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The regularization paths of total variation-penalized regression splines

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第10期53卷 5047-5058页

作者： Bak, Kwan-Young Sungshin Womens Univ Data Sci Ctr Sch Math Stat & Data Sci Seoul 02844 South Korea

This paper reports on our study of a regularization path algorithm for a regression spline estimator based on B-splines and total variation penalty. The total variation-penalized regression spline estimation method enjoys a spatial adaptation property, since the penalty function enables data-adaptive knot selection. Although the theoretical properties of the related methods have been well established in the literature, the existing implementation algorithms are usually based on techniques with a high computational cost. In particular, the selection of the optimal complexity parameter, required to strike a balance in bias-variance tradeoff, is based on the computationally intensive grid search method. In this study, we propose an efficient path algorithm by formulating an equivalent l1 penalized optimization problem. The least angle regression algorithm is applied to the reformulated problem to obtain an entire path of the jump size of B-spline derivatives that represents the knot removal condition. Numerical studies based on real and simulated data are provided to illustrate the advantages of the proposed algorithm. The simulation result shows that the proposed algorithm is significantly faster than an existing algorithm. The proposed algorithm has an additional benefit of obtaining an entire regularization path, which can provide additional statistical insights into the given problem.

关键词： l(1) penalization Least angle regression path algorithm Spline Total variation

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Characterization of the solutions set of the generalized LASSO problems for non-full rank cases

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ELECTRONIC JOURNAL OF STATISTICS 2023年第1期17卷 1663-1710页

作者： Hwang, Jaesung Won, Joongho Kim, Yongdai SKTelecom Seoul South Korea Seoul Natl Univ Dept Stat Seoul South Korea

Generalized Lasso has received much attention for sparse learning in statistics and machine learning, since it extends many existing sparse learning methods and provides estimators with flexible sparsity structures. When the design matrix is rank-deficient, however, the objective function of generalized Lasso may not be strictly convex, in which case multiple solutions exist. In practice, a small l2 penalty is added to the objective function to make it strictly convex but its validity is largely unknown. In this paper, we study the solutions set of the G-Lasso problem with a rank-deficient design matrix. The main contributions of this paper are (1) to develop a solution path algorithm to find an exact solution even when the design matrix is rank-deficient and (2) to characterize the solutions set by a linear subspace with linear inequalities. Using the solution path algorithm and the characterization of the solutions set, we explain how to find a solution with specific properties, such as one with the least l & INFIN;norm. By analyzing simulated and real data sets, we illustrate that there exist quite different multiple solutions and finding a solution with a specific property is important to have better accuracy as well as better interpretability. In addition, we show that the approach of adding a small l2 penalty to the objective function is sometimes numerically unstable and the resulting estimator is inaccurate.

关键词： Generalized lasso characterization convex op-timization path algorithm

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Development of a UAV system for estimation of structure from movement for a random target

Development of a UAV system for estimation of structure from...

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IEEE Latin American Electron Devices Conference (LAEDC)

作者： Pereira-Santos, Roberto Alberto Chavarria-Zamora, Luis Inst Tecnol Costa Rica Comp Engn Cartago Costa Rica

ISBN: (数字)9781665497671

ISBN: (纸本)9781665497671

This paper describes a solution to automate the 3D model of an arbitrary object using an embedded UAV system through its movement and an image sensor to take pictures of an arbitrary static target, which is located with a trajectory algorithm that allows the quadcopter to travel, photograph and come back. Then, the images are sent to a server, stored in a computer to run the photogrammetry process, and finally create the three-dimensional object without human intervention. It's important to mention that the algorithm parameters are set through an application that obtains the object's height, coordinates, size, and other parameters. Also, this kind of UAV device costs around 200 dollars, and an application could control it, or if it's open-source, It could be configured by some programming language. This UAV system can be beneficial in different disciplinary fields, such as agriculture, construction, surveying, inventory control, surveillance, geology, biology, and other applications.

关键词： path algorithm UAV Automation Database Application Photogrammetry Arbitrary Object 2D and 3D Images

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Computational Time Reduction in Stream Field Navigation Through Dynamic path Search and Selection in Kinematic Environments

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ARRAY 2022年 14卷

作者： Fawzy, Hussein M. El-Sherif, Hisham M. Baumann, Gerd German Univ Cairo Field Robot Cairo Egypt German Univ Cairo Ind Automat Dept Cairo Egypt German Univ Cairo Math Dept Cairo Egypt

path planning algorithms based on physical models have been in development to allow navigating an environment in a way that mimics nature. Contrary to combinatorial and sampling-based algorithms, which represent the field by a set of nodes then use searching techniques to find a path, the artificial potential field method solves this problem by attracting the robot to the target and repelling it from the obstacles While the Stream Field Navigation (SFN) algorithm solves the problem by simulating a fluid field. This research proposes a dynamic path search and selection schema to allow the SFN algorithm to deal with moving obstacles. This research shows how the algorithm deals with a kinematic (variable) environment using the discretized path calculations. The dynamic search and selection algorithm is also capable of updating the robot's path when the goal is relocated. The developed approach is shown to greatly reduce the computational time required to obtain a path compared to re -simulating the field when a change is introduced to the environment.

关键词： path planning Mobile robot Navier-Stokes path algorithm Fluid dynamics Kinematic environments

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Shrinkage Method for Categorical Explanatory Variables 20

Shrinkage Method for Categorical Explanatory Variables

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Proceedings of the 4th International Conference on Advances in Image Processing

作者： Siyao Zhang Columbia University in the city of New York USA

ISBN: (纸本)9781450388368

Significantly more immigrant students are served by US public schools. To provide more efficient support to those immigrant students, we need to investigate the current situation of those immigrant students and graduation rate is used as a reference of their situation. In this article, fused lasso model is used as a shrinkage method for categorical explanatory variables. Data from graduation rate of New York state are considered. The result is given that students with better English skills and from Asian/Pacific Islander are more likely to have a higher graduation rate, which may suggest language support can be an efficient way to help those immigrant students.

关键词： social science path algorithm Fused lasso model

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Sparse Dictionary Learning for Blind Hyperspectral Unmixing

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 2019年第4期16卷 578-582页

作者： Liu, Yang Guo, Yi Li, Feng Xin, Lei Huang, Puming Xian Inst Space Radio Technol CAST Xian 710100 Shaanxi Peoples R China Qian Xuesen Lab Space Technol Beijing 100094 Peoples R China Western Sydney Univ Sch Comp Engn & Math Parramatta NSW 2150 Australia

Dictionary learning (DL) has been successfully applied to blind hyperspectral unmixing due to the similarity of underlying mathematical models. Both of them are linear mixture models and quite often sparsity and nonnegativity are incorporated. However, the mainstream sparse DL algorithms are crippled by the difficulty in prespecifying suitable sparsity. To solve this problem, this paper proposes an efficient algorithm to find all paths of the l(1)-regularization problem and select the best set of variables for the final abundances estimation. Based on the proposed algorithm, a DL framework is designed for hyperspectral unmixing. Our experimental results indicate that our method performs much better than conventional methods in terms of DL and hyperspectral data reconstruction. More importantly, it alleviates the difficulty of prescribing the sparsity.

关键词： Dictionary learning (DL) hyperspectral unmixing l(1)-regularization path algorithm sparse coding

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Research on Core algorithms of 3-D Aided UHV Transmission Line Selection Design Platform 6

Research on Core Algorithms of 3-D Aided UHV Transmission Li...

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6th International Conference on Information Science and Control Engineering (ICISCE)

作者： Song, Yang Hu, Haohan Wang, Ruying Tianjin Richsoft Elect Power Informat Technol Co Smart Energy Div Tianjin Peoples R China Tianjin Richsoft Elect Power Informat Technol Co Tianjin Peoples R China

ISBN: (纸本)9781728157122

UHV power transmission lines are playing very important role in the UHV power system, and the design of transmission line selection is the leading part of the power transmission line project, which is playing a most important role. The rationality of transmission line design impacts cost, difficulty and security of the whole UHV project construction, also impacts overall benefit of power transmission project. Furthermore, it also impacts the whole planning of grid system and country's security and stability. Along with the development of data gathering technology and hardware of computer, 3-D Aided UHV transmission Line Selection Design Platform (based on 3-D topographic data and 3-D device modeling data,) is already available from both theoretical and technology prospect. And its most key point is the algorithm of 3-D visible Aided transmission Line Selection Design Platform, this paper investigates the algorithm related researches, also includes the technical selection of the algorithm.

关键词： UHV power transmission line 3-D GIS platform aided design path algorithm

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Website Information Extraction Method and algorithms Based on Big Data Technology

Website Information Extraction Method and Algorithms Based o...

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4th International Workshop on Materials Engineering and Computer Sciences (IWMECS)

作者： Zhang Guoming Nanchang Inst Sci & Technol Nanchang 330108 Jiangxi Peoples R China

ISBN: (纸本)9781912407408

Based on the rich experience of teaching practice and theoretical analysis, it scientifically explained the cognitive semantic theory in vocabulary teaching methods, and apply them to the practice, in order to test the effectiveness of new vocabulary teaching method. This paper has conducted the empirical research combined vocabulary teaching empirical analysis with questionnaire survey. The results show that, English vocabulary teaching in higher vocational colleges under the guidance of the cognitive semantics theory helps to strengthen the students' vocabulary cognitive thinking, to construct complete and systematic vocabulary semantic network, greatly stimulate students' vocabulary learning interest and initiative, improve the students' vocabulary learning efficiency, to improve students' vocabulary level in a maximum degree.

关键词： Data segmentation path algorithm Big data technology Web site information extraction

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Modelling Interactions in High-dimensional Data with Backtracking

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JOURNAL OF MACHINE LEARNING RESEARCH 2016年第1期17卷 1-31页

作者： Shah, Rajen D. Univ Cambridge Stat Lab Cambridge CB3 0WB England

We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso can be useful for producing interpretable models. However, when the number variables runs into the thousands, and so even two-way interactions number in the millions, these methods may become computationally infeasible. Typically variable screening based on model fits using only main effects must be performed first. One problem with screening is that important variables may be missed if they are only useful for prediction when certain interaction terms are also present in the model. To tackle this issue, we introduce a new method we call Backtracking. It can be incorporated into many existing high-dimensional methods based on penalty functions, and works by building increasing sets of candidate interactions iteratively. Models fitted on the main effects and interactions selected early on in this process guide the selection of future interactions. By also making use of previous fits for computation, as well as performing calculations is parallel, the overall run-time of the algorithm can be greatly reduced. The effectiveness of our method when applied to regression and classification problems is demonstrated on simulated and real data sets. In the case of using Backtracking with the Lasso, we also give some theoretical support for our procedure.

关键词： high-dimensional data interactions Lasso path algorithm

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Modelling interactions in high-dimensional data with backtracking

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2016年第1期17卷

作者： Kevin Murphy Bernhard Schölkopf Rajen D. Shah Google MPI for Intelligent Systems Statistical Laboratory University of Cambridge Cambridge UK

We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso can be useful for producing interpretable models. However, when the number variables runs into the thousands, and so even two-way interactions number in the millions, these methods may become computationally infeasible. Typically variable screening based on model fits using only main effects must be performed first. One problem with screening is that important variables may be missed if they are only useful for prediction when certain interaction terms are also present in the *** tackle this issue, we introduce a new method we call Backtracking. It can be incorporated into many existing high-dimensional methods based on penalty functions, and works by building increasing sets of candidate interactions iteratively. Models fitted on the main effects and interactions selected early on in this process guide the selection of future interactions. By also making use of previous fits for computation, as well as performing calculations is parallel, the overall run-time of the algorithm can be greatly *** effectiveness of our method when applied to regression and classification problems is demonstrated on simulated and real data sets. In the case of using Backtracking with the Lasso, we also give some theoretical support for our procedure.

关键词： high-dimensional data interactions lasso path algorithm

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