Related papers: Geometrically Inspired Kernel Machines for Collabo…
Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…
In this paper we first identify a basic limitation in gradient descent-based optimization methods when used in conjunctions with smooth kernels. An analysis based on the spectral properties of the kernel demonstrates that only a vanishingly…
Many supervised learning tasks have intrinsic symmetries, such as translational and rotational symmetry in image classifications. These symmetries can be exploited to enhance performance. We formulate the symmetry constraints into a concise…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…
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…
This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel methods tied to the neural tangent kernel theory, the diagonal…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…
This paper proposes a method for constructing one-step prediction tubes for nonlinear systems using reproducing kernel Hilbert spaces. We approximate a bounded reproducing kernel Hilbert space (RKHS) hypothesis set by a finite-dimensional…
We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions…
We propose a framework for transfer learning of discount curves across different fixed-income product classes. Motivated by challenges in estimating discount curves from sparse or noisy data, we extend kernel ridge regression (KR) to a…
In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…
Deep kernel learning aims at designing nonlinear combinations of multiple standard elementary kernels by training deep networks. This scheme has proven to be effective, but intractable when handling large-scale datasets especially when the…
Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…