Related papers: Sketching the Heat Kernel: Using Gaussian Processe…

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

In this work, we investigate Gaussian Processes indexed by multidimensional distributions. While directly constructing radial positive definite kernels based on the Wasserstein distance has been proven to be possible in the unidimensional…

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…

We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

Gaussian processes (GPs) are flexible models that can capture complex structure in large-scale dataset due to their non-parametric nature. However, the usage of GPs in real-world application is limited due to their high computational cost…

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

A device called a 'Gaussian Boson Sampler' has initially been proposed as a near-term demonstration of classically intractable quantum computation. As recently shown, it can also be used to decide whether two graphs are isomorphic. Based on…

The state-of-the-art linked Gaussian process offers a way to build analytical emulators for systems of computer models. We generalize the closed form expressions for the linked Gaussian process under the squared exponential kernel to a…

Efficient scene representations are essential for many computer graphics applications. A general unified representation that can handle both surfaces and volumes simultaneously, remains a research challenge. Inspired by recent methods for…

Dataset distillation aims to synthesize a compact subset of the original data, enabling models trained on it to achieve performance comparable to those trained on the original large dataset. Existing distribution-matching methods are…

This paper presents a kernelized version of the t-SNE algorithm, capable of mapping high-dimensional data to a low-dimensional space while preserving the pairwise distances between the data points in a non-Euclidean metric. This can be…

Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…

Modeling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned…