Related papers: Fast Spectrum Estimation of Some Kernel Matrices
Applying kernel methods to matchings is challenging due to their discrete, non-Euclidean nature. In this paper, we develop a principled framework for constructing geometric kernels that respect the natural geometry of the space of…
Low-rank approximation is a common tool used to accelerate kernel methods: the $n \times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\tilde K$ which can be stored in much less space and processed more quickly. In this work…
Bursts of images exhibit significant self-similarity across both time and space. This motivates a representation of the kernels as linear combinations of a small set of basis elements. To this end, we introduce a novel basis prediction…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…
Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner…
It is critical to understand the properties of spatial correlation matrices in massive multiple-input multiple-output (MIMO) systems. We derive new bounds on the extreme eigenvalues of a spatial correlation matrix that is characterized by…
Kernel regression is an essential and ubiquitous tool for non-parametric data analysis, particularly popular among time series and spatial data. However, the central operation which is performed many times, evaluating a kernel on the data…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…
In this PhD thesis, we propose a novel framework for uncertainty quantification in machine learning, which is based on proper scores. Uncertainty quantification is an important cornerstone for trustworthy and reliable machine learning…
For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…
Recent advances in self-supervised learning and neural network scaling have enabled the creation of large models, known as foundation models, which can be easily adapted to a wide range of downstream tasks. The current paradigm for…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…
Tree kernels have demonstrated their ability to deal with hierarchical data, as the intrinsic tree structure often plays a discriminative role. While such kernels have been successfully applied to various domains such as nature language…
We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…
We continue investigating spectral properties of a Hermitised random matrix product, which, contrary to previous product ensembles, allows for eigenvalues on the full real line. When a GUE matrix with an external source is involved, we…