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Optimal projection filters with information geometry 具有信息几何的最优投影滤波器
Information geometry Pub Date : 2023-06-02 DOI: 10.1007/s41884-023-00108-x
J. Armstrong, D. Brigo, B. Hanzon
{"title":"Optimal projection filters with information geometry","authors":"J. Armstrong, D. Brigo, B. Hanzon","doi":"10.1007/s41884-023-00108-x","DOIUrl":"https://doi.org/10.1007/s41884-023-00108-x","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47534415","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: 2
Geometry and convergence of natural policy gradient methods 自然政策梯度方法的几何与收敛性
Information geometry Pub Date : 2023-06-02 DOI: 10.1007/s41884-023-00106-z
Johannes Müller, Guido Montúfar
{"title":"Geometry and convergence of natural policy gradient methods","authors":"Johannes Müller, Guido Montúfar","doi":"10.1007/s41884-023-00106-z","DOIUrl":"https://doi.org/10.1007/s41884-023-00106-z","url":null,"abstract":"Abstract We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries, based on which we obtain global convergence guarantees and convergence rates. In particular, we show linear convergence for unregularized and regularized NPG flows with the metrics proposed by Kakade and Morimura and co-authors by observing that these arise from the Hessian geometries of conditional entropy and entropy respectively. Further, we obtain sublinear convergence rates for Hessian geometries arising from other convex functions like log-barriers. Finally, we interpret the discrete-time NPG methods with regularized rewards as inexact Newton methods if the NPG is defined with respect to the Hessian geometry of the regularizer. This yields local quadratic convergence rates of these methods for step size equal to the inverse penalization strength.","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136000767","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
Publisher Correction: Invariance properties of the natural gradient in overparametrised systems 出版者更正:过度参数化系统中自然梯度的不变性
Information geometry Pub Date : 2023-06-01 DOI: 10.1007/s41884-023-00112-1
Jesse van Oostrum, J. Müller, N. Ay
{"title":"Publisher Correction: Invariance properties of the natural gradient in overparametrised systems","authors":"Jesse van Oostrum, J. Müller, N. Ay","doi":"10.1007/s41884-023-00112-1","DOIUrl":"https://doi.org/10.1007/s41884-023-00112-1","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"6 1","pages":"383 - 384"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45404264","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
Publisher Correction: Coarse geometric kernels for networks embedding 发布者更正:用于网络嵌入的粗糙几何核
Information geometry Pub Date : 2023-06-01 DOI: 10.1007/s41884-023-00113-0
Emil Saucan, Vladislav Barkanass, J. Jost
{"title":"Publisher Correction: Coarse geometric kernels for networks embedding","authors":"Emil Saucan, Vladislav Barkanass, J. Jost","doi":"10.1007/s41884-023-00113-0","DOIUrl":"https://doi.org/10.1007/s41884-023-00113-0","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"6 1","pages":"381 - 381"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49140805","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
Differential geometry for the optimal design of the contingent valuation method 微分几何中用于优化设计的条件估值方法
Information geometry Pub Date : 2023-05-31 DOI: 10.1007/s41884-023-00109-w
Hisatoshi Tanaka
{"title":"Differential geometry for the optimal design of the contingent valuation method","authors":"Hisatoshi Tanaka","doi":"10.1007/s41884-023-00109-w","DOIUrl":"https://doi.org/10.1007/s41884-023-00109-w","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48005256","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
Anomaly detection in the probability simplex under different geometries 不同几何形状下概率单纯形的异常检测
Information geometry Pub Date : 2023-05-30 DOI: 10.1007/s41884-023-00107-y
Uriel Legaria, Sergio Mota, Sergio Martinez, Alfredo Cobá, Argenis Chable, Antonio Neme
{"title":"Anomaly detection in the probability simplex under different geometries","authors":"Uriel Legaria, Sergio Mota, Sergio Martinez, Alfredo Cobá, Argenis Chable, Antonio Neme","doi":"10.1007/s41884-023-00107-y","DOIUrl":"https://doi.org/10.1007/s41884-023-00107-y","url":null,"abstract":"Abstract An open problem in data science is that of anomaly detection. Anomalies are instances that do not maintain a certain property that is present in the remaining observations in a dataset. Several anomaly detection algorithms exist, since the process itself is ill-posed mainly because the criteria that separates common or expected vectors from anomalies are not unique. In the most extreme case, data is not labelled and the algorithm has to identify the vectors that are anomalous, or assign a degree of anomaly to each vector. The majority of anomaly detection algorithms do not make any assumptions about the properties of the feature space in which observations are embedded, which may affect the results when those spaces present certain properties. For instance, compositional data such as normalized histograms, that can be embedded in a probability simplex, constitute a particularly relevant case. In this contribution, we address the problem of detecting anomalies in the probability simplex, relying on concepts from Information Geometry, mainly by focusing our efforts in the distance functions commonly applied in that context. We report the results of a series of experiments and conclude that when a specific distance-based anomaly detection algorithm relies on Information Geometry-related distance functions instead of the Euclidean distance, the performance is significantly improved.","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135693124","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
A parameterisation-invariant modification of the score test 分数测试的参数化不变修改
Information geometry Pub Date : 2023-03-07 DOI: 10.1007/s41884-023-00101-4
P. Jupp
{"title":"A parameterisation-invariant modification of the score test","authors":"P. Jupp","doi":"10.1007/s41884-023-00101-4","DOIUrl":"https://doi.org/10.1007/s41884-023-00101-4","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"53251971","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
Non-negative low-rank approximations for multi-dimensional arrays on statistical manifold 统计流形上多维数组的非负低秩近似
Information geometry Pub Date : 2023-02-24 DOI: 10.1007/s41884-023-00100-5
Kazu Ghalamkari, M. Sugiyama
{"title":"Non-negative low-rank approximations for multi-dimensional arrays on statistical manifold","authors":"Kazu Ghalamkari, M. Sugiyama","doi":"10.1007/s41884-023-00100-5","DOIUrl":"https://doi.org/10.1007/s41884-023-00100-5","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"6 1","pages":"257 - 292"},"PeriodicalIF":0.0,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49310143","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
Coarse geometric kernels for networks embedding 网络嵌入的粗几何核
Information geometry Pub Date : 2023-01-26 DOI: 10.1007/s41884-022-00095-5
Emil Saucan, Vladislav Barkanass, J. Jost
{"title":"Coarse geometric kernels for networks embedding","authors":"Emil Saucan, Vladislav Barkanass, J. Jost","doi":"10.1007/s41884-022-00095-5","DOIUrl":"https://doi.org/10.1007/s41884-022-00095-5","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"6 1","pages":"157 - 169"},"PeriodicalIF":0.0,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48919750","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
Gram matrices of quantum channels via quantum Fisher information with applications to decoherence and uncertainty 基于量子Fisher信息的量子通道Gram矩阵及其在退相干和不确定度中的应用
Information geometry Pub Date : 2023-01-22 DOI: 10.1007/s41884-023-00096-y
S. Luo, Yuan Sun
{"title":"Gram matrices of quantum channels via quantum Fisher information with applications to decoherence and uncertainty","authors":"S. Luo, Yuan Sun","doi":"10.1007/s41884-023-00096-y","DOIUrl":"https://doi.org/10.1007/s41884-023-00096-y","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47638073","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
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