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Robust Multi-Task Regression with Shifting Low-Rank Patterns
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-02-15 DOI: 10.1007/s10114-025-3362-8
Junfeng Cui, Guanghui Wang, Fengyi Song, Xiaoyan Ma, Changliang Zou
{"title":"Robust Multi-Task Regression with Shifting Low-Rank Patterns","authors":"Junfeng Cui,&nbsp;Guanghui Wang,&nbsp;Fengyi Song,&nbsp;Xiaoyan Ma,&nbsp;Changliang Zou","doi":"10.1007/s10114-025-3362-8","DOIUrl":"10.1007/s10114-025-3362-8","url":null,"abstract":"<div><p>We consider the problem of multi-task regression with time-varying low-rank patterns, where the collected data may be contaminated by heavy-tailed distributions and/or outliers. Our approach is based on a piecewise robust multi-task learning formulation, in which a robust loss function—not necessarily to be convex, but with a bounded derivative—is used, and each piecewise low-rank pattern is induced by a nuclear norm regularization term. We propose using the composite gradient descent algorithm to obtain stationary points within a data segment and employing the dynamic programming algorithm to determine the optimal segmentation. The theoretical properties of the detected number and time points of pattern shifts are studied under mild conditions. Numerical results confirm the effectiveness of our method.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 2","pages":"677 - 702"},"PeriodicalIF":0.8,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Segmented Linear Regression Trees
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-02-15 DOI: 10.1007/s10114-025-3349-5
Xiangyu Zheng, Songxi Chen
{"title":"Segmented Linear Regression Trees","authors":"Xiangyu Zheng,&nbsp;Songxi Chen","doi":"10.1007/s10114-025-3349-5","DOIUrl":"10.1007/s10114-025-3349-5","url":null,"abstract":"<div><p>Tree-based models have been widely applied in both academic and industrial settings due to the natural interpretability, good predictive accuracy, and high scalability. In this paper, we focus on improving the single-tree method and propose the segmented linear regression trees (SLRT) model that replaces the traditional constant leaf model with linear ones. From the parametric view, SLRT can be employed as a recursive change point detect procedure for segmented linear regression (SLR) models, which is much more efficient and flexible than the traditional grid search method. Along this way, we propose to use the conditional Kendall’s <i>τ</i> correlation coefficient to select the underlying change points. From the non-parametric view, we propose an efficient greedy splitting method that selects the splits by analyzing the association between residuals and each candidate split variable. Further, with the SLRT as a single-tree predictor, we propose a linear random forest approach that aggregates the SLRTs by a weighted average. Both simulation and empirical studies showed significant improvements than the CART trees and even the random forest.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 2","pages":"498 - 521"},"PeriodicalIF":0.8,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relative Auslander Bijection in Extriangulated Categories
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI: 10.1007/s10114-025-2074-4
Tiwei Zhao
{"title":"Relative Auslander Bijection in Extriangulated Categories","authors":"Tiwei Zhao","doi":"10.1007/s10114-025-2074-4","DOIUrl":"10.1007/s10114-025-2074-4","url":null,"abstract":"<div><p>Extriangulated categories were introduced by Nakaoka and Palu, which unify exact categories and extension-closed subcategories of triangulated categories. In this paper, we develop the relative homology aspect of Auslander bijection in extriangulated categories. Namely, we introduce the notion of generalized ARS-duality relative to an additive subfunctor, and prove that there is a bijective triangle which involves the generalized ARS-duality and the restricted Auslander bijection relative to the subfunctor. We give the Auslander’s defect formula in terms of the generalized ARS-duality, show the interplay of morphisms being determined by objects and a kind of extriangles, and characterize a class of objects which are somehow controlled by this kind of extriangles. We also give a realization for a functor relating the Auslander bijection and the generalized ARS-duality.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"985 - 1014"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strassen’s Law of the Iterated Logarithm under Sub-linear Expectations
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI: 10.1007/s10114-025-2759-8
Wangyun Gu, Lixin Zhang
{"title":"Strassen’s Law of the Iterated Logarithm under Sub-linear Expectations","authors":"Wangyun Gu,&nbsp;Lixin Zhang","doi":"10.1007/s10114-025-2759-8","DOIUrl":"10.1007/s10114-025-2759-8","url":null,"abstract":"<div><p>We establish the Strassen’s law of the iterated logarithm (LIL for short) for independent and identically distributed random variables with <span>({hat {mathbb E}}[X_{1}]={hat {cal E}}[X_{1}]=0)</span> and <span>(C_{mathbb V}[X_{1}^{2}]&lt;infty)</span> under a sub-linear expectation space with a countably sub-additive capacity <span>({mathbb V})</span>. We also show the LIL for upper capacity with <span>(sigma={overline sigma})</span> under some certain conditions.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"827 - 846"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite Element Method Resolution and Error Estimators for p-Laplacian Problem with a New Boundary Condition
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI: 10.1007/s10114-025-3561-3
Omar El Moutea, Hassan El Amri
{"title":"Finite Element Method Resolution and Error Estimators for p-Laplacian Problem with a New Boundary Condition","authors":"Omar El Moutea,&nbsp;Hassan El Amri","doi":"10.1007/s10114-025-3561-3","DOIUrl":"10.1007/s10114-025-3561-3","url":null,"abstract":"<div><p>In this article, we discuss the approach to solving a nonlinear PDE equation, specifically the <i>p</i>-Laplacian equation, with a general (nonlinear) boundary condition. We establish the existence and uniqueness of the solution, subject to certain assumptions outlined in this paper. To solve our nonlinear problem using the Finite Element Method (FEM), we derive an appropriate variational formulation. Additionally, we introduce a study of the residual a posteriori-error indicator, establishing both upper and lower bounds to control the error. The upper bound is determined using averaging interpolators in some quasi-norms defined by Barrett and Liu. Furthermore, we prove the equivalence between the residual error and the true error <i>e</i> = <i>u</i> − <i>u</i><sub><i>h</i></sub>. Lastly, we perform a simulation of the <i>p</i>-Laplacian problem in the <i>L</i>-shape domain using a Matlab program in two-dimensional space.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"854 - 872"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Positively Complete Einstein Square Metrics
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI: 10.1007/s10114-025-2578-y
Zhongmin Shen, Hongmei Zhu
{"title":"On Positively Complete Einstein Square Metrics","authors":"Zhongmin Shen,&nbsp;Hongmei Zhu","doi":"10.1007/s10114-025-2578-y","DOIUrl":"10.1007/s10114-025-2578-y","url":null,"abstract":"<div><p>The well-known Berwald square metric is a positively complete and projectively flat Finsler metric with vanishing flag curvature. In this paper, we study a positively complete square metric on a manifold. We show a rigidity result that if the Ricci curvature is constant, then it must be isometric to the Berwald square metric. This is not true without assumption on the completeness of the metric.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"1015 - 1022"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Differential Games of Mean-Field Dynamics and Second-Order Bellman–Isaacs Equations on the Wasserstein Space
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI: 10.1007/s10114-025-2666-z
Tao Hao, Jie Xiong
{"title":"Stochastic Differential Games of Mean-Field Dynamics and Second-Order Bellman–Isaacs Equations on the Wasserstein Space","authors":"Tao Hao,&nbsp;Jie Xiong","doi":"10.1007/s10114-025-2666-z","DOIUrl":"10.1007/s10114-025-2666-z","url":null,"abstract":"<div><p>This paper concerns two-player zero-sum stochastic differential games with <i>nonanticipative strategies against closed-loop controls</i> in the case where the coefficients of mean-field stochastic differential equations and cost functional depend on the joint distribution of the state and the control. In our game, both the (lower and upper) value functions and the (lower and upper) second-order Bellman–Isaacs equations are defined on the Wasserstein space <span>({cal P}_{2}({mathbb R}^{n}))</span> which is an infinite dimensional space. The dynamic programming principle for the value functions is proved. If the (upper and lower) value functions are smooth enough, we show that they are the classical solutions to the second-order Bellman–Isaacs equations. On the other hand, the classical solutions to the (upper and lower) Bellman–Isaacs equations are unique and coincide with the (upper and lower) value functions. As an illustrative application, the linear quadratic case is considered. Under the Isaacs condition, the explicit expressions of optimal closed-loop controls for both players are given. Finally, we introduce the intrinsic notion of viscosity solution of our second-order Bellman–Isaacs equations, and characterize the (upper and lower) value functions as their viscosity solutions.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"873 - 907"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
List Edge Colorings of Planar Graphs without Non-induced 7-cycles
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI: 10.1007/s10114-025-2761-1
Li Zhang, Hajo Broersma, You Lu, Shenggui Zhang
{"title":"List Edge Colorings of Planar Graphs without Non-induced 7-cycles","authors":"Li Zhang,&nbsp;Hajo Broersma,&nbsp;You Lu,&nbsp;Shenggui Zhang","doi":"10.1007/s10114-025-2761-1","DOIUrl":"10.1007/s10114-025-2761-1","url":null,"abstract":"<div><p>A graph <i>G</i> is edge-<i>k</i>-choosable if, for any assignment of lists <i>L</i>(<i>e</i>)of at least <i>k</i> colors to all edges <i>e</i> ∈ <i>E</i>(<i>G</i>), there exists a proper edge coloring such that the color of <i>e</i> belongs to <i>L</i>(<i>e</i>) for all <i>e</i> ∈ <i>E</i>(<i>G</i>). One of Vizing’s classic conjectures asserts that every graph is edge-(Δ + 1)-choosable. It is known since 1999 that this conjecture is true for general graphs with Δ ≤ 4. More recently, in 2015, Bonamy confirmed the conjecture for planar graph with Δ ≥ 8, but the conjecture is still open for planar graphs with 5 ≤ Δ ≤ 7. We confirm the conjecture for planar graphs with Δ ≥ 6 in which every 7-cycle (if any) induces a <i>C</i><sub>7</sub> (so, without chords), thereby extending a result due to Dong, Liu and Li.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"1037 - 1054"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tangent Measures of Homogeneous Cantor Sets Satisfying the Strong Separation Condition
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI: 10.1007/s10114-025-3326-z
Xiangyu Liang, Yongtao Wang
{"title":"Tangent Measures of Homogeneous Cantor Sets Satisfying the Strong Separation Condition","authors":"Xiangyu Liang,&nbsp;Yongtao Wang","doi":"10.1007/s10114-025-3326-z","DOIUrl":"10.1007/s10114-025-3326-z","url":null,"abstract":"<div><p>This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝ<sup><i>d</i></sup> generated by specific iterated function systems that satisfy the strong separation condition. Through the dynamics of “zooming in” on typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝ<sup><i>d</i></sup>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"938 - 974"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp Morrey Regularity for an Even Order Elliptic System
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-24 DOI: 10.1007/s10114-025-3353-9
Changyu Guo, Wenjuan Qi
{"title":"Sharp Morrey Regularity for an Even Order Elliptic System","authors":"Changyu Guo,&nbsp;Wenjuan Qi","doi":"10.1007/s10114-025-3353-9","DOIUrl":"10.1007/s10114-025-3353-9","url":null,"abstract":"<div><p>In this short note, we establish a sharp Morrey regularity theory for an even order elliptic system of Rivière type: </p><div><div><span>$$Delta^{m}u=sum_{l=0}^{m-1}Delta^{l}langle{V}_{l}, durangle+sum_{l=0}^{m-2}Delta^{l}delta(w_{l}du)+f quad {rm in} ; B^{2m}$$</span></div></div><p> under minimal regularity assumptions on the coefficients functions <i>V</i><sub><i>l</i></sub>, <i>w</i><sub><i>l</i></sub> and that <i>f</i> belongs to certain Morrey space. This can be regarded as a further extension of the recent <i>L</i><sup><i>p</i></sup>-regularity theory obtained by Guo–Xiang–Zheng [<i>J. Math. Pures Appl.</i> (9), <b>165</b>, 286–324 (2022)], and generalizes [<i>Proc. Amer. Math. Soc.</i>, <b>152</b>(10), 4261–4268 (2024)], [<i>Acta Math. Sci. Ser. B</i> (<i>Engl. Ed.</i>), <b>44</b>(2), 420–430 (2024)] for second and fourth order elliptic systems.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"925 - 937"},"PeriodicalIF":0.8,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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