Related papers: Dataset Meta-Learning from Kernel Ridge-Regression
The current trend in data regulation requirements and privacy-preserving machine learning has emphasized the importance of machine unlearning. The naive approach to unlearning training data by retraining over the complement of the forget…
A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…
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…
Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…
Physics-informed machine learning typically integrates physical priors into the learning process by minimizing a loss function that includes both a data-driven term and a partial differential equation (PDE) regularization. Building on the…
Generative artificial intelligence has transformed the generation of synthetic data, providing innovative solutions to challenges like data scarcity and privacy, which are particularly critical in fields such as medicine. However, the…
We prove minimax optimal learning rates for kernel ridge regression, resp.~support vector machines based on a data dependent partition of the input space, where the dependence of the dimension of the input space is replaced by the fractal…
This paper focuses on generalization performance analysis for distributed algorithms in the framework of learning theory. Taking distributed kernel ridge regression (DKRR) for example, we succeed in deriving its optimal learning rates in…
Recent research shows that for training with $\ell_2$ loss, convolutional neural networks (CNNs) whose width (number of channels in convolutional layers) goes to infinity correspond to regression with respect to the CNN Gaussian Process…
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of…
Machine unlearning -- efficiently removing the effect of a small "forget set" of training data on a pre-trained machine learning model -- has recently attracted significant research interest. Despite this interest, however, recent work…
Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…
The ability to identify useful features or representations of the input data based on training data that achieves low prediction error on test data across multiple prediction tasks is considered the key to multitask learning success. In…
We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…
The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…
Learned image compression sits at the intersection of machine learning and image processing. With advances in deep learning, neural network-based compression methods have emerged. In this process, an encoder maps the image to a…
One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the space…
Reinforcement learning (RL) has shown empirical success in various real world settings with complex models and large state-action spaces. The existing analytical results, however, typically focus on settings with a small number of…
This paper presents a practical, and theoretically well-founded, approach to improve the speed of kernel manifold learning algorithms relying on spectral decomposition. Utilizing recent insights in kernel smoothing and learning with…
Data augmentation, a technique in which a training set is expanded with class-preserving transformations, is ubiquitous in modern machine learning pipelines. In this paper, we seek to establish a theoretical framework for understanding data…