Proceedings of machine learning research最新文献

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Typed Markers and Context for Clinical Temporal Relation Extraction. 用于临床时空关系提取的类型标记和上下文。
Cheng Cheng, Jeremy C Weiss
{"title":"Typed Markers and Context for Clinical Temporal Relation Extraction.","authors":"Cheng Cheng, Jeremy C Weiss","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Reliable extraction of temporal relations from clinical notes is a growing need in many clinical research domains. Our work introduces typed markers to the task of clinical temporal relation extraction. We demonstrate that the addition of medical entity information to clinical text as tags with context sentences then input to a transformer-based architecture can outperform more complex systems requiring feature engineering and temporal reasoning. We propose several strategies of typed marker creation that incorporate entity type information at different granularities, with extensive experiments to test their effectiveness. Our system establishes the best result on I2B2, a clinical benchmark dataset for temporal relation extraction, with a F1 at 83.5% that provides a substantial 3.3% improvement over the previous best system.</p>","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"219 ","pages":"94-109"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10929572/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140112398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
EASL: A Framework for Designing, Implementing, and Evaluating ML Solutions in Clinical Healthcare Settings. EASL:在临床医疗环境中设计、实施和评估 ML 解决方案的框架。
Eric Prince, Todd C Hankinson, Carsten Görg
{"title":"EASL: A Framework for Designing, Implementing, and Evaluating ML Solutions in Clinical Healthcare Settings.","authors":"Eric Prince, Todd C Hankinson, Carsten Görg","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>We introduce the Explainable Analytical Systems Lab (EASL) framework, an end-to-end solution designed to facilitate the development, implementation, and evaluation of clinical machine learning (ML) tools. EASL is highly versatile and applicable to a variety of contexts and includes resources for data management, ML model development, visualization and user interface development, service hosting, and usage analytics. To demonstrate its practical applications, we present the EASL framework in the context of a case study: designing and evaluating a deep learning classifier to predict diagnoses from medical imaging. The framework is composed of three modules, each with their own set of resources. The Workbench module stores data and develops initial ML models, the Canvas module contains a medical imaging viewer and web development framework, and the Studio module hosts the ML model and provides web analytics and support for conducting user studies. EASL encourages model developers to take a holistic view by integrating the model development, implementation, and evaluation into one framework, and thus ensures that models are both effective and reliable when used in a clinical setting. EASL contributes to our understanding of machine learning applied to healthcare by providing a comprehensive framework that makes it easier to develop and evaluate ML tools within a clinical setting.</p>","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"219 ","pages":"612-630"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11235083/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141581781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Assessing the Impact of Context Inference Error and Partial Observability on RL Methods for Just-In-Time Adaptive Interventions. 评估上下文推理误差和部分可观察性对用于及时适应性干预的 RL 方法的影响。
Karine Karine, Predrag Klasnja, Susan A Murphy, Benjamin M Marlin
{"title":"Assessing the Impact of Context Inference Error and Partial Observability on RL Methods for Just-In-Time Adaptive Interventions.","authors":"Karine Karine, Predrag Klasnja, Susan A Murphy, Benjamin M Marlin","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Just-in-Time Adaptive Interventions (JITAIs) are a class of personalized health interventions developed within the behavioral science community. JITAIs aim to provide the right type and amount of support by iteratively selecting a sequence of intervention options from a pre-defined set of components in response to each individual's time varying state. In this work, we explore the application of reinforcement learning methods to the problem of learning intervention option selection policies. We study the effect of context inference error and partial observability on the ability to learn effective policies. Our results show that the propagation of uncertainty from context inferences is critical to improving intervention efficacy as context uncertainty increases, while policy gradient algorithms can provide remarkable robustness to partially observed behavioral state information.</p>","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"216 ","pages":"1047-1057"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10506656/pdf/nihms-1926373.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10309493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Half-Hop: A graph upsampling approach for slowing down message passing 半跳:一种降低消息传递速度的图形上采样方法
Proceedings of machine learning research Pub Date : 2023-07-01 DOI: 10.48550/arXiv.2308.09198
Mehdi Azabou, Venkataraman Ganesh, Shantanu Thakoor, Chi-Heng Lin, Lakshmi Sathidevi, Ran Liu, M. Vaĺko, Petar Velickovic, Eva L. Dyer
{"title":"Half-Hop: A graph upsampling approach for slowing down message passing","authors":"Mehdi Azabou, Venkataraman Ganesh, Shantanu Thakoor, Chi-Heng Lin, Lakshmi Sathidevi, Ran Liu, M. Vaĺko, Petar Velickovic, Eva L. Dyer","doi":"10.48550/arXiv.2308.09198","DOIUrl":"https://doi.org/10.48550/arXiv.2308.09198","url":null,"abstract":"Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding \"slow nodes\" at each edge that can mediate communication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths.","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"202 1","pages":"1341-1360"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45894268","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: 1
A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging. 用于加速多线圈磁共振成像的条件归一化流程
Jeffrey Wen, Rizwan Ahmad, Philip Schniter
{"title":"A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging.","authors":"Jeffrey Wen, Rizwan Ahmad, Philip Schniter","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Accelerated magnetic resonance (MR) imaging attempts to reduce acquisition time by collecting data below the Nyquist rate. As an ill-posed inverse problem, many plausible solutions exist, yet the majority of deep learning approaches generate only a single solution. We instead focus on sampling from the posterior distribution, which provides more comprehensive information for downstream inference tasks. To do this, we design a novel conditional normalizing flow (CNF) that infers the signal component in the measurement operator's nullspace, which is later combined with measured data to form complete images. Using fastMRI brain and knee data, we demonstrate fast inference and accuracy that surpasses recent posterior sampling techniques for MRI. Code is available at https://github.com/jwen307/mri_cnf.</p>","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"202 ","pages":"36926-36939"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10712023/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138814682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Radiology Reports Improve Visual Representations Learned from Radiographs. 放射学报告改进了从射线照片中学到的可视化表达。
Haoxu Huang, Samyak Rawlekar, Sumit Chopra, Cem M Deniz
{"title":"Radiology Reports Improve Visual Representations Learned from Radiographs.","authors":"Haoxu Huang, Samyak Rawlekar, Sumit Chopra, Cem M Deniz","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Although human's ability to visually understand the structure of the World plays a crucial role in perceiving the World and making appropriate decisions, human perception does not solely rely on vision but amalgamates the information from acoustic, verbal, and visual stimuli. An active area of research has been revolving around designing an efficient framework that adapts to multiple modalities and ideally improves the performance of existing tasks. While numerous frameworks have proved effective on natural datasets like ImageNet, a limited number of studies have been carried out in the biomedical domain. In this work, we extend the available frameworks for natural data to biomedical data by leveraging the abundant, unstructured multi-modal data available as radiology images and reports. We attempt to answer the question, \"For multi-modal learning, self-supervised learning and joint learning using both learning strategies, which one improves the visual representation for downstream chest radiographs classification tasks the most?\". Our experiments indicated that in limited labeled data settings with 1% and 10% labeled data, the joint learning with multi-modal and self-supervised models outperforms self-supervised learning and is at par with multi-modal learning. Additionally, we found that multi-modal learning is generally more robust on out-of-distribution datasets. The code is publicly available online.</p>","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"227 ","pages":"1385-1405"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11234265/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141581782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes. 具有潜在稀疏高斯过程的完全贝叶斯自动编码器。
Ba-Hien Tran, Babak Shahbaba, Stephan Mandt, Maurizio Filippone
{"title":"Fully Bayesian Autoencoders with Latent Sparse Gaussian Processes.","authors":"Ba-Hien Tran, Babak Shahbaba, Stephan Mandt, Maurizio Filippone","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>We present a fully Bayesian autoencoder model that treats both local latent variables and global decoder parameters in a Bayesian fashion. This approach allows for flexible priors and posterior approximations while keeping the inference costs low. To achieve this, we introduce an amortized MCMC approach by utilizing an implicit stochastic network to learn sampling from the posterior over local latent variables. Furthermore, we extend the model by incorporating a Sparse Gaussian Process prior over the latent space, allowing for a fully Bayesian treatment of inducing points and kernel hyperparameters and leading to improved scalability. Additionally, we enable Deep Gaussian Process priors on the latent space and the handling of missing data. We evaluate our model on a range of experiments focusing on dynamic representation learning and generative modeling, demonstrating the strong performance of our approach in comparison to existing methods that combine Gaussian Processes and autoencoders.</p>","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"202 ","pages":"34409-34430"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11031196/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140856806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Half-Hop: A graph upsampling approach for slowing down message passing. 半跳:一种用于减慢消息传递速度的图形上采样方法。
Mehdi Azabou, Venkataramana Ganesh, Shantanu Thakoor, Chi-Heng Lin, Lakshmi Sathidevi, Ran Liu, Michal Valko, Petar Veličković, Eva L Dyer
{"title":"Half-Hop: A graph upsampling approach for slowing down message passing.","authors":"Mehdi Azabou,&nbsp;Venkataramana Ganesh,&nbsp;Shantanu Thakoor,&nbsp;Chi-Heng Lin,&nbsp;Lakshmi Sathidevi,&nbsp;Ran Liu,&nbsp;Michal Valko,&nbsp;Petar Veličković,&nbsp;Eva L Dyer","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding \"slow nodes\" at each edge that can mediate communication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths.</p>","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"202 ","pages":"1341-1360"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10559225/pdf/nihms-1931959.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41184447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Controlled Differential Equations on Long Sequences via Non-standard Wavelets. 通过非标准小波控制长序列上的微分方程
Sourav Pal, Zhanpeng Zeng, Sathya N Ravi, Vikas Singh
{"title":"Controlled Differential Equations on Long Sequences via Non-standard Wavelets.","authors":"Sourav Pal, Zhanpeng Zeng, Sathya N Ravi, Vikas Singh","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>Neural Controlled Differential equations (NCDE) are a powerful mechanism to model the dynamics in temporal sequences, e.g., applications involving physiological measures, where apart from the initial condition, the dynamics also depend on subsequent measures or even a different \"control\" sequence. But NCDEs do not scale well to longer sequences. Existing strategies adapt rough path theory, and instead model the dynamics over summaries known as <i>log signatures</i>. While rigorous and elegant, invertibility of these summaries is difficult, and limits the scope of problems where these ideas can offer strong benefits (reconstruction, generative modeling). For tasks where it is sensible to assume that the (long) sequences in the training data are a <i>fixed</i> length of temporal measurements - this assumption holds in most experiments tackled in the literature - we describe an efficient simplification. First, we recast the regression/classification task as an integral transform. We then show how restricting the class of operators (permissible in the integral transform), allows the use of a known algorithm that leverages non-standard Wavelets to decompose the operator. Thereby, our task (learning the operator) radically simplifies. A neural variant of this idea yields consistent improvements across a wide gamut of use cases tackled in existing works. We also describe a novel application on modeling tasks involving coupled differential equations.</p>","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"202 ","pages":"26820-26836"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11178150/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141332696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
p -Regression in the Arbitrary Partition Model of Communication. 通信任意划分模型中的回归。
Yi Li, Honghao Lin, David P Woodruff
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\"><ns0:math> <ns0:mrow><ns0:msub><ns0:mi>ℓ</ns0:mi> <ns0:mi>p</ns0:mi></ns0:msub> </ns0:mrow> </ns0:math> -Regression in the Arbitrary Partition Model of Communication.","authors":"Yi Li, Honghao Lin, David P Woodruff","doi":"","DOIUrl":"","url":null,"abstract":"&lt;p&gt;&lt;p&gt;We consider the randomized communication complexity of the distributed &lt;math&gt; &lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;ℓ&lt;/mi&gt; &lt;mi&gt;p&lt;/mi&gt;&lt;/msub&gt; &lt;/mrow&gt; &lt;/math&gt; -regression problem in the coordinator model, for &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mn&gt;0&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mn&gt;2&lt;/mn&gt; &lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; . In this problem, there is a coordinator and &lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/math&gt; servers. The &lt;math&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/math&gt; -th server receives &lt;math&gt; &lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt; &lt;mi&gt;i&lt;/mi&gt;&lt;/msup&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mi&gt;M&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mi&gt;M&lt;/mi&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mo&gt;…&lt;/mo&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;M&lt;/mi&gt; &lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt; &lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt; &lt;mo&gt;×&lt;/mo&gt; &lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt; &lt;/msup&gt; &lt;/mrow&gt; &lt;/math&gt; and &lt;math&gt; &lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;b&lt;/mi&gt; &lt;mi&gt;i&lt;/mi&gt;&lt;/msup&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mi&gt;M&lt;/mi&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mi&gt;M&lt;/mi&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mo&gt;…&lt;/mo&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mi&gt;M&lt;/mi&gt; &lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt; &lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt; &lt;/mrow&gt; &lt;/math&gt; and the coordinator would like to find a &lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mi&gt;ε&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; -approximate solution to &lt;math&gt; &lt;mrow&gt; &lt;msub&gt; &lt;mrow&gt;&lt;msub&gt;&lt;mtext&gt;min&lt;/mtext&gt; &lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;msup&gt;&lt;mtext&gt;R&lt;/mtext&gt; &lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt; &lt;/mrow&gt; &lt;/msub&gt; &lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt; &lt;mrow&gt; &lt;mrow&gt; &lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mrow&gt;&lt;msub&gt;&lt;mo&gt;∑&lt;/mo&gt; &lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt; &lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt; &lt;mi&gt;i&lt;/mi&gt;&lt;/msup&gt; &lt;/mrow&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mi&gt;x&lt;/mi&gt; &lt;mo&gt;-&lt;/mo&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mrow&gt;&lt;munder&gt;&lt;mo&gt;∑&lt;/mo&gt; &lt;mi&gt;i&lt;/mi&gt;&lt;/munder&gt; &lt;msup&gt;&lt;mi&gt;b&lt;/mi&gt; &lt;mi&gt;i&lt;/mi&gt;&lt;/msup&gt; &lt;/mrow&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/mrow&gt; &lt;/mrow&gt; &lt;mi&gt;p&lt;/mi&gt;&lt;/msub&gt; &lt;/mrow&gt; &lt;/math&gt; . Here &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt; &lt;mo&gt;≤&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; poly(nd) for convenience. This model, where the data is additively shared across servers, is commonly referred to as the arbitrary partition model. We obtain significantly improved bounds for this problem. For &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;=&lt;/mo&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt; &lt;/math&gt; , i.e., least squares regression, we give the first optimal bound of &lt;math&gt; &lt;mrow&gt;&lt;mover&gt;&lt;mtext&gt;Θ&lt;/mtext&gt; &lt;mo&gt;˜&lt;/mo&gt;&lt;/mover&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt; &lt;msup&gt;&lt;mi&gt;d&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mi&gt;s&lt;/mi&gt; &lt;mi&gt;d&lt;/mi&gt; &lt;mo&gt;/&lt;/mo&gt; &lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; ) bits. For &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt; &lt;mo&gt;∈&lt;/mo&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;,&lt;/mo&gt; &lt;mn&gt;2&lt;/mn&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/math&gt; , we obtain an &lt;math&gt; &lt;mrow&gt;&lt;mover&gt;&lt;mi&gt;O&lt;/mi&gt; &lt;mo&gt;˜&lt;/mo&gt;&lt;/mover&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt; &lt;msup&gt;&lt;mi&gt;d&lt;/mi&gt; &lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt; &lt;mo&gt;/&lt;/mo&gt; &lt;mi&gt;ε&lt;/mi&gt; &lt;mo&gt;+&lt;/mo&gt; &lt;mi&gt;s&lt;/mi&gt; &lt;mi&gt;d&lt;/mi&gt; &lt;mo&gt;/&lt;/mo&gt; &lt;mtext&gt;poly&lt;/mtext&gt; &lt;mo&gt;(&lt;/mo&gt; &lt;mi&gt;ε&lt;/mi&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt; &lt;/mrow&gt; &lt;/math&gt; upper bound. Notably, for &lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt; sufficiently large, our leading order term only depends linearly on &lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt; &lt;mo&gt;/&lt;/mo&gt; &lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt; &lt;/math&gt; rather than quadratically. We also show communication lower bounds of &lt;math&gt;&lt;mrow&gt;&lt;mtext&gt;Ω&lt;/mtext&gt; &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt; &lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt; &lt;msup&gt;&lt;mi&gt;d&lt;/mi&gt; &lt;mn&gt;","PeriodicalId":74504,"journal":{"name":"Proceedings of machine learning research","volume":"195 ","pages":"4902-4928"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11646800/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142839750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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