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NEUROCOMPUTING 2023年第1期522卷 1-10页

作者： Wu, Yun Xiong, Shifeng Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China Chinese Acad Sci Acad Math & Syst Sci NCMIS KLSC Beijing Peoples R China

This paper proposes a class of kernel interpolation-based methods, called kernel reconstruction learning, for solving machine learning problems. Kernel reconstruction learning uses kernel interpolators to recon-struct the unknown functions, which are needed to estimate in the problem, with estimated function val-ues at selected knots. It can be applied to any learning problem that involves function estimation. We prove a reconstruction representer theorem, which indicates that conventional kernel methods, including kernel ridge regression, kernel support vector machine, and kernel logistic regression, can be viewed as special cases of kernel reconstruction learning. Furthermore, kernel reconstruction learning provides new algorithms for large datasets. The kernel reconstruction vector machine, kernel reconstruction logistic regression, and kernel reconstruction density estimation are discussed in detail. With appropriate imple-mentations, they are shown to have higher prediction/estimation accuracy and/or less computational cost than popular kernel methods.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Kernel method Representer theorem Interpolation Classification Density estimation sequential algorithm

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FINDING THE CLOSED PARTITION OF A PLANAR GRAPH

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algorithmICA 1994年第5期11卷 443-468页

作者： RAMACHANDRAN, V YANG, H 1. Department of Computer Sciences The University of Texas at Austin 78712 Austin TX USA

In this paper we consider the problem of finding a closed partition in a directed graph. This problem has applications in concurrent probabilistic program verification. The best sequential algorithm known for this problem runs in O(mn) time where m is the number of directed edges and n is the number of vertices in the given digraph. In this paper we present a linear-time sequential algorithm to solve the closed partition problem for planar digraphs that are compact. We then build on this algorithm to obtain an O(n1.5)-time sequential algorithm to solve the closed partition problem for a general planar digraph.

关键词： CLOSED PARTITION COMPACT DIIGRAPH DIRECTED GRAPH DUAL GRAPH PLANAR GRAPH sequential algorithm STRONGLY CONNECTED COMPONENT

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Nonparametric, tuning-free estimation of S-shaped functions

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 2022年第4期84卷 1324-1352页

作者： Feng, Oliver Y. Chen, Yining Han, Qiyang Carroll, Raymond J. Samworth, Richard J. Univ Cambridge Stat Lab Cambridge England London Sch Econ & Polit Sci Dept Stat London England Rutgers State Univ Dept Stat Piscataway NJ USA Texas A&M Univ Dept Stat College Stn TX USA Univ Technol Sydney Sch Math & Phys Sci Sydney NSW Australia

We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimization problem, since the inflection point is unknown. We show that the estimator may nevertheless be regarded as a projection onto a finite union of convex cones, which allows us to propose a mixed primal-dual bases algorithm for its efficient, sequential computation. After developing a projection framework that demonstrates the consistency and robustness to misspecification of the estimator, our main theoretical results provide sharp oracle inequalities that yield worst-case and adaptive risk bounds for the estimation of the regression function, as well as a rate of convergence for the estimation of the inflection point. These results reveal not only that the estimator achieves the minimax optimal rate of convergence for both the estimation of the regression function and its inflection point (up to a logarithmic factor in the latter case), but also that it is able to achieve an almost-parametric rate when the true regression function is piecewise affine with not too many affine pieces. Simulations and a real data application to air pollution modelling also confirm the desirable finite-sample properties of the estimator, and our algorithm is implemented in the R package Sshaped.

关键词： sequential algorithm shape-constrained regression S-shaped functions

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An efficient algorithm for Elastic I-optimal design of generalized linear models

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2021年第2期49卷 438-470页

作者： Li, Yiou Deng, Xinwei Depaul Univ Dept Math Sci Chicago IL 60604 USA Virginia Tech Dept Stat Blacksburg VA 24061 USA

The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients. The prediction accuracy is usually critical in modern decision-making and artificial intelligence applications. It is of importance to study optimal designs from the prediction aspects for GLMs. In this work, we consider Elastic I-optimality as a prediction-oriented design criterion for GLMs, and develop an efficient algorithm for such EI-optimal designs. By investigating theoretical properties for the optimal weights of any set of design points and extending the general equivalence theorem to the EI-optimality for GLMs, the proposed efficient algorithm adequately combines the Fedorov-Wynn algorithm and the multiplicative algorithm. It achieves great computational efficiency with guaranteed convergence. Numerical examples are conducted to evaluate the feasibility and computational efficiency of the proposed algorithm.

关键词： Fast convergence multiplicative algorithm prediction-oriented sequential algorithm

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Computing regularities in strings: A survey

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EUROPEAN JOURNAL OF COMBINATORICS 2013年第1期34卷 3-14页

作者： Smyth, W. F. McMaster Univ Dept Comp & Software Algorithms Res Grp Hamilton ON L8S 4K1 Canada

The aim of this survey is to provide insight into the sequential algorithms that have been proposed to compute exact "regularities" in strings;that is, covers (or quasiperiods), seeds, repetitions, runs (or maximal periodicities), and repeats. After outlining and evaluating the algorithms that have been proposed for their computation, I suggest possibly productive future directions of research. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Exact Insight sequential algorithm Cosmic strings

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A two-pheromone trail ant colony system-tabu search approach for the heterogeneous vehicle routing problem with time windows and multiple products

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JOURNAL OF HEURISTICS 2013年第2期19卷 233-252页

作者： De la Cruz, Jair J. Paternina-Arboleda, Carlos D. Cantillo, Victor Montoya-Torres, Jairo R. Univ Norte Dept Ind Engn Barranquilla Colombia Univ Norte Escuela Negocios Barranquilla Colombia Univ Norte Dept Civil & Environm Engn Barranquilla Colombia Univ La Sabana Escuela Ciencias Econ & Adm Chia Cundinamarca Colombia

This paper considers a practical variant of the Vehicle Routing Problem (VRP) known as the Heterogeneous Vehicle Routing Problem with Time Windows and Multiple Products (HVRPTWMP). As the problem is NP-hard, the resolution approach proposed here is a sequential Ant Colony System (ACS)-Tabu Search algorithm. The approach introduces a two pheromone trail strategy to accelerate agents' (ants) learning process. Its convergence to good solutions is given in terms of fleet size and travel time while completing tours and service to all customers. The proposed procedure uses regency and frequency memories form Tabu Search to further improve the quality of solutions. Experiments are carried out using instances from literature and show the effectiveness of this procedure.

关键词： Vehicle routing Multiple products Time windows Ant colony Tabu search sequential algorithm

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An algorithm based on singular spectrum analysis for change-point detection

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2003年第2期32卷 319-352页

作者： Moskvina, V Zhigljavsky, A Univ Wales Coll Cardiff Sch Math Cardiff CF24 4YH S Glam Wales

This paper is devoted to application of the singular-spectrum analysis to sequential detection of changes in time series. An algorithm of change-point detection in time series, based on sequential application of the singular-spectrum analysis is developed and studied. The algorithm is applied to different data sets and extensively studied numerically. For specific models, several numerical approximations to the error probabilities and the power function of the algorithm are obtained. Numerical comparisons with other methods are given.

关键词： change-point detection singular-spectrum analysis sequential algorithm singular value decomposition

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Proficiency of transient elastography compared to liver biopsy for the assessment of fibrosis in HIV/HBV-coinfected patients

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JOURNAL OF VIRAL HEPATITIS 2011年第1期18卷 61-69页

作者： Miailhes, P. Pradat, P. Chevallier, M. Lacombe, K. Bailly, F. Cotte, L. Trabaud, M. -A. Boibieux, A. Bottero, J. Trepo, C. Zoulim, F. Hop Hotel Dieu Hosp Civils Lyon Serv Hepatogastroenterol F-69288 Lyon France INSERM U871 F-69008 Lyon France Univ Lyon 1 IFR62 Lyon Est F-69365 Lyon France Lab Biomnis Lyon France Hop St Antoine AP HP Serv Malad Infect F-75571 Paris France INSERM UMR S707 Paris France UMPC Fac Pierre & Marie Curie Paris France Hop Croix Rousse Hosp Civils Lyon Virol Lab F-69317 Lyon France Hop Croix Rousse Hosp Civils Lyon Serv Malad Infect F-69317 Lyon France

Transient elastography (TE) is a noninvasive technique to evaluate liver fibrosis. We compared the performance of TE with liver biopsy (LB) in patients with human immunodeficiency virus (HIV) and hepatitis B virus (HBV) coinfection. Patients prospectively underwent TE and LB. The diagnosis accuracy of TE was calculated using receiver operating characteristic (ROC) curves for different stages of fibrosis, and optimal cut-off values were defined. A sequential algorithm combining TE with biochemical score (Fibrotest (R)) is proposed. Fifty-seven patients had both TE and LB (median time: 3 days) and two with proven cirrhosis, only TE. Forty-six (78%) were under antiretroviral therapy with anti-HBV drugs in 98%, and 19 (32%) had elevated alanine aminotransferase (ALT). A significant correlation was observed between liver stiffness measurement (LSM) and METAVIR fibrosis stages (P < 0.0001). Patients with elevated ALT tended to have higher LSM than those with normal ALT. The areas under the ROC curves were 0.85 for significant fibrosis (>= F2), 0.92 for advanced fibrosis (>= F3) and 0.96 for cirrhosis. Using a cut-off of 5.9 kPa for F >= 2 and 7.6 kPa for F >= 3, the diagnosis accuracy was 83% and 86%, respectively. With an algorithm combining TE and Fibrotest (R), 97% of patients were well classified for significant fibrosis. Using this algorithm, the need for LB can be reduced by 67%. In HIV/HBV-coinfected patients, most of them with normal ALT under antiretroviral treatment including HBV active drugs, TE was proficient in discriminating moderate to severe fibrosis from minimal liver disease.

关键词： fibrosis assessment HIV HBV coinfection liver biopsy sequential algorithm transient elastography

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Treatment of spondylodiscitis

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INTERNATIONAL ORTHOPAEDICS 2012年第2期36卷 405-411页

作者： Zarghooni, Kourosh Roellinghoff, Marc Sobottke, Rolf Eysel, Peer Univ Cologne Dept Orthopaed & Trauma Surg ZKS BMBF 01KN1106 D-50931 Cologne Germany Univ Halle Wittenberg Dept Orthopaed & Trauma Surg Halle Germany

Pyogenic infections of the spine are relatively rare with an incidence between 1:100,000 and 1:250,000 per year, but the incidence is increasing due to increases in average life-expectancy, risk factors, and medical comorbidities. The mean time in hospital varies from 30 to 57 days and the hospital mortality is reported to be 2-17%. This article presents the relevant literature and our experience of conservative and surgical treatment of pyogenic spondylodiscitis. We have performed a review of the relevant literature and report the results of our own research in the diagnosis and treatment of pyogenic spondylodiscitis. We present a sequential algorithm for identification of the pathogen with blood cultures, CT-guided biopsies and intraoperative tissue samples. Basic treatment principles and indications for surgery and our surgical strategies are discussed. Recent efforts have been directed toward early mobilisation of patients using primary stable surgical techniques that lead to a further reduction of the mortality. Currently our hospital mortality in patients with spondylodiscitis is around 2%. With modern surgical and antibiotic treatment, a relapse of spondylodiscitis is unlikely to occur. In literature the relapse rate of 0-7% has been recorded. Overall the quality of life seems to be more favourable in patients following surgical treatment of spondylodiscitis. With close clinical and radiological monitoring of patients with spondylodiscitis, conservative and surgical therapies have become more successful. When indicated, surgical stabilisation of the infected segments is mandatory for control of the disease and immediate mobilisation of the patients.

关键词： Patients Surgery sequential algorithm Discitis Hospital Mortality Conservative Operative Surgical Procedures

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Two-dimensional periodicity in rectangular arrays

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SIAM JOURNAL ON COMPUTING 1998年第1期27卷 90-106页

作者： Amir, A Benson, G Georgia Inst Technol Coll Comp Atlanta GA 30332 USA Mt Sinai Med Ctr Dept Biomath Sci New York NY 10029 USA

String matching is rich with a variety of algorithmic tools. In contrast, multidimensional matching has had a rather sparse set of techniques. This paper presents a new algorithmic technique for two-dimensional matching: periodicity analysis. Its strength appears to lie in the fact that it is inherently two-dimensional. Periodicity in strings has been used to solve string matching problems. Multidimensional periodicity, however, is not as simple as it is in strings and was not formally studied or used in pattern matching. In this paper, we define and analyze two-dimensional periodicity in rectangular arrays. One definition of string periodicity is that a periodic string can self-overlap in a particular way. An analogous concept is true in two dimensions. The self-overlap vectors of a rectangle generate a regular pattern of locations where the rectangle may originate. Based on this regularity, we define four categories of periodic arrays-nonperiodic, lattice periodic, line periodic, and radiant periodic-and prove theorems about the properties of the classes. We give serial and parallel algorithms that find all locations where an overlap originates. In addition, our algorithms find a witness proving that the array does not self-overlap in any other location. The serial algorithm runs in time O(m(2)) (linear time) when the alphabet size is finite, and in O(m(2) log m) otherwise. The parallel algorithm runs in time O(log m) using O(m(2)) CRCW processors.

关键词： string matching two-dimensional periodicity witness sequential algorithm parallel algorithm

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