Journal of Complexity最新文献

{"title":"On a class of linear regression methods","authors":"Ying-Ao Wang ,&nbsp;Qin Huang ,&nbsp;Zhigang Yao ,&nbsp;Ye Zhang","doi":"10.1016/j.jco.2024.101826","DOIUrl":"10.1016/j.jco.2024.101826","url":null,"abstract":"<div><p>In this paper, a unified study is presented for the design and analysis of a broad class of linear regression methods. The proposed general framework includes the conventional linear regression methods (such as the least squares regression and the Ridge regression) and some new regression methods (e.g. the Landweber regression and Showalter regression), which have recently been introduced in the fields of optimization and inverse problems. The strong consistency, the reduced mean squared error, the asymptotic Gaussian property, and the best worst case error of this class of linear regression methods are investigated. Various numerical experiments are performed to demonstrate the consistency and efficiency of the proposed class of methods for linear regression.</p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear Tikhonov regularization in Hilbert scales for inverse learning","authors":"Abhishake Rastogi","doi":"10.1016/j.jco.2024.101824","DOIUrl":"10.1016/j.jco.2024.101824","url":null,"abstract":"<div><p>In this paper, we study Tikhonov regularization scheme in Hilbert scales for a nonlinear statistical inverse problem with general noise. The regularizing norm in this scheme is stronger than the norm in the Hilbert space. We focus on developing a theoretical analysis for this scheme based on conditional stability estimates. We utilize the concept of the distance function to establish high probability estimates of the direct and reconstruction errors in the Reproducing Kernel Hilbert space setting. Furthermore, explicit rates of convergence in terms of sample size are established for the oversmoothing case and the regular case over the regularity class defined through an appropriate source condition. Our results improve upon and generalize previous results obtained in related settings.</p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0885064X24000013/pdfft?md5=1a65eb323b09b712bcf07de5eb47b8eb&pid=1-s2.0-S0885064X24000013-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139375520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Randomized complexity of parametric integration and the role of adaption II. Sobolev spaces","authors":"Stefan Heinrich","doi":"10.1016/j.jco.2023.101823","DOIUrl":"10.1016/j.jco.2023.101823","url":null,"abstract":"<div><p><span>We study the complexity of randomized computation of integrals depending on a parameter, with integrands<span> from Sobolev spaces. That is, for </span></span><span><math><mi>r</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>N</mi></math></span>, <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>≤</mo><mo>∞</mo></math></span>, <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup></math></span>, and <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><msup><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup></math></span> we are given <span><math><mi>f</mi><mo>∈</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> and we seek to approximate<span><span><span><math><mo>(</mo><mi>S</mi><mi>f</mi><mo>)</mo><mo>(</mo><mi>s</mi><mo>)</mo><mo>=</mo><munder><mo>∫</mo><mrow><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></munder><mi>f</mi><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo><mi>d</mi><mi>t</mi><mspace></mspace><mo>(</mo><mi>s</mi><mo>∈</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>,</mo></math></span></span></span> with error measured in the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></math></span>-norm. Information is standard, that is, function values of <em>f</em>. Our results extend previous work of Heinrich and Sindambiwe (1999) <span>[10]</span> for <span><math><mi>p</mi><mo>=</mo><mi>q</mi><mo>=</mo><mo>∞</mo></math></span> and Wiegand (2006) <span>[15]</span> for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>=</mo><mi>q</mi><mo>&lt;</mo><mo>∞</mo></math></span>. Wiegand's analysis was carried out under the assumption that <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span> is continuously embedded in <span><math><mi>C</mi><mo>(</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></math></span><span> (embedding condition). We also study the case that the embedding condition does not hold. For this purpose a new ingredient is developed – a stochastic discretization","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sharp lower error bounds for strong approximation of SDEs with piecewise Lipschitz continuous drift coefficient","authors":"Simon Ellinger","doi":"10.1016/j.jco.2023.101822","DOIUrl":"10.1016/j.jco.2023.101822","url":null,"abstract":"<div><p><span>We study pathwise approximation of strong solutions of scalar stochastic differential equations (SDEs) at a single time in the presence of discontinuities of the drift coefficient. Recently, it has been shown by Müller-Gronbach and Yaroslavtseva (2022) that for all </span><span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> a transformed Milstein-type scheme reaches an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span><span><span>-error rate of at least 3/4 when the drift coefficient is a piecewise Lipschitz-continuous function with a piecewise Lipschitz-continuous derivative and the diffusion coefficient is constant. It has been proven by Müller-Gronbach and Yaroslavtseva (2023) that this rate 3/4 is optimal if one additionally assumes that the drift coefficient is bounded, increasing and has a point of discontinuity. While </span>boundedness and monotonicity of the drift coefficient are crucial for the proof of the matching lower bound from Müller-Gronbach and Yaroslavtseva (2023), we show that both conditions can be dropped. For the proof we apply a transformation technique which was so far only used to obtain upper bounds.</span></p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complexity for a class of elliptic ordinary integro-differential equations","authors":"A.G. Werschulz","doi":"10.1016/j.jco.2023.101820","DOIUrl":"10.1016/j.jco.2023.101820","url":null,"abstract":"<div><p>Consider the variational form of the ordinary integro-differential equation (OIDE)<span><span><span><math><mo>−</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>″</mo></mrow></msup><mo>+</mo><mi>u</mi><mo>+</mo><munderover><mo>∫</mo><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></munderover><mi>q</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mi>y</mi><mo>)</mo><mi>u</mi><mo>(</mo><mi>y</mi><mo>)</mo><mrow><mtext>dy</mtext></mrow><mo>=</mo><mi>f</mi></math></span></span></span> on the unit interval <em>I</em><span>, subject to homogeneous Neumann boundary conditions. Here, </span><em>f</em> and <em>q</em> respectively belong to the unit ball of <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>(</mo><mi>I</mi><mo>)</mo></math></span> and the ball of radius <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> of <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>(</mo><msup><mrow><mi>I</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. For <span><math><mi>ε</mi><mo>&gt;</mo><mn>0</mn></math></span>, we want to compute <em>ε</em>-approximations for this problem, measuring error in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>I</mi><mo>)</mo></math></span> sense in the worst case setting. Assuming that standard information is admissible, we find that the <em>n</em>th minimal error is <span><math><mi>Θ</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>/</mo><mn>2</mn><mo>}</mo></mrow></msup><mo>)</mo></math></span>, so that the information <em>ε</em>-complexity is <span><math><mi>Θ</mi><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>/</mo><mn>2</mn><mo>}</mo></mrow></msup><mo>)</mo></math></span><span>; moreover, finite element methods of degree </span><span><math><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>}</mo></math></span><span> are minimal-error algorithms. We use a Picard method to approximate the solution of the resulting linear systems, since Gaussian elimination will be too expensive. We find that the total </span><em>ε</em>-complexity of the problem is at least <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>/</mo><mn>2</mn><mo>}</mo></mrow></msup><mo>)</mo></math></span> and at most <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>r</mi><mo>,</mo><mi>s</mi><mo>/</mo><mn>2</mn><mo>}</mo></mrow></msup><mi>ln</mi><mo>⁡</mo><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>1</mn></m","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139071062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Randomized complexity of parametric integration and the role of adaption I. Finite dimensional case","authors":"Stefan Heinrich","doi":"10.1016/j.jco.2023.101821","DOIUrl":"10.1016/j.jco.2023.101821","url":null,"abstract":"<div><p>We study the randomized <em>n</em><span>-th minimal errors (and hence the complexity) of vector valued mean computation, which is the discrete version of parametric<span> integration. The results of the present paper form the basis for the complexity analysis of parametric integration in Sobolev spaces, which will be presented in Part 2. Altogether this extends previous results of Heinrich and Sindambiwe (1999) </span></span><span>[12]</span> and Wiegand (2006) <span>[27]</span>. Moreover, a basic problem of Information-Based Complexity on the power of adaption for linear problems in the randomized setting is solved.</p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139071056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the information complexity for integration in subspaces of the Wiener algebra","authors":"Liang Chen,&nbsp;Haixin Jiang","doi":"10.1016/j.jco.2023.101819","DOIUrl":"10.1016/j.jco.2023.101819","url":null,"abstract":"<div><p>Recently, Goda proved the polynomial tractability of integration on the following function subspace of the Wiener algebra<span><span><span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>:</mo><mo>=</mo><mrow><mo>{</mo><mi>f</mi><mo>∈</mo><mi>C</mi><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo><mo>|</mo><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub></mrow><mspace></mspace><mspace></mspace><mspace></mspace><mo>:</mo><mo>=</mo><munder><mo>∑</mo><mrow><mi>k</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></munder><mo>|</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>k</mi><mo>)</mo><mo>|</mo><mi>max</mi><mo>⁡</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><munder><mi>min</mi><mrow><mi>j</mi><mo>∈</mo><mi>supp</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></munder><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>|</mo><mo>)</mo></mrow><mo>&lt;</mo><mo>∞</mo><mo>}</mo><mo>,</mo></math></span></span></span> where <span><math><mi>T</mi><mo>:</mo><mo>=</mo><mi>R</mi><mo>/</mo><mi>Z</mi><mo>=</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>k</mi><mo>)</mo></math></span> is the <strong><em>k</em></strong><span>-th Fourier coefficient of </span><em>f</em> and <span><math><mi>supp</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>{</mo><mi>j</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>d</mi><mo>}</mo><mo>|</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>≠</mo><mn>0</mn><mo>}</mo></math></span>. Goda raised an open question as to whether the upper bound of the information complexity for integration in <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span><span> can be improved. In this note, we give a positive answer. By establishing a Monte Carlo sampling method and using Rademacher complexity to estimate the uniform convergence rate, the upper bound can be improved to </span><span><math><mi>Θ</mi><mo>(</mo><mi>d</mi><mo>/</mo><msup><mrow><mi>ϵ</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span>, where <span><math><mi>ϵ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></math></span> is the target accuracy. We also use the same technique to estimate the information complexity for a Hölder continuous subspace of Wiener algebra. Compared to the previous upper bound <span><math><mi>Θ</mi><mo>(</mo><mi>max</mi><mo>⁡</mo><mo>(</mo><mfrac><mrow><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>ϵ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>,</mo><mfrac><mrow><msup><mrow><mi>d</mi></mrow><mrow><mn>1</mn><mo>/</mo><mi>q</mi></mrow></","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139071325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A duality approach to regularized learning problems in Banach spaces","authors":"Raymond Cheng ,&nbsp;Rui Wang ,&nbsp;Yuesheng Xu","doi":"10.1016/j.jco.2023.101818","DOIUrl":"10.1016/j.jco.2023.101818","url":null,"abstract":"<div><p><span>Regularized learning problems in Banach spaces, which often minimize the sum of a data fidelity term in one Banach norm and a </span>regularization<span><span> term in another Banach norm, is challenging to solve. We construct a direct sum space based on the Banach spaces for the fidelity term and the regularization term, and recast the objective function as the norm of a quotient space of the direct sum space. We then express the original regularized problem as an optimization problem in the dual space of the direct sum space. It is to find the maximum of a linear function on a convex polytope, which may be solved by linear programming. A solution of the original problem is then obtained by using related </span>extremal properties of norming functionals from a solution of the dual problem. Numerical experiments demonstrate that the proposed duality approach is effective for solving the regularization learning problems.</span></p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal recovery and volume estimates","authors":"A. Kushpel","doi":"10.1016/j.jco.2023.101780","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101780","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54746253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The rate of convergence for sparse and low-rank quantile trace regression","authors":"Xiangyong Tan, Ling Peng, Peiwen Xiao, Qing Liu, Xiaohui Liu","doi":"10.1016/j.jco.2023.101778","DOIUrl":"https://doi.org/10.1016/j.jco.2023.101778","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"54746217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}