Related papers: New Generalization Bounds for Learning Kernels

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise…

We discuss recent developments regarding the use of kernels in complex Langevin simulations. In particular, we outline how a kernel can be used to solve the problem of wrong convergence in a simple toy model. Since conventional correctness…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Understanding why trained Transformers generalize well is a fundamental problem in modern machine learning theory, and complexity-based generalization bounds provide a principled way to study this question. While existing norm-based bounds…

We study approximation and learning capacities of convolutional neural networks (CNNs) with one-side zero-padding and multiple channels. Our first result proves a new approximation bound for CNNs with certain constraint on the weights. Our…

Despite the tremendous empirical success of deep learning models to solve various learning tasks, our theoretical understanding of their generalization ability is very limited. Classical generalization bounds based on tools such as the VC…

Kernelization is a significant topic in parameterized complexity. Turing kernelization is a general form of kernelization. In the aspect of kernelization, an impressive hardness theory has been established [Bodlaender etc. (ICALP 2008,…

We show that learning a convex body in $\RR^d$, given random samples from the body, requires $2^{\Omega(\sqrt{d/\eps})}$ samples. By learning a convex body we mean finding a set having at most $\eps$ relative symmetric difference with the…

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in…

In this work, we analyze the learnability of reproducing kernel Hilbert spaces (RKHS) under the $L^\infty$ norm, which is critical for understanding the performance of kernel methods and random feature models in safety- and…

We study the generalization of deep learning models in relation to the convex hull of their training sets. A trained image classifier basically partitions its domain via decision boundaries and assigns a class to each of those partitions.…

This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform…

It has been recently observed in much of the literature that neural networks exhibit a bottleneck rank property: for larger depths, the activation and weights of neural networks trained with gradient-based methods tend to be of…

In this work we consider the learning setting where, in addition to the training set, the learner receives a collection of auxiliary hypotheses originating from other tasks. We focus on a broad class of ERM-based linear algorithms that can…

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…

In this paper, we provide a new framework to obtain the generalization bounds of the learning process for domain adaptation, and then apply the derived bounds to analyze the asymptotical convergence of the learning process. Without loss of…

Deep learning methods have predominantly been applied to large artificial neural networks. Despite their state-of-the-art performance, these large networks typically do not generalize well to datasets with limited sample sizes. In this…

This paper studies the fundamental limits of reinforcement learning (RL) in the challenging \emph{partially observable} setting. While it is well-established that learning in Partially Observable Markov Decision Processes (POMDPs) requires…

In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the…

We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to…