Comparing Tikhonov and Convex Optimization Regularization 103
Infinite-σ Limits For Tikhonov Regularization
... strictly convex loss functions, such as the square loss used in regularized least squares, problem 11 will have a unique minimizer as ...non-strictly convex loss function, such as the hinge loss used in ...
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Tree based ensemble models regularization by convex optimization
... a convex optimization problem allowing to regularize a tree based ensemble model by adjusting either (or both) the labels attached to the leaves of an ensemble of regression trees or the outputs of the ob- ...
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Tikhonov Regularization Within Ensemble Kalman Inversion
... results comparing EKI with the regularized TEKI ...additional regularization of prior samples required for the TEKI ...experiments comparing EKI and ...
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Nondifferentiable Convex Optimization: An Algorithm Using Moreau-Yosida Regularization
... Abstract— In this paper we present an algorithm for minimization of a nondifferentiable proper closed convex function. Using the second order Dini upper directional derivative of the Moreau-Yosida ...
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Tikhonov Regularization as a Complexity Measure in Multiobjective Genetic Programming
... GP optimization could discover the optimal decision surface by chance which should return the Bayes-optimal test error but the key issue here is that this optimal solution could not be systematically identified ...
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Tikhonov regularization as a complexity measure in multiobjective genetic programming
... of Regularization The results of directly applying zeroth-order regular- ization in MOGP are shown in Table III for both 2D (MSE/regularizer) and 3D objective vectors (MSE/node ...typical. Comparing columns ...
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A hybrid splitting method for smoothing Tikhonov regularization problem
... updated. The proposed method is essentially to a hybrid splitting method since it com- bines the parallel splitting method and the alternating direction method, which are two power tools for the convex ...
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On Representer Theorems and Convex Regularization
... and convex regularization The Tikhonov regu- larization ( 2 ) is a powerful tool when the number m of observations is large and the operator Φ is not too ...using convex regularizers, with ...
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A Multi-Scale Tikhonov Regularization Scheme for Implicit Surface Modelling
... ten engaged in traditional methods which usually generate two off-surface points along each normal vector of the sur- face. The off-surface points are used to avoid intersection with other parts and to make the fitting ...
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Variance-based Regularization with Convex Objectives
... In proposing any new estimator, it is essential to understand the limits of the pro- posed procedure and identify situations in which its performance may be worse than ex- isting estimators. There are indeed situations ...
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A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems
... of Tikhonov regularization to solve inverse PDE problems, we consider an inverse obstacle problem for an acoustic waveguide in the time harmonic ...the Convex Scattering support [5] or the Direct ...
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Robust frontier estimation from noisy data: a Tikhonov regularization approach
... any convex combination of these envelope estimators would have sufficed as a definition of q S α Y x , but we do not see any reason to bias the restricted estimator one way or the ...
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Robust frontier estimation from noisy data: a Tikhonov regularization approach
... any convex combination of these envelope estimators would have sufficed as a definition of q S α Y x , but we do not see any reason to bias the restricted estimator one way or the ...
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An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
... Abstract The adaptive cubic overestimation algorithm described in Cartis, Gould and Toint (2007) is adapted to the problem of minimizing a nonlinear, possibly nonconvex, smooth objective function over a convex ...
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Iterative Regularization for Learning with Convex Loss Functions
... general convex loss ...consider convex loss functions and propose a new form of iterative regularization based on the subgradient method, or the gradient descent if the loss is ...iterative ...
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A convex approach to superresolution and regularization of lines in images
... a convex approach to the recovery of a superpo- sition of point sources from samples of its Fourier transform along radial ...nonconvex optimization problem for which there are guarantees for recovering the ...
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TIKHONOV REGULARIZATION ENHANCES EEG-BASED SPATIAL FILTERING FOR SINGLE-TRIAL REGRESSION
... maximally different between classes. While the CSP algorithm proved very efficient and has become a gold standard in BCI, it is sensitive to noise, non-stationarity and limited data. To address these limitations, various ...
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An Inexact Newton Regularization in Banach Spaces based on the Nonstationary Iterated Tikhonov Method
... (10) δ := max {δ j : j = 0, . . . , d − 1} > 0. As the spaces Y j are arbitrary, the duality mapping J r does not need to be single-valued (for any r > 1). Then, j r : Y j → Y j ∗ represents a selection of J r . Now, we ...
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Discrete tomography by convex–concave regularization and D.C. programming
... of optimization which, when properlyapplied, is notori- ouslyslow, whereas a multiscale implementation of a coordinate-wise sequential update technique (a special version of the well-known ICM-technique) is ...
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Nonstationary lterated Tikhonov Regularization
... A convergence rate is established for nonstationary iterated Tik- honov regularization, applied to ill-posed problems involving closed, densely defined linear operator[r] ...
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