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Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function.
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Spatially and temporally varying adaptive covariance inflation for ensemble filters
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F. Bauer, T. Hohage and A. Munk, Iteratively regularized Gauss–Newton method for nonlinear inverse problems with random noise, · 2009
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Inverse problems: A Bayesian perspective
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Adaptive Subgradient Methods for Online Learning and Stochastic Optimization,
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Nonlinear stability of the ensemble Kalman filter with adaptive covariance inflation
X. T. Tong, A. J. Majda and D. Kelly, · 2016
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Kalman-based stochastic gradient method with stop condition and insensitivity to conditioning
V. Patel, · 2017
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Analysis of the ensemble Kalman filter for inverse problems
C. Schillings and A. M. Stuart, · 2017
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Analysis of hierarchical ensemble Kalman inversion, ArXiv preprint arXiv:1801.00847, (2018)
N. K. Chada, · 2018
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Parameterizations for ensemble Kalman inversion
N. K. Chada, M. A. Iglesias, L. Roininen and A. M. Stuart, · 2018
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E. Haber, F. Lucka, L. Ruthotto, · 2018
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Bayesian inversion in resin transfer molding
M. A. Iglesias, M. Park and M. V. Tretyakov, · 2018
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Performance of ensemble Kalman filters in large dimensions
A. J. Majda and X. T. Tong, · 2018
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Performance analysis of local ensemble Kalman filter
X. T. Tong, · 2018
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Well posedness and convergence analysis of the ensemble Kalman inversion
D. Blomker, C. Schillings, P. Wacker and S. Weissmann, · 2019
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