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Spectral baseline estimation using penalized least squares with weights derived from the Bayesian method

Nuclear Science and Techniques 2022年第11期33卷 144-157页

作者： Qian Wang Xin-Liang Yan Xiang-Cheng Chen Peng Shuai Meng Wang Yu-Hu Zhang Institute of Modern Physics Chinese Academy of SciencesLanzhou 730000China University of Chinese Academy of Sciences Beijing 100049China Van Swinderen Institute University of GroningenGroningen 9747 AAThe Netherlands

The penalized least squares(PLS)method with appropriate weights has proved to be a successful baseline estimation method for various spectral analyses.It can extract the baseline from the spectrum while retaining the signal peaks in the presence of random noise.The algorithm is implemented by iterating over the weights of the data points.In this study,we propose a new approach for assigning weights based on the Bayesian rule.The proposed method provides a self-consistent weighting formula and performs well,particularly for baselines with different curvature components.This method was applied to analyze Schottky spectra obtained in 86Kr projectile fragmentation measurements in the experimental Cooler Storage Ring(CSRe)at Lanzhou.It provides an accurate and reliable storage lifetime with a smaller error bar than existing PLS methods.It is also a universal baseline-subtraction algorithm that can be used for spectrum-related experiments,such as precision nuclear mass and lifetime measurements in storage rings.

关键词： penalized least squares Baseline correction Bayesian rule Spectrum analysis

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An Alternating Direction Method of Multipliers for MCP-penalized Regression with High-dimensional Data

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1892-1906页

作者： Yue Yong SHI Yu Ling JIAO Yong Xiu CAO Yan Yan LIU School of Economics and Management China University of Geosciences Wuhan 430074 P. R. China Center for Resources and Environmental Economic Research China University of Geosciences Wuhan 430074 P. R. China School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan 430073 P. R. China School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China

The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers （ADMM） with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush-Kuhn-Tucker （KKT） optimality con- ditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.

关键词： Alternating direction method of multipliers coordinate descent continuation high-dimen-sional BIC minimax concave penalty penalized least squares

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penalized least SQUARE IN SPARSE SETTING WITH CONVEX PENALTY AND NON GAUSSIAN ERRORS

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Acta Mathematica Scientia 2021年第6期41卷 2198-2216页

作者： Doualeh ABDILLAHI-ALI Nourddine AZZAOUI Arnaud GUILLIN Guillaume LE MAILLOUX Tomoko MATSUI Laboratoire de Mathématiques Blaise Pascal CNRS-UMR 6620Université Clermont-Auvergne(UCA)63000Clermont-FerrandFrance Department of Statistical Modeling Institute of Statistical Mathematics10-3 Midori-choTachikawa-shiTokyo1908562Japan

This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the particular cases of Lasso and Group Lasso estimators in a regression setting.The main contribution is that our oracle inequalities are established for the more general case where the observations noise is issued from probability measures that satisfy a weak spectral gap(or Poincaré)inequality instead of Gaussian distributions.We illustrate our results on a heavy tailed example and a sub Gaussian one;we especially give the explicit bounds of the oracle inequalities for these two special examples.

关键词： penalized least squares Gaussian errors convex penalty

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