arXiv - STAT - Statistics Theory最新文献_第4页

Asymptotics for Random Quadratic Transportation Costs 随机二次运输成本的渐近线

arXiv - STAT - Statistics Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08612

Martin Huesmann, Michael Goldman, Dario Trevisan

引用次数: 0

On spiked eigenvalues of a renormalized sample covariance matrix from multi-population 关于来自多人群的重归一化样本协方差矩阵的尖峰特征值

arXiv - STAT - Statistics Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08715

Weiming Li, Zeng Li, Junpeng Zhu

引用次数: 0

Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent 改进斯坦因变分梯度下降的有限粒子收敛速率

arXiv - STAT - Statistics Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08469

Krishnakumar Balasubramanian, Sayan Banerjee, Promit Ghosal

{"title":"Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent","authors":"Krishnakumar Balasubramanian, Sayan Banerjee, Promit Ghosal","doi":"arxiv-2409.08469","DOIUrl":"https://doi.org/arxiv-2409.08469","url":null,"abstract":"We provide finite-particle convergence rates for the Stein Variational\u0000Gradient Descent (SVGD) algorithm in the Kernel Stein Discrepancy\u0000($mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is the observation\u0000that the time derivative of the relative entropy between the joint density of\u0000$N$ particle locations and the $N$-fold product target measure, starting from a\u0000regular initial distribution, splits into a dominant `negative part'\u0000proportional to $N$ times the expected $mathsf{KSD}^2$ and a smaller `positive\u0000part'. This observation leads to $mathsf{KSD}$ rates of order $1/sqrt{N}$,\u0000providing a near optimal double exponential improvement over the recent result\u0000by~cite{shi2024finite}. Under mild assumptions on the kernel and potential,\u0000these bounds also grow linearly in the dimension $d$. By adding a bilinear\u0000component to the kernel, the above approach is used to further obtain\u0000Wasserstein-2 convergence. For the case of `bilinear + Mat'ern' kernels, we\u0000derive Wasserstein-2 rates that exhibit a curse-of-dimensionality similar to\u0000the i.i.d. setting. We also obtain marginal convergence and long-time\u0000propagation of chaos results for the time-averaged particle laws.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal Classification-based Anomaly Detection with Neural Networks: Theory and Practice 基于分类的神经网络优化异常检测：理论与实践

arXiv - STAT - Statistics Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08521

Tian-Yi Zhou, Matthew Lau, Jizhou Chen, Wenke Lee, Xiaoming Huo

引用次数: 0

On the maximal correlation coefficient for the bivariate Marshall Olkin distribution 关于二元马歇尔-奥尔金分布的最大相关系数

arXiv - STAT - Statistics Theory Pub Date : 2024-09-13 DOI: arxiv-2409.08661

Axel Bücher, Torben Staud

引用次数: 0

On Admissibility in Bipartite Incidence Graph Sampling 论双方位发生图抽样中的可采性

arXiv - STAT - Statistics Theory Pub Date : 2024-09-12 DOI: arxiv-2409.07970

Pedro García-Segador, Li-Chung Zhang

引用次数: 0

Generalized Independence Test for Modern Data 现代数据的广义独立性检验

arXiv - STAT - Statistics Theory Pub Date : 2024-09-12 DOI: arxiv-2409.07745

Mingshuo Liu, Doudou Zhou, Hao Chen

引用次数: 0

Quickest Change Detection Using Mismatched CUSUM 使用不匹配 CUSUM 快速检测变化

arXiv - STAT - Statistics Theory Pub Date : 2024-09-12 DOI: arxiv-2409.07948

Austin Cooper, Sean Meyn

引用次数: 0

Foundation of Calculating Normalized Maximum Likelihood for Continuous Probability Models 计算连续概率模型归一化最大似然的基础

arXiv - STAT - Statistics Theory Pub Date : 2024-09-12 DOI: arxiv-2409.08387

Atsushi Suzuki, Kota Fukuzawa, Kenji Yamanishi

{"title":"Foundation of Calculating Normalized Maximum Likelihood for Continuous Probability Models","authors":"Atsushi Suzuki, Kota Fukuzawa, Kenji Yamanishi","doi":"arxiv-2409.08387","DOIUrl":"https://doi.org/arxiv-2409.08387","url":null,"abstract":"The normalized maximum likelihood (NML) code length is widely used as a model\u0000selection criterion based on the minimum description length principle, where\u0000the model with the shortest NML code length is selected. A common method to\u0000calculate the NML code length is to use the sum (for a discrete model) or\u0000integral (for a continuous model) of a function defined by the distribution of\u0000the maximum likelihood estimator. While this method has been proven to\u0000correctly calculate the NML code length of discrete models, no proof has been\u0000provided for continuous cases. Consequently, it has remained unclear whether\u0000the method can accurately calculate the NML code length of continuous models.\u0000In this paper, we solve this problem affirmatively, proving that the method is\u0000also correct for continuous cases. Remarkably, completing the proof for\u0000continuous cases is non-trivial in that it cannot be achieved by merely\u0000replacing the sums in discrete cases with integrals, as the decomposition trick\u0000applied to sums in the discrete model case proof is not applicable to integrals\u0000in the continuous model case proof. To overcome this, we introduce a novel\u0000decomposition approach based on the coarea formula from geometric measure\u0000theory, which is essential to establishing our proof for continuous cases.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Ratio Divergence Learning Using Target Energy in Restricted Boltzmann Machines: Beyond Kullback--Leibler Divergence Learning 利用受限玻尔兹曼机中的目标能量进行比率发散学习：超越库尔贝克--莱布勒发散学习

arXiv - STAT - Statistics Theory Pub Date : 2024-09-12 DOI: arxiv-2409.07679

Yuichi Ishida, Yuma Ichikawa, Aki Dote, Toshiyuki Miyazawa, Koji Hukushima

{"title":"Ratio Divergence Learning Using Target Energy in Restricted Boltzmann Machines: Beyond Kullback--Leibler Divergence Learning","authors":"Yuichi Ishida, Yuma Ichikawa, Aki Dote, Toshiyuki Miyazawa, Koji Hukushima","doi":"arxiv-2409.07679","DOIUrl":"https://doi.org/arxiv-2409.07679","url":null,"abstract":"We propose ratio divergence (RD) learning for discrete energy-based models, a\u0000method that utilizes both training data and a tractable target energy function.\u0000We apply RD learning to restricted Boltzmann machines (RBMs), which are a\u0000minimal model that satisfies the universal approximation theorem for discrete\u0000distributions. RD learning combines the strength of both forward and reverse\u0000Kullback-Leibler divergence (KLD) learning, effectively addressing the\u0000\"notorious\" issues of underfitting with the forward KLD and mode-collapse with\u0000the reverse KLD. Since the summation of forward and reverse KLD seems to be\u0000sufficient to combine the strength of both approaches, we include this learning\u0000method as a direct baseline in numerical experiments to evaluate its\u0000effectiveness. Numerical experiments demonstrate that RD learning significantly\u0000outperforms other learning methods in terms of energy function fitting,\u0000mode-covering, and learning stability across various discrete energy-based\u0000models. Moreover, the performance gaps between RD learning and the other\u0000learning methods become more pronounced as the dimensions of target models\u0000increase.","PeriodicalId":501379,"journal":{"name":"arXiv - STAT - Statistics Theory","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0