Related papers: A global structure-preserving kernel method for th…

This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…

Logistic regression is a standard method in multivariate analysis for binary outcome data in epidemiological and clinical studies; however, the resultant odds-ratio estimates fail to provide directly interpretable effect measures. The…

A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…

Conformal prediction (CP) is a distribution-free method to construct reliable prediction intervals that has gained significant attention in recent years. Despite its success and various proposed extensions, a significant practical feature…

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training…

In this manuscript we consider Kernel Ridge Regression (KRR) under the Gaussian design. Exponents for the decay of the excess generalization error of KRR have been reported in various works under the assumption of power-law decay of…

We introduce ParK, a new large-scale solver for kernel ridge regression. Our approach combines partitioning with random projections and iterative optimization to reduce space and time complexity while provably maintaining the same…

Restoration of digital images from their degraded measurements has always been a problem of great theoretical and practical importance in numerous applications of imaging sciences. A specific solution to the problem of image restoration is…

Quantum machine learning is a growing research field that aims to perform machine learning tasks assisted by a quantum computer. Kernel-based quantum machine learning models are paradigmatic examples where the kernel involves quantum…

This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the…

Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and commonly used in nonparametric…

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…

The choice of the kernel is critical to the success of many learning algorithms but it is typically left to the user. Instead, the training data can be used to learn the kernel by selecting it out of a given family, such as that of…

Kernel ridge regression (KRR), also known as the least-squares support vector machine, is a fundamental method for learning functions from finite samples. While most existing analyses focus on the noisy setting with constant-level label…

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

In many applications such as medical imaging, the measurement data represent counts of photons hitting a detector. Such counts in low-photon settings are often modeled using a Poisson distribution. However, this model assumes that the mean…

The broad sense genetic heritability, which quantifies the total proportion of phenotypic variation in a population due to genetic factors, is crucial for understanding trait inheritance. While many existing methods focus on estimating…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…