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Paluš M, Chvosteková M, Manshour P. Causes of extreme events revealed by Rényi information transfer. SCIENCE ADVANCES 2024; 10:eadn1721. [PMID: 39058777 PMCID: PMC11277395 DOI: 10.1126/sciadv.adn1721] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2023] [Accepted: 06/21/2024] [Indexed: 07/28/2024]
Abstract
Information-theoretic generalization of Granger causality principle, based on evaluation of conditional mutual information, also known as transfer entropy (CMI/TE), is redefined in the framework of Rényi entropy (RCMI/RTE). Using numerically generated data with a defined causal structure and examples of real data from the climate system, it is demonstrated that RCMI/RTE is able to identify the cause variable responsible for the occurrence of extreme values in an effect variable. In the presented example, the Siberian High was identified as the cause responsible for the increased probability of cold extremes in the winter and spring surface air temperature in Europe, while the North Atlantic Oscillation and blocking events can induce shifts of the whole temperature probability distribution.
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Affiliation(s)
- Milan Paluš
- Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 00 Prague 8, Czech Republic
| | - Martina Chvosteková
- Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 00 Prague 8, Czech Republic
- Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská cesta 9, 841 04 Bratislava, Slovakia
| | - Pouya Manshour
- Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 00 Prague 8, Czech Republic
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Qin X, Hu J, Ma S, Wu M. Estimation of multiple networks with common structures in heterogeneous subgroups. J MULTIVARIATE ANAL 2024; 202:105298. [PMID: 38433779 PMCID: PMC10907012 DOI: 10.1016/j.jmva.2024.105298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/05/2024]
Abstract
Network estimation has been a critical component of high-dimensional data analysis and can provide an understanding of the underlying complex dependence structures. Among the existing studies, Gaussian graphical models have been highly popular. However, they still have limitations due to the homogeneous distribution assumption and the fact that they are only applicable to small-scale data. For example, cancers have various levels of unknown heterogeneity, and biological networks, which include thousands of molecular components, often differ across subgroups while also sharing some commonalities. In this article, we propose a new joint estimation approach for multiple networks with unknown sample heterogeneity, by decomposing the Gaussian graphical model (GGM) into a collection of sparse regression problems. A reparameterization technique and a composite minimax concave penalty are introduced to effectively accommodate the specific and common information across the networks of multiple subgroups, making the proposed estimator significantly advancing from the existing heterogeneity network analysis based on the regularized likelihood of GGM directly and enjoying scale-invariant, tuning-insensitive, and optimization convexity properties. The proposed analysis can be effectively realized using parallel computing. The estimation and selection consistency properties are rigorously established. The proposed approach allows the theoretical studies to focus on independent network estimation only and has the significant advantage of being both theoretically and computationally applicable to large-scale data. Extensive numerical experiments with simulated data and the TCGA breast cancer data demonstrate the prominent performance of the proposed approach in both subgroup and network identifications.
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Affiliation(s)
- Xing Qin
- School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, China
| | - Jianhua Hu
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
| | - Shuangge Ma
- Department of Biostatistics, Yale School of Public Health, New Haven, USA
| | - Mengyun Wu
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
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Dupuis DJ, Engelke S, Trapin L. Modeling panels of extremes. Ann Appl Stat 2023. [DOI: 10.1214/22-aoas1639] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
| | | | - Luca Trapin
- Department of Statistics, University of Bologna
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Engelke S, Volgushev S. Structure learning for extremal tree models. J R Stat Soc Series B Stat Methodol 2022. [DOI: 10.1111/rssb.12556] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Sebastian Engelke
- Research Center for Statistics University of Geneva Geneva Switzerland
| | - Stanislav Volgushev
- Department of Statistical Sciences University of Toronto Toronto Ontario Canada
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Abstract
Abstract
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously large. Various alternative dependence measures and representations have been proposed, with the most well-known being hidden regular variation and the conditional extreme value model. These varying depictions of extremal dependence arise through consideration of different parts of the multivariate domain, and particularly through exploring what happens when extremes of one variable may grow at different rates from other variables. Thus far, these alternative representations have come from distinct sources, and links between them are limited. In this work we elucidate many of the relevant connections through a geometrical approach. In particular, the shape of the limit set of scaled sample clouds in light-tailed margins is shown to provide a description of several different extremal dependence representations.
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Fomichov V, Ivanovs J. Spherical clustering in detection of groups of concomitant extremes. Biometrika 2022. [DOI: 10.1093/biomet/asac020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Summary
There is growing empirical evidence that spherical k-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results supporting this approach, but also demonstrate some pitfalls. Furthermore, we show that an alternative cost function may be more appropriate for identifying concomitant extremes, and it results in a novel spherical k-principal-components clustering algorithm. Our main result establishes a broadly satisfied sufficient condition guaranteeing the success of this method, albeit in a rather basic setting. Finally, we illustrate in simulations that k-principal-components outperforms k-means in the difficult case of weak asymptotic dependence within the groups.
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Affiliation(s)
- V Fomichov
- Department of Mathematics, Aarhus University, Ny Munkegade 118,DK-8000 Aarhus C, Denmark
| | - J Ivanovs
- Department of Mathematics, Aarhus University, Ny Munkegade 118,DK-8000 Aarhus C, Denmark
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Améndola C, Klüppelberg C, Lauritzen S, Tran NM. Conditional independence in max-linear Bayesian networks. ANN APPL PROBAB 2022. [DOI: 10.1214/21-aap1670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Carlos Améndola
- Center for Mathematical Sciences, Technical University of Munich
| | | | | | - Ngoc M. Tran
- Department of Mathematics, University of Texas at Austin
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Krupskii P, Huser R. Modeling spatial tail dependence with Cauchy convolution processes. Electron J Stat 2022. [DOI: 10.1214/22-ejs2081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Affiliation(s)
- Pavel Krupskii
- University of Melbourne, Parkville, Victoria, 3010, Australia Statistics Program, Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Ar
| | - Raphaël Huser
- University of Melbourne, Parkville, Victoria, 3010, Australia Statistics Program, Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Ar
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Lalancette M, Engelke S, Volgushev S. Rank-based estimation under asymptotic dependence and independence, with applications to spatial extremes. Ann Stat 2021. [DOI: 10.1214/20-aos2046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Gnecco N, Meinshausen N, Peters J, Engelke S. Causal discovery in heavy-tailed models. Ann Stat 2021. [DOI: 10.1214/20-aos2021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Nicola Gnecco
- Research Center for Statistics, University of Geneva
| | | | - Jonas Peters
- Department of Mathematical Sciences, University of Copenhagen
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Affiliation(s)
- Johannes Buck
- Center for Mathematical Sciences, Technical University of Munich, Boltzmanstrasse 3, 85748 Garching, Germany
| | - Claudia Klüppelberg
- Center for Mathematical Sciences, Technical University of Munich, Boltzmanstrasse 3, 85748 Garching, Germany
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Rohrbeck C, Tawn JA. Bayesian Spatial Clustering of Extremal Behavior for Hydrological Variables. J Comput Graph Stat 2020. [DOI: 10.1080/10618600.2020.1777139] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Christian Rohrbeck
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
- Department of Mathematical Sciences, University of Bath, Bath, UK
| | - Jonathan A. Tawn
- Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
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Mhalla L, Chavez‐Demoulin V, Dupuis DJ. Causal mechanism of extreme river discharges in the upper Danube basin network. J R Stat Soc Ser C Appl Stat 2020. [DOI: 10.1111/rssc.12415] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Gissibl N, Klüppelberg C, Lauritzen S. Identifiability and estimation of recursive max‐linear models. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12446] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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