An effective method for identifying clusters of robot strengths

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY Computational Statistics Pub Date : 2023-12-11 DOI:10.1007/s00180-023-01442-5
Jen-Chieh Teng, Chin-Tsang Chiang, Alvin Lim
{"title":"An effective method for identifying clusters of robot strengths","authors":"Jen-Chieh Teng, Chin-Tsang Chiang, Alvin Lim","doi":"10.1007/s00180-023-01442-5","DOIUrl":null,"url":null,"abstract":"<p>In the analysis of qualification stage data from FIRST Robotics Competition (FRC) championships, the ratio (1.67–1.68) of the number of observations (110–114 matches) to the number of parameters (66–68 robots) in each division has been found to be quite small for the most commonly used winning margin power rating (WMPR) model. This usually leads to imprecise estimates and inaccurate predictions in such three-on-three matches that FRC tournaments are composed of. With the recognition of a clustering feature in estimated robot strengths, a more flexible model with latent clusters of robots was proposed to alleviate overparameterization of the WMPR model. Since its structure can be regarded as a dimension reduction of the parameter space in the WMPR model, the identification of clusters of robot strengths is naturally transformed into a model selection problem. Instead of comparing a huge number of competing models <span>\\((7.76\\times 10^{67}\\)</span> to <span>\\(3.66\\times 10^{70})\\)</span>, we develop an effective method to estimate the number of clusters, clusters of robots and robot strengths in the format of qualification stage data from the FRC championships. The new method consists of two parts: (i) a combination of hierarchical and non-hierarchical classifications to determine candidate models; and (ii) variant goodness-of-fit criteria to select optimal models. In contrast to existing hierarchical classification, each step of our proposed non-hierarchical classification is based on estimated robot strengths from a candidate model in the preceding non-hierarchical classification step. A great advantage of the proposed methodology is its ability to consider the possibility of reassigning robots to other clusters. To reduce overestimation of the number of clusters by the mean squared prediction error criteria, corresponding Bayesian information criteria are further established as alternatives for model selection. With a coherent assembly of these essential elements, a systematic procedure is presented to perform the estimation of parameters. In addition, we propose two indices to measure the nested relation between clusters from any two models and monotonic association between robot strengths from any two models. Data from the 2018 and 2019 FRC championships and a simulation study are also used to illustrate the applicability and superiority of our proposed methodology.</p>","PeriodicalId":55223,"journal":{"name":"Computational Statistics","volume":"12 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00180-023-01442-5","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

Abstract

In the analysis of qualification stage data from FIRST Robotics Competition (FRC) championships, the ratio (1.67–1.68) of the number of observations (110–114 matches) to the number of parameters (66–68 robots) in each division has been found to be quite small for the most commonly used winning margin power rating (WMPR) model. This usually leads to imprecise estimates and inaccurate predictions in such three-on-three matches that FRC tournaments are composed of. With the recognition of a clustering feature in estimated robot strengths, a more flexible model with latent clusters of robots was proposed to alleviate overparameterization of the WMPR model. Since its structure can be regarded as a dimension reduction of the parameter space in the WMPR model, the identification of clusters of robot strengths is naturally transformed into a model selection problem. Instead of comparing a huge number of competing models \((7.76\times 10^{67}\) to \(3.66\times 10^{70})\), we develop an effective method to estimate the number of clusters, clusters of robots and robot strengths in the format of qualification stage data from the FRC championships. The new method consists of two parts: (i) a combination of hierarchical and non-hierarchical classifications to determine candidate models; and (ii) variant goodness-of-fit criteria to select optimal models. In contrast to existing hierarchical classification, each step of our proposed non-hierarchical classification is based on estimated robot strengths from a candidate model in the preceding non-hierarchical classification step. A great advantage of the proposed methodology is its ability to consider the possibility of reassigning robots to other clusters. To reduce overestimation of the number of clusters by the mean squared prediction error criteria, corresponding Bayesian information criteria are further established as alternatives for model selection. With a coherent assembly of these essential elements, a systematic procedure is presented to perform the estimation of parameters. In addition, we propose two indices to measure the nested relation between clusters from any two models and monotonic association between robot strengths from any two models. Data from the 2018 and 2019 FRC championships and a simulation study are also used to illustrate the applicability and superiority of our proposed methodology.

Abstract Image

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
识别机器人优势集群的有效方法
在对 FIRST 机器人竞赛(FRC)锦标赛资格赛阶段的数据进行分析时发现,对于最常用的获胜能力评级(WMPR)模型而言,每个分区的观察数(110-114 场比赛)与参数数(66-68 个机器人)之比(1.67-1.68)相当小。这通常会导致在 FRC 锦标赛这种三对三比赛中出现不精确的估计和不准确的预测。由于认识到了机器人实力估算中的聚类特征,因此提出了一种具有潜在机器人聚类的更灵活模型,以减轻 WMPR 模型的参数过多问题。由于其结构可被视为 WMPR 模型参数空间的降维,因此机器人强度集群的识别自然而然地转化为模型选择问题。我们并没有比较大量的竞争模型((7.76乘以10^{67})到(3.66乘以10^{70})),而是开发了一种有效的方法,以FRC锦标赛资格赛阶段数据的形式来估计机器人集群的数量、机器人集群和机器人强度。新方法由两部分组成:(i) 结合层次分类法和非层次分类法确定候选模型;(ii) 采用变异拟合优度标准选择最优模型。与现有的分层分类法不同,我们提出的非分层分类法的每一步都是基于前一步非分层分类法中候选模型的机器人强度估计值。所提方法的一大优势是能够考虑将机器人重新分配到其他群组的可能性。为了减少均方预测误差标准对集群数量的过高估计,还进一步建立了相应的贝叶斯信息标准,作为模型选择的替代方案。通过对这些基本要素的整合,我们提出了一套系统的参数估计程序。此外,我们还提出了两个指数,用于衡量任意两个模型的聚类之间的嵌套关系,以及任意两个模型的机器人强度之间的单调关联。我们还使用了 2018 年和 2019 年 FRC 锦标赛的数据以及一项模拟研究来说明我们提出的方法的适用性和优越性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Computational Statistics
Computational Statistics 数学-统计学与概率论
CiteScore
2.90
自引率
0.00%
发文量
122
审稿时长
>12 weeks
期刊介绍: Computational Statistics (CompStat) is an international journal which promotes the publication of applications and methodological research in the field of Computational Statistics. The focus of papers in CompStat is on the contribution to and influence of computing on statistics and vice versa. The journal provides a forum for computer scientists, mathematicians, and statisticians in a variety of fields of statistics such as biometrics, econometrics, data analysis, graphics, simulation, algorithms, knowledge based systems, and Bayesian computing. CompStat publishes hardware, software plus package reports.
期刊最新文献
Bayes estimation of ratio of scale-like parameters for inverse Gaussian distributions and applications to classification Multivariate approaches to investigate the home and away behavior of football teams playing football matches Kendall correlations and radar charts to include goals for and goals against in soccer rankings Bayesian adaptive lasso quantile regression with non-ignorable missing responses Statistical visualisation of tidy and geospatial data in R via kernel smoothing methods in the eks package
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1