol Esfahan Iran

New approaches adopted by behavioral science researchers to use modern modeling and predicting tools such as artificial neural networks have necessitated the study and comparison of the efficiency of different learning algorithms of these networks for various applications. By using well-known and different learning algorithms, this study examines and compares the Perceptron artificial neural network as predicting tendency for suicide based on risk factors within 33 input parameters framework used in neural network. To find the "best" learning algorithm, the algorithms were compared in terms of train and capability. The experimental data were collected through questionnaires distributed among 800 university students. All questionnaires used in this research were standardized with appropriate validity and reliability. The study findings indicated that LM and BFG algorithms had close evaluation in terms of performance index and true acceptance rate (TAR), and they showed higher predictive accuracy than the other algorithms. Furthermore, CFG algorithm had the minimum training time.

关键词： Neural computing Artificial neural network learning algorithm Prediction Tendency for suicide

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A comparison of learning algorithms for Bayesian networks:: a case study based on data from an emergency medical service

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ARTIFICIAL INTELLIGENCE IN MEDICINE 2004年第3期30卷 215-232页

作者： Acid, S de Campos, LM Fernández-Luna, JM Rodríguez, S Rodríguez, JM Salcedo, JL Univ Granada Escuela Tecn Super Ingn Informat Dept Ciencias Computac & IA E-18071 Granada Spain Univ Jaen Dept Informat Jaen Spain Hosp Univ Virgen Nieves Granada Granada Spain

Due to the uncertainty of many of the factors that influence the performance of an emergency medical service, we propose using Bayesian networks to model this kind of system. We use different algorithms for learning Bayesian networks in order to build several models, from the hospital manager's point of view, and apply them to the specific case of the emergency service of a Spanish hospital. This first study of a real problem includes preliminary data processing, the experiments carried out, the comparison of the algorithms from different perspectives, and some potential uses of Bayesian networks for management problems in the health service. (C) 2004 Elsevier B.V. All rights reserved.

关键词： Bayesian networks learning algorithm scoring functions independence emergency medical service management decision support in the health service

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Hyperbolic Gradient Operator and Hyperbolic Back-Propagation learning algorithms

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND learning SYSTEMS 2018年第5期29卷 1689-1702页

作者： Nitta, Tohru Kuroe, Yasuaki Natl Inst Adv Ind Sci & Technol Human Informat Res Inst Tsukuba Ibaraki Japan Kyoto Inst Technol Kyoto Japan

In this paper, we first extend the Wirtinger derivative which is defined for complex functions to hyperbolic functions, and derive the hyperbolic gradient operator yielding the steepest descent direction by using it. Next, we derive the hyperbolic backpropagation learning algorithms for some multilayered hyperbolic neural networks (NNs) using the hyperbolic gradient operator. It is shown that the use of the Wirtinger derivative reduces the effort necessary for the derivation of the learning algorithms by half, simplifies the representation of the learning algorithms, and makes their computer programs easier to code. In addition, we discuss the differences between the derived Hyperbolic-BP rules and the complex-valued backpropagation learning rule (Complex-BP). Finally, we make some experiments with the derived learning algorithms. As a result, we find that the convergence rates of the Hyperbolic-BP learning algorithms are high even if the fully activation functions are used, and discover that the Hyperbolic-BP learning algorithm for the hyperbolic NN with the split-type hyperbolic activation function has an ability to learn hyperbolic rotation as its inherent property.

关键词： Backpropagation hyperbolic number learning algorithm neural network (NN) Wirtinger calculus

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A Fuzzy Restricted Boltzmann Machine: Novel learning algorithms Based on the Crisp Possibilistic Mean Value of Fuzzy Numbers

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2018年第1期26卷 117-130页

作者： Feng, Shuang Chen, C. L. Philip Beijing Normal Univ Sch Appl Math Zhuhai 519085 Peoples R China Univ Macau Fac Sci & Technol Macau 99999 Peoples R China UMacau Res Inst Zhuhai 519080 Peoples R China Dalian Maritime Univ Dalian 116026 Peoples R China

A fuzzy restricted Boltzmann machine (FRBM) is extended from a restricted Boltzmann machine (RBM) by replacing all the real-valued parameters with fuzzy numbers. A new FRBM that employs the crisp possibilistic mean value of a fuzzy number to defuzzify the fuzzy free energy function is presented. This approach is much clearer and easier to obtain the expression of the defuzzified free energy function and its approximation than the centroid method. Several theorems that discuss the error bounds of the approximation to ensure the rationality and validity are also investigated. learning algorithms are given for the designed FRBM with symmetric triangular fuzzy numbers (STFNs), asymmetric triangular fuzzy numbers, and Gaussian fuzzy numbers. By appropriately choosing the parameters, a theorem is concluded that all FRBMs with symmetric fuzzy numbers will have identical learning algorithm to that of FRBMs with STFNs. This is illustrated by a case of FRBM with Gaussian fuzzy numbers. Two experiments including the MNIST handwriting recognition and the Bars-and-Stripes benchmark are carried out. The results show that the proposed FRBMs significantly outperform RBMs in learning accuracy and generalization ability, especially when encountering unlearned samples and recovering incomplete images.

关键词： Crisp possibilistic mean value fuzzy number fuzzy restricted Boltzmann machine (FRBM) learning algorithm

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UCB-Type learning algorithms with Kaplan-Meier Estimator for Lost-Sales Inventory Models with Lead Times

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OPERATIONS RESEARCH 2024年第4期72卷 iii-vi, 1317-1750, C2-C3页

作者： Lyu, Chengyi Zhang, Huanan Xin, Linwei Univ Colorado Boulder Leeds Sch Business Boulder CO 80309 USA Univ Chicago Booth Sch Business Chicago IL 60637 USA

In this paper, we consider a classic periodic -review lost -sales inventory system with lead times, which is notoriously challenging to optimize with a wide range of realworld applications. We consider a joint learning and optimization problem in which the decision maker does not know the demand distribution a priori and can only use past sales information (i.e., censored demand). Departing from existing learning algorithms on this learning problem that require the convexity property of the underlying system, we develop an upper confidence bound (UCB)-type learning framework that incorporates simulations with the Kaplan-Meier estimator and demonstrate its applicability to learning not only the optimal capped base -stock policy in which convexity no longer holds, but also the optimal base -stock policy with a regret that matches the best existing result. Compared with a classic multi -armed bandit problem, our problem has unique challenges because of the nature of the inventory system, because (1) each action has long-term impacts on future costs, and (2) the system state space is exponentially large in the lead time. As such, our learning algorithms are not naive adoptions of the classic UCB algorithm;in fact, the design of the simulation steps with the Kaplan-Meier estimator and averaging steps is novel in our algorithms, and the confidence width in the UCB index is also different from the classic one. We prove the regrets of our learning algorithms are tight up to a logarithmic term in the planning horizon T. Our extensive numerical experiments suggest the proposed algorithms (almost) dominate existing learning algorithms. We also demonstrate how to select which learning algorithm to use with limited demand data.

关键词： lost sales censored demand learning algorithm capped base-stock policy Kaplan-Meier estimator

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learning and non-learning algorithms for cuffless blood pressure measurement: a review

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MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING 2021年第6期59卷 1201-1222页

作者： Agham, Nishigandha Dnyaneshwar Chaskar, Uttam M. Coll Engn Pune Instrumentat Engn Wellesely Rd Pune 411005 Maharashtra India Coll Engn Pune Dept Instrumentat & Control Wellesely Rd Pune 411005 Maharashtra India

The machine learning approach has gained a significant attention in the healthcare sector because of the prospect of developing new techniques for medical devices and handling the critical database of chronic diseases. The learning approach has potential to analyze complex medical data, disease diagnosis, and patient monitoring system, and to monitor e-health record. Non-invasive cuffless blood pressure (CLBP) measurement secured a significant position in the patient monitoring system. From a few recent decades, the importance of cuffless technology has been perceived towards continuous monitoring of blood pressure (BP) and supplementary efforts have been made towards its continuous monitoring. However, the optimal method that measures BP unambiguously and continuously has not yet emerged along with issues like calibration time, accuracy and long-term estimation of BP with miniaturizing hardware. The present study provides an insight into several learning algorithms along with their feature selection models. Various challenges and future improvements towards the current state of machine learning in healthcare industries are discussed in the present review. The bottom line of this study is to provide a comprehensive perspective of the machine learning approach of CLBP for the generation of highly precise predictive models for continuous BP measurement.

关键词： Blood pressure Machine learning learning algorithm Non-learning algorithm

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