Related papers: Consistency of the group Lasso and multiple kernel…

We study the complexity of the entire regularization path for least squares regression with 1-norm penalty, known as the Lasso. Every regression parameter in the Lasso changes linearly as a function of the regularization value. The number…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…

Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…

We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the…

Object Categorization is a challenging problem, especially when the images have clutter background, occlusions or different lighting conditions. In the past, many descriptors have been proposed which aid object categorization even in such…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Beside the minimization of the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we propose continuous-domain formulations for one-dimensional…

This paper studies the leaderless consensus problem of {heterogeneous} multiple networked Euler-Lagrange systems subject to persistent disturbances with unknown constant biases, amplitudes, initial phases, and frequencies. The main…

It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…

The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…

Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the…

This paper proposes that Lipschitz continuity is a natural outcome of regularized least squares in kernel-based learning. Lipschitz continuity is an important proxy for robustness of input-output operators. It is also instrumental for…

Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…

In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…

Doubly stochastic learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

We show that minimum-norm interpolation in the Reproducing Kernel Hilbert Space corresponding to the Laplace kernel is not consistent if input dimension is constant. The lower bound holds for any choice of kernel bandwidth, even if selected…