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L2 regularization for learning kernels
- In: Proceedings of the 25th Conference in Uncertainty in Artificial Intelligence
, 2009
"... The choice of the kernel is critical to the success of many learning algorithms but it is typically left to the user. Instead, the training data can be used to learn the kernel by selecting it out of a given family, such as that of non-negative linear combinations of p base kernels, constrained by a ..."
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Cited by 44 (4 self)
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by a trace or L1 regularization. This paper studies the problem of learning kernels with the same family of kernels but with an L2 regularization instead, and for regression problems. We analyze the problem of learning kernels with ridge regression. We derive the form of the solution
with L2 regularization, the Averaged
"... This paper presents a comparative study of five parameter estimation algorithms on four NLP tasks. Three of the five algorithms are well-known in the computational linguistics community: Maximum Entropy (ME) estimation ..."
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This paper presents a comparative study of five parameter estimation algorithms on four NLP tasks. Three of the five algorithms are well-known in the computational linguistics community: Maximum Entropy (ME) estimation
AN L2-REGULARITY RESULT FOR THE EVOLUTIONARY
"... Dedicated to Professor Vsevolod A. Solonnikov on the occasion of his 75th birthday. Abstract. We establish an L2-regularity result for a weak solution of the evolutionary Stokes-Fourier system. Although this system does not contain the convective terms, the fact that the viscosity depends on the tem ..."
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Dedicated to Professor Vsevolod A. Solonnikov on the occasion of his 75th birthday. Abstract. We establish an L2-regularity result for a weak solution of the evolutionary Stokes-Fourier system. Although this system does not contain the convective terms, the fact that the viscosity depends
Feature selection, l1 vs. l2 regularization, and rotational invariance
- In ICML
, 2004
"... We consider supervised learning in the presence of very many irrelevant features, and study two different regularization methods for preventing overfitting. Focusing on logistic regression, we show that using L1 regularization of the parameters, the sample complexity (i.e., the number of training ex ..."
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Cited by 204 (6 self)
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as there are training examples. We also give a lowerbound showing that any rotationally invariant algorithm—including logistic regression with L2 regularization, SVMs, and neural networks trained by backpropagation—has a worst case sample complexity that grows at least linearly in the number of irrelevant features. 1.
Multilinear Model Estimation with L 2-Regularization
"... Abstract. Many challenging computer vision problems can be formulated as a multilinear model. Classical methods like principal component analysis use singular value decomposition to infer model parameters. Although it can solve a given problem easily if all measurements are known this prerequisite i ..."
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function is generalized by introducing an L 2-regularization on the parameter space. We show a quantitative and qualitative evaluation of the proposed approach on an application from structure-from-motion using synthetic and real image data, and compare it with other works. 1
L1 AND L2 REGULARIZATION FOR MULTICLASS HINGE LOSS MODELS
"... This paper investigates the relationship between the loss function, the type of regularization, and the resulting model sparsity of discriminatively-trained multiclass linear models. The effects on sparsity of optimizing log loss are straightforward: L2 regularization produces very dense models whil ..."
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This paper investigates the relationship between the loss function, the type of regularization, and the resulting model sparsity of discriminatively-trained multiclass linear models. The effects on sparsity of optimizing log loss are straightforward: L2 regularization produces very dense models
Enhancing statistical performance of data-driven controller tuningviaL2-regularization
"... Noniterative data-driven techniques are design methods that allow optimal feedback control laws to be derived from input-output (I/O) data only, without the need of a model of the process. A drawback of these methods is that, in their standard formulation, they are not statistically efficient. In th ..."
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. In this paper, it is shown that they can be reformulated as L2-regularized optimization problems, by keeping the same assumptions and features, such that their statistical performance can be enhanced using the same identification dataset. A convex optimization method is also introduced to find
Feature selection, L 1 vs. L 2 regularization, and rotational invariance
- In ICML
, 2004
"... We consider supervised learning in the presence of very many irrelevant features, and study two di#erent regularization methods for preventing overfitting. Focusing on logistic regression, we show that using L 1 regularization of the parameters, the sample complexity (i.e., the number of train ..."
Abstract
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Cited by 16 (0 self)
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We consider supervised learning in the presence of very many irrelevant features, and study two di#erent regularization methods for preventing overfitting. Focusing on logistic regression, we show that using L 1 regularization of the parameters, the sample complexity (i.e., the number
A review of image denoising algorithms, with a new one
- SIMUL
, 2005
"... The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding perf ..."
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Cited by 508 (6 self)
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and their explanation as a violation of the image model; quantitative experimental: by tables of L 2 distances of the denoised version to the original image. The most powerful evaluation method seems, however, to be the visualization of the method noise on natural images. The more this method noise looks like a real
Results 1 - 10
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3,707