相关论文: Multi-Kernel Regression with Sparsity Constraint

Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to…

We present a theory of feature learning in wide L2-regularized networks showing that supervised learning is inherently compressive. We derive a kernel ODE that predicts a "water-filling" spectral evolution and prove that for any stable…

Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary…

This paper proposes a novel parameter selection strategy for kernel-based gradient descent (KGD) algorithms, integrating bias-variance analysis with the splitting method. We introduce the concept of empirical effective dimension to quantify…

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and…

In this paper we propose a general framework to integrate supervised and unsupervised examples with background knowledge expressed by a collection of first-order logic clauses into kernel machines. In particular, we consider a multi-task…

We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional…

We present a non-asymptotic theory of generalization in deep learning where the empirical neural tangent kernel partitions the output space. In directions corresponding to signal, error dissipates rapidly; in the vast orthogonal dimensions…

Teacher-student models provide a framework in which the typical-case performance of high-dimensional supervised learning can be described in closed form. The assumptions of Gaussian i.i.d. input data underlying the canonical teacher-student…

Inference and learning for probabilistic generative networks is often very challenging and typically prevents scalability to as large networks as used for deep discriminative approaches. To obtain efficiently trainable, large-scale and well…

In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale…

We study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary…

Generative Adversarial Networks (GANs) can successfully approximate a probability distribution and produce realistic samples. However, open questions such as sufficient convergence conditions and mode collapse still persist. In this paper,…

This paper presents a RKHS, in general, of vector-valued functions intended to be used as hypothesis space for multi-task classification. It extends similar hypothesis spaces that have previously considered in the literature. Assuming this…

Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a…

We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV) regularization, in image denoising problems. We describe…

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

Characterizing the function spaces defined by neural networks helps understanding the corresponding learning models and their inductive bias. While in some limits neural networks correspond to function spaces that are Hilbert spaces, these…

For semi-supervised learning on graphs, we study how initial kernels in a supervised learning regime can be augmented with additional information from known priors or from unsupervised learning outputs. These augmented kernels are…