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Edgeworth expansion for semi-hard triplet loss
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-23 DOI: 10.1016/j.spl.2025.110441
Masanari Kimura
{"title":"Edgeworth expansion for semi-hard triplet loss","authors":"Masanari Kimura","doi":"10.1016/j.spl.2025.110441","DOIUrl":"10.1016/j.spl.2025.110441","url":null,"abstract":"<div><div>We develop a higher-order asymptotic analysis for the semi-hard triplet loss using the Edgeworth expansion. It is known that this loss function enforces that embeddings of similar samples are close while those of dissimilar samples are separated by a specified margin. By refining the classical central limit theorem, our approach quantifies the impact of the margin parameter and the skewness of the underlying data distribution on the loss behavior. In particular, we derive explicit Edgeworth expansions that reveal first-order corrections in terms of the third cumulant, thereby characterizing non-Gaussian effects present in the distribution of distance differences between anchor-positive and anchor-negative pairs. Our findings provide detailed insight into the sensitivity of the semi-hard triplet loss to its parameters and offer guidance for choosing the margin to ensure training stability.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110441"},"PeriodicalIF":0.9,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 reverse inequalities for Besov integral probability metrics between smooth densities
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-21 DOI: 10.1016/j.spl.2025.110437
Jeongjik Lee, Minwoo Chae
{"title":"On reverse inequalities for Besov integral probability metrics between smooth densities","authors":"Jeongjik Lee,&nbsp;Minwoo Chae","doi":"10.1016/j.spl.2025.110437","DOIUrl":"10.1016/j.spl.2025.110437","url":null,"abstract":"<div><div>For smooth probability densities, we prove certain reverse inequalities between Besov integral probability metrics with different orders of smoothness. Our results provide a substantial generalization and improvement of the existing results in the literature.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110437"},"PeriodicalIF":0.9,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A note on the long time behavior of the elephant random walk with stops
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-19 DOI: 10.1016/j.spl.2025.110436
Tatsuya Akimoto , Masato Takei , Keisuke Taniguchi
{"title":"A note on the long time behavior of the elephant random walk with stops","authors":"Tatsuya Akimoto ,&nbsp;Masato Takei ,&nbsp;Keisuke Taniguchi","doi":"10.1016/j.spl.2025.110436","DOIUrl":"10.1016/j.spl.2025.110436","url":null,"abstract":"<div><div>We study the long time behavior of the elephant random walk with stops, introduced by Kumar, Harbola and Lindenberg (2010), and establish the phase transition of the number of visited points up to time <span><math><mi>n</mi></math></span>, and the correlation between the position at time <span><math><mi>n</mi></math></span> and the number of moves up to time <span><math><mi>n</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110436"},"PeriodicalIF":0.9,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Preferential attachment with choice-based edge step
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-19 DOI: 10.1016/j.spl.2025.110438
Y.A. Malyshkin
{"title":"Preferential attachment with choice-based edge step","authors":"Y.A. Malyshkin","doi":"10.1016/j.spl.2025.110438","DOIUrl":"10.1016/j.spl.2025.110438","url":null,"abstract":"<div><div>We study the asymptotic behavior of the maximum degree in the preferential attachment model with a choice-based edge step. We add vertex type to the model and prove, among others types of behavior, the effect of condensation on multiple vertices with different types.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110438"},"PeriodicalIF":0.9,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143863514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Limit theorems for a critical branching process with immigration at zero in a random environment
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-19 DOI: 10.1016/j.spl.2025.110435
Yinxuan Zhao, Mei Zhang
{"title":"Limit theorems for a critical branching process with immigration at zero in a random environment","authors":"Yinxuan Zhao,&nbsp;Mei Zhang","doi":"10.1016/j.spl.2025.110435","DOIUrl":"10.1016/j.spl.2025.110435","url":null,"abstract":"<div><div>In this paper, we study a critical branching process with immigration at zero in a random environment <span><math><mi>Z</mi></math></span>, where the immigration is allowed entering a generation iff the previous generation is empty. Firstly, we analyze the asymptotic behavior of the survival probability at generation <span><math><mi>n</mi></math></span> of <span><math><mover><mrow><mi>Z</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>, a critical branching process in a random environment with random initial number of particles. Then, the convergence rate of the transition probabilities <span><math><msubsup><mrow><mi>p</mi></mrow><mrow><mi>k</mi><mo>,</mo><mn>0</mn></mrow><mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></msubsup></math></span> (<span><math><mrow><mi>k</mi><mo>≥</mo><mn>0</mn></mrow></math></span>) of <span><math><mi>Z</mi></math></span> are obtained, which can be compared with the corresponding results for non-random case in literatures.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110435"},"PeriodicalIF":0.9,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Approximate formulas for renewal-reward process with dependent components and normally distributed interference of chance
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-18 DOI: 10.1016/j.spl.2025.110439
Aynura Poladova , Salih Tekin , Tahir Khaniyev
{"title":"Approximate formulas for renewal-reward process with dependent components and normally distributed interference of chance","authors":"Aynura Poladova ,&nbsp;Salih Tekin ,&nbsp;Tahir Khaniyev","doi":"10.1016/j.spl.2025.110439","DOIUrl":"10.1016/j.spl.2025.110439","url":null,"abstract":"<div><div>In this study a modification of renewal-reward process with dependent components and normally distributed interference of chance are investigated. The approximate formulas for the ergodic distribution of the process and its moments are proposed.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"224 ","pages":"Article 110439"},"PeriodicalIF":0.9,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Lp-minimal solutions of BDSDEs with left continuous and stochastic linear growth coefficients and p∈(1,2)
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-17 DOI: 10.1016/j.spl.2025.110433
J.M. Owo
{"title":"Lp-minimal solutions of BDSDEs with left continuous and stochastic linear growth coefficients and p∈(1,2)","authors":"J.M. Owo","doi":"10.1016/j.spl.2025.110433","DOIUrl":"10.1016/j.spl.2025.110433","url":null,"abstract":"<div><div>In this work, we investigate backward doubly stochastic differential equations. Via suitable approximations and comparison theorem, we prove the existence of a minimal solution in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> sense, for any <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, when the coefficients are left continuous with stochastic linear growth.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110433"},"PeriodicalIF":0.9,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Complete convergence with regularly varying moments and norming constants
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-17 DOI: 10.1016/j.spl.2025.110434
George Stoica , Deli Li
{"title":"Complete convergence with regularly varying moments and norming constants","authors":"George Stoica ,&nbsp;Deli Li","doi":"10.1016/j.spl.2025.110434","DOIUrl":"10.1016/j.spl.2025.110434","url":null,"abstract":"<div><div>We prove an extension of the Heyde–Rohatgi theorem on complete convergence of partial sums of i.i.d. random variables with general regularly varying moments and norming constants.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110434"},"PeriodicalIF":0.9,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Semi-log-convexity of M/M/∞ queues on Z+
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-15 DOI: 10.1016/j.spl.2025.110432
Huige Chen , Huaiqian Li
{"title":"Semi-log-convexity of M/M/∞ queues on Z+","authors":"Huige Chen ,&nbsp;Huaiqian Li","doi":"10.1016/j.spl.2025.110432","DOIUrl":"10.1016/j.spl.2025.110432","url":null,"abstract":"<div><div>We solve the problem left in the recent paper by N. Gozlan et al [Potential Analysis 58, 2023, 123–158], establishing the semi-log-convexity of semigroups associated with <span><math><mrow><mi>M</mi><mo>/</mo><mi>M</mi><mo>/</mo><mi>∞</mi></mrow></math></span> queuing processes on the set of non-negative integers. Our approach is global in nature and yields the sharp constant.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110432"},"PeriodicalIF":0.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Variable-selection consistency of linear quantile regression by validation set approach
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-04-15 DOI: 10.1016/j.spl.2025.110431
Suin Kim, Sarang Lee, Nari Shin, Yoonsuh Jung
{"title":"Variable-selection consistency of linear quantile regression by validation set approach","authors":"Suin Kim,&nbsp;Sarang Lee,&nbsp;Nari Shin,&nbsp;Yoonsuh Jung","doi":"10.1016/j.spl.2025.110431","DOIUrl":"10.1016/j.spl.2025.110431","url":null,"abstract":"<div><div>We consider the problem of variable selection in the quantile regression model by cross-validation. Although cross-validation is commonly used in quantile regression for model selection, its theoretical justification has not yet been verified. In this work, we prove that cross-validation with the check loss function can lead to variable-selection consistency in quantile regression. Specifically, we investigate its asymptotic properties in linear quantile regression and its penalized version under both fixed and diverging number of parameters. For penalized models, penalties with the oracle property combined with cross-validation are shown to provide variable-selection consistency. In general, one of the crucial requirements for this consistency to hold is that the validation set size should be asymptotically equivalent to the total number of observations, which is also required in the conditional mean linear regression.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110431"},"PeriodicalIF":0.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143838558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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