Related papers: Enhancing Kernel Flexibility via Learning Asymmetr…

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

Kernel methods have been successfully applied to the areas of pattern recognition and data mining. In this paper, we mainly discuss the issue of propagating labels in kernel space. A Kernel-Induced Label Propagation (Kernel-LP) framework by…

Kernel methods provide a theoretically grounded framework for non-linear and non-parametric learning, with strong analytic foundations and statistical guarantees. Yet, their scalability has long been limited by prohibitive time and memory…

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…

In this article, we present a method for increasing adaptivity of an existing robust estimation algorithm by learning two parameters to better fit the residual distribution. The analyzed method uses these two parameters to calculate weights…

Random feature (RF) has been widely used for node consistency in decentralized kernel ridge regression (KRR). Currently, the consistency is guaranteed by imposing constraints on coefficients of features, necessitating that the random…

Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…

Neural networks are generally built by interleaving (adaptable) linear layers with (fixed) nonlinear activation functions. To increase their flexibility, several authors have proposed methods for adapting the activation functions…

Adaptive bandwidth selection is a fundamental challenge in nonparametric regression. This paper introduces a new bandwidth selection procedure inspired by the optimality criteria for $\ell_0$-penalized regression. Although similar in spirit…

Quantum kernels (QK) are widely used in quantum machine learning applications; yet, their potential to surpass classical machine learning methods on classical datasets remains uncertain. This limitation can be attributed to the exponential…

We introduce an original method of multidimensional ridge penalization in functional local linear regressions. The nonparametric regression of functional data is extended from its multivariate counterpart, and is known to be sensitive to…

Gradient-based optimization has been a cornerstone of machine learning that enabled the vast advances of Artificial Intelligence (AI) development over the past decades. However, this type of optimization requires differentiation, and with…

In continuum-armed bandit problems where the underlying function resides in a reproducing kernel Hilbert space (RKHS), namely, the kernelised bandit problems, an important open problem remains of how well learning algorithms can adapt if…

Kernel-based learning methods such as Kernel Logistic Regression (KLR) can substantially increase the storage capacity of Hopfield networks, but the principles governing their performance and stability remain largely uncharacterized. This…

Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…

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…

Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…