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

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

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

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.

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

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

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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

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

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