{"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}
{"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}
{"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}
{"title":"The exponential Orlicz space in quantum information geometry","authors":"A. Jenčová","doi":"10.1007/s41884-023-00097-x","DOIUrl":"https://doi.org/10.1007/s41884-023-00097-x","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46175594","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}
Information geometryPub Date : 2023-01-01Epub Date: 2022-12-14DOI: 10.1007/s41884-022-00089-3
Amanjit Singh Kainth, Ting-Kam Leonard Wong, Frank Rudzicz
{"title":"Conformal mirror descent with logarithmic divergences.","authors":"Amanjit Singh Kainth, Ting-Kam Leonard Wong, Frank Rudzicz","doi":"10.1007/s41884-022-00089-3","DOIUrl":"10.1007/s41884-022-00089-3","url":null,"abstract":"<p><p>The logarithmic divergence is an extension of the Bregman divergence motivated by optimal transport and a generalized convex duality, and satisfies many remarkable properties. Using the geometry induced by the logarithmic divergence, we introduce a generalization of continuous time mirror descent that we term the conformal mirror descent. We derive its dynamics under a generalized mirror map, and show that it is a time change of a corresponding Hessian gradient flow. We also prove convergence results in continuous time. We apply the conformal mirror descent to online estimation of a generalized exponential family, and construct a family of gradient flows on the unit simplex via the Dirichlet optimal transport problem.</p>","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":" ","pages":"303-327"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10752856/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43014963","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}
Henrique K. Miyamoto, Fábio C. C. Meneghetti, S. Costa
{"title":"Publisher Correction: The Fisher–Rao loss for learning under label noise","authors":"Henrique K. Miyamoto, Fábio C. C. Meneghetti, S. Costa","doi":"10.1007/s41884-022-00092-8","DOIUrl":"https://doi.org/10.1007/s41884-022-00092-8","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"6 1","pages":"379 - 379"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45327264","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}
{"title":"Uncertainty and Quantum Variance at the light of Quantum Information Geometry","authors":"P. Gibilisco","doi":"10.1007/s41884-022-00087-5","DOIUrl":"https://doi.org/10.1007/s41884-022-00087-5","url":null,"abstract":"","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43290803","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}