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Related papers: L2 Regularization for Learning Kernels

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Regularization has long been utilized to learn sparsity in deep neural network pruning. However, its role is mainly explored in the small penalty strength regime. In this work, we extend its application to a new scenario where the…

Computer Vision and Pattern Recognition · Computer Science 2021-04-07 Huan Wang , Can Qin , Yulun Zhang , Yun Fu

This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…

Numerical Analysis · Mathematics 2025-10-15 Sebastian Banert , Christoph Brauer , Dirk Lorenz , Lionel Tondji

We study generalization properties of kernel regularized least squares regression based on a partitioning approach. We show that optimal rates of convergence are preserved if the number of local sets grows sufficiently slowly with the…

Statistics Theory · Mathematics 2019-02-26 Nicole Mücke

State estimation is a key ingredient in most robotic systems. Often, state estimation is performed using some form of least squares minimization. Basically, all error minimization procedures that work on real-world data use robust kernels…

Robotics · Computer Science 2021-02-19 Nived Chebrolu , Thomas Läbe , Olga Vysotska , Jens Behley , Cyrill Stachniss

This paper considers a canonical problem in kernel regression: how good are the model performances when it is trained by the popular online first-order algorithms, compared to the offline ones, such as ridge and ridgeless regression? In…

Machine Learning · Statistics 2025-05-29 Haihan Zhang , Weicheng Lin , Yuanshi Liu , Cong Fang

We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…

Machine Learning · Statistics 2020-08-11 Henry Gouk , Eibe Frank , Bernhard Pfahringer , Michael J. Cree

In supervised machine learning, feature selection plays a very important role by potentially enhancing explainability and performance as measured by computing time and accuracy-related metrics. In this paper, we investigate a method for…

Machine Learning · Computer Science 2024-02-02 Raisa Islam , Subhasish Mazumdar , Rakibul Islam

Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement…

Statistics Theory · Mathematics 2013-11-13 Shachar Kaufman , Saharon Rosset

This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR…

Machine Learning · Computer Science 2023-12-12 Shao-Bo Lin

We theoretically investigate the convergence rate and support consistency (i.e., correctly identifying the subset of non-zero coefficients in the large sample limit) of multiple kernel learning (MKL). We focus on MKL with block-l1…

Machine Learning · Statistics 2011-07-29 Taiji Suzuki , Ryota Tomioka , Masashi Sugiyama

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

Machine Learning · Statistics 2014-11-26 Ernesto De Vito , Lorenzo Rosasco , Alessandro Toigo

L2 regularization for weights in neural networks is widely used as a standard training trick. However, L2 regularization for gamma, a trainable parameter of batch normalization, remains an undiscussed mystery and is applied in different…

Computer Vision and Pattern Recognition · Computer Science 2022-05-17 Bum Jun Kim , Hyeyeon Choi , Hyeonah Jang , Dong Gu Lee , Wonseok Jeong , Sang Woo Kim

The problem of learning from label proportions (LLP) involves training classifiers with weak labels on bags of instances, rather than strong labels on individual instances. The weak labels only contain the label proportion of each bag. The…

Machine Learning · Computer Science 2019-10-30 Kuen-Han Tsai , Hsuan-Tien Lin

Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the tradeoff between minimizing the fitting error and the norm of the learned model…

Machine Learning · Computer Science 2023-11-27 Gabriele Maroni , Loris Cannelli , Dario Piga

The problem of multiple kernel learning based on penalized empirical risk minimization is discussed. The complexity penalty is determined jointly by the empirical $L_2$ norms and the reproducing kernel Hilbert space (RKHS) norms induced by…

Statistics Theory · Mathematics 2012-11-14 Vladimir Koltchinskii , Ming Yuan

This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This…

Machine Learning · Computer Science 2012-02-20 Corinna Cortes , Mehryar Mohri , Afshin Rostamizadeh

We investigate $L_2$ boosting in the context of kernel regression. Kernel smoothers, in general, lack appealing traits like symmetry and positive definiteness, which are critical not only for understanding theoretical aspects but also for…

Methodology · Statistics 2023-11-14 Suneel Babu Chatla

Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…

Machine Learning · Computer Science 2022-06-07 Haohan Wang , Zeyi Huang , Xindi Wu , Eric P. Xing

Adversarial training provides a principled approach for training robust neural networks. From an optimization perspective, adversarial training is essentially solving a bilevel optimization problem. The leader problem is trying to learn a…

Machine Learning · Computer Science 2021-05-04 Haoming Jiang , Zhehui Chen , Yuyang Shi , Bo Dai , Tuo Zhao

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties…

Statistics Theory · Mathematics 2023-01-16 El Mehdi Achour , François Malgouyres , Franck Mamalet