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Sparse model identification enables nonlinear dynamical system discovery from data.
The large-sample distribution of the likelihood ratio for testing composite hypotheses
Samuel S Wilks · 1938
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Computers and the theory of statistics: thinking the unthinkable
Bradley Efron · 1979
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David A Freedman · 1981
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The bayesian bootstrap
Donald B Rubin · 1981
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Bayesian variable selection in linear regression
Toby J Mitchell and John J Beauchamp · 1988
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Linear model selection by cross-validation
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Ideal spatial adaptation by wavelet shrinkage
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Bradley Efron and Robert J Tibshirani · 1994
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Asymptotics for lasso-type estimators
Wenjiang Fu and Keith Knight · 2000
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Variable selection via nonconcave penalized likelihood and its oracle properties
Jianqing Fan and Runze Li · 2001
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Analyzing bagging
Peter Bühlmann and Bin Yu · 2002
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Spike and slab variable selection: frequentist and bayesian strategies
Hemant Ishwaran and J Sunil Rao · 2005
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Sparse boosting
Peter Bühlmann, Bin Yu, Yoram Singer, and Larry Wasserman · 2006
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Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
Emmanuel J Candès, Justin Romberg, and Terence Tao · 2006
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Stable signal recovery from incomplete and inaccurate measurements
Emmanuel J Candes, Justin K Romberg, and Terence Tao · 2006
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On model selection consistency of lasso
Peng Zhao and Bin Yu · 2006
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The adaptive lasso and its oracle properties
Hui Zou · 2006
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Bolasso: model consistent lasso estimation through the bootstrap
Francis R Bach · 2008
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Asymptotic properties of bridge estimators in sparse high-dimensional regression models
Jian Huang, Joel L Horowitz, and Shuangge Ma · 2008
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The bayesian lasso
Trevor Park and George Casella · 2008
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Handling sparsity via the horseshoe
Carlos M Carvalho, Nicholas G Polson, and James G Scott · 2009
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Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ 1 \ell_{1} -constrained quadratic programming (lasso)
Martin J Wainwright · 2009
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The horseshoe estimator for sparse signals
Carlos M Carvalho, Nicholas G Polson, and James G Scott · 2010
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Asymptotic properties of the residual bootstrap for lasso estimators
Arindam Chatterjee and S Lahiri · 2010
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Stability selection
Nicolai Meinshausen and Peter Bühlmann · 2010
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Robust principal component analysis?
Emmanuel J Candès, Xiaodong Li, Yi Ma, and John Wright · 2011
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Bootstrapping lasso estimators
Arindam Chatterjee and Soumendra Nath Lahiri · 2011
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The bootstrap and Edgeworth expansion
Peter Hall · 2013
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Bayesian and frequentist regression methods
Jon Wakefield · 2013
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Emvs: The em approach to bayesian variable selection
Veronika Ročková and Edward I George · 2014
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Controlling the false discovery rate via knockoffs
Rina Foygel Barber and Emmanuel J Candès · 2015
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Robust regression via hard thresholding
Kush Bhatia, Prateek Jain, and Purushottam Kar · 2015
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Data-driven identification of parametric partial differential equations
Samuel Rudy, Alessandro Alla, Steven L Brunton, and J Nathan Kutz · 2019
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High-dimensional statistics: A non-asymptotic viewpoint
Martin J Wainwright · 2019
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On the convergence of the sindy algorithm
Linan Zhang and Hayden Schaeffer · 2019
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Formulating turbulence closures using sparse regression with embedded form invariance
Sarah Beetham and Jesse Capecelatro · 2020
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Sindy-pi: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
Kadierdan Kaheman, J Nathan Kutz, and Steven L Brunton · 2020
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Data-driven modeling of the chaotic thermal convection in an annular thermosyphon
Jean-Christophe Loiseau · 2020
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Steven L Brunton, Joshua L Proctor, and J Nathan Kutz · 2016
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Thresholding least-squares inference in high-dimensional regression models
Mihai Giurcanu · 2016
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Can we trust the bootstrap in high-dimension?
Noureddine El Karoui and Elizabeth Purdom · 2016
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Inferring biological networks by sparse identification of nonlinear dynamics
Niall M Mangan, Steven L Brunton, Joshua L Proctor, and J Nathan Kutz · 2016
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Sparse identification for nonlinear optical communication systems: Sino method
Mariia Sorokina, Stylianos Sygletos, and Sergei Turitsyn · 2016
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Central limit theorems and bootstrap in high dimensions
Victor Chernozhukov, Denis Chetverikov, and Kengo Kato · 2017
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Using noisy or incomplete data to discover models of spatiotemporal dynamics
Patrick AK Reinbold, Daniel R Gurevich, and Roman O Grigoriev · 2020
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Discovery of algebraic reynolds-stress models using sparse symbolic regression
Martin Schmelzer, Richard P Dwight, and Paola Cinnella · 2020
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Data-driven equation discovery of ocean mesoscale closures
Laure Zanna and Thomas Bolton · 2020
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On the non-asymptotic and sharp lower tail bounds of random variables
Anru R Zhang and Yuchen Zhou · 2020
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Sparse identification of multiphase turbulence closures for coupled fluid–particle flows
Sarah Beetham, Rodney O Fox, and Jesse Capecelatro · 2021
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Nonlinear stochastic modelling with langevin regression
Jared L Callaham, J-C Loiseau, Georgios Rigas, and Steven L Brunton · 2021
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Robust data-driven discovery of partial differential equations with time-dependent coefficients
Aoxue Chen and Guang Lin · 2021
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Galerkin force model for transient and post-transient dynamics of the fluidic pinball
Nan Deng, Bernd R Noack, Marek Morzyński, and Luc R Pastur · 2021
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Sparse nonlinear models of chaotic electroconvection
Yifei Guan, Steven L Brunton, and Igor Novosselov · 2021
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Promoting global stability in data-driven models of quadratic nonlinear dynamics
Alan A Kaptanoglu, Jared L Callaham, Aleksandr Aravkin, Christopher J Hansen, and Steven L Brunton · 2021
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Pysindy: A comprehensive python package for robust sparse system identification
Alan A Kaptanoglu, Brian M de Silva, Urban Fasel, Kadierdan Kaheman, Jared L Callaham, Charles B Delahunt, Kathleen Champion, Jean-Christophe Loiseau, J Nathan Kutz, and Steven L Brunton · 2021
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Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches
Alan A Kaptanoglu, Kyle D Morgan, Chris J Hansen, and Steven L Brunton · 2021
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Weak sindy: Galerkin-based data-driven model selection
Daniel A Messenger and David M Bortz · 2021
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Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
Patrick AK Reinbold, Logan M Kageorge, Michael F Schatz, and Roman O Grigoriev · 2021
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Data-driven discovery of reduced plasma physics models from fully kinetic simulations
E Paulo Alves and Frederico Fiuza · 2022
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Discovering governing equations from partial measurements with deep delay autoencoders
Joseph Bakarji, Kathleen Champion, J Nathan Kutz, and Steven L Brunton · 2022
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An empirical mean-field model of symmetry-breaking in a turbulent wake
Jared L Callaham, Georgios Rigas, Jean-Christophe Loiseau, and Steven L Brunton · 2022
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Ensemble-sindy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
Urban Fasel, J Nathan Kutz, Bingni W Brunton, and Steven L Brunton · 2022
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Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants
L Mars Gao and J Nathan Kutz · 2022
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Sparsifying priors for bayesian uncertainty quantification in model discovery
Seth M Hirsh, David A Barajas-Solano, and J Nathan Kutz · 2022
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Bayesian bootstrap spike-and-slab lasso
Lizhen Nie and Veronika Ročková · 2022
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Deep bootstrap for bayesian inference
Lizhen Nie and Veronika Rockova · 2022
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Loss-guided stability selection
Tino Werner · 2022
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Data-driven discovery of the governing equation of granular flow in the homogeneous cooling state using sparse regression
Bidan Zhao, Mingming He, and Junwu Wang · 2022
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