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Related papers: Graphical lasso for extremes

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Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…

Machine Learning · Statistics 2023-06-16 Feynman Liang , Liam Hodgkinson , Michael W. Mahoney

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…

Statistics Theory · Mathematics 2019-12-23 Hai Shu , Bin Nan

We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…

Methodology · Statistics 2018-08-21 Ginette Lafit , Francisco J. Nogales , Marcelo Ruiz , Ruben H. Zamar

In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems.…

Machine Learning · Statistics 2017-11-28 Salar Fattahi , Richard Y. Zhang , Somayeh Sojoudi

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…

Statistics Theory · Mathematics 2013-12-20 J. L. Wadsworth , J. A. Tawn

Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…

Statistics Theory · Mathematics 2023-11-16 Philipp Dettling , Mathias Drton , Mladen Kolar

We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…

Machine Learning · Statistics 2016-09-14 Nguyen Tran Quang , Alexander Jung

A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…

Probability · Mathematics 2019-04-29 Sebastian Engelke , Thomas Opitz , Jennifer Wadsworth

Employing the framework of regular variation, we propose two decompositions which help to summarize and describel high-dimensional tail dependence. Via transformation, we define a vector space on the positive orthant, yielding the notion of…

Methodology · Statistics 2018-04-27 Daniel Cooley , Emeric Thibaud

Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…

Probability · Mathematics 2016-03-25 Anja Janssen , Holger Drees

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a…

Risk Management · Quantitative Finance 2023-04-12 Bikramjit Das , Vicky Fasen-Hartmann

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Applications · Statistics 2018-08-07 Donald R. Williams , Juho Piironen , Aki Vehtari , Philippe Rast

The statistics of peaks in weak gravitational lensing maps is a promising technique to constrain cosmological parameters in present and future surveys. Here we investigate its power when using general extreme value statistics which is very…

Cosmology and Nongalactic Astrophysics · Physics 2016-12-12 Robert Reischke , Matteo Maturi , Matthias Bartelmann

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

Statistics Theory · Mathematics 2026-05-06 Stephan Clémençon , Anne Sabourin

We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In…

Machine Learning · Statistics 2017-06-06 Qiang Sun , Kean Ming Tan , Han Liu , Tong Zhang

Motivated by the empirical observation of power-law distributions in the credits (e.g., ``likes'') of viral posts in social media, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference…

Machine Learning · Statistics 2026-01-19 Yuya Sasaki , Jing Tao , Yulong Wang

In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…

Methodology · Statistics 2017-08-21 Flávio B Gonçalves , Marcos O. Prates , Victor H. Lachos

We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…

Statistics Theory · Mathematics 2018-01-26 Jana Jankova , Sara van de Geer

We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…

Machine Learning · Computer Science 2012-03-06 Animashree Anandkumar , Vincent Y. F. Tan , Alan. S. Willsky

We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished…

Statistics Theory · Mathematics 2009-03-17 Shuheng Zhou , Sara van de Geer , Peter Bühlmann