Related papers: Fast Spectrum Estimation of Some Kernel Matrices

In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…

We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…

Stein kernel has recently shown promising performance on classifying images represented by symmetric positive definite (SPD) matrices. It evaluates the similarity between two SPD matrices through their eigenvalues. In this paper, we argue…

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

The paper addresses the problem to estimate the power spectral density of an ARMA zero mean Gaussian process. We propose a kernel based maximum entropy spectral estimator. The latter searches the optimal spectrum over a class of high order…

Shapley values have emerged as a critical tool for explaining which features impact the decisions made by machine learning models. However, computing exact Shapley values is difficult, generally requiring an exponential (in the feature…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…

Learning a kernel matrix from relative comparison human feedback is an important problem with applications in collaborative filtering, object retrieval, and search. For learning a kernel over a large number of objects, existing methods face…

Efficient and accurate low-rank approximations of multiple data sources are essential in the era of big data. The scaling of kernel-based learning algorithms to large datasets is limited by the O(n^2) computation and storage complexity of…

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…

Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…

We prove edge universality of local eigenvalue statistics for orthogonal invariant matrix models with real analytic potentials and one interval limiting spectrum. Our starting point is the result of \cite{S:08} on the representation of the…

In many machine learning and data related applications, it is required to have the knowledge of approximate ranks of large data matrices at hand. In this paper, we present two computationally inexpensive techniques to estimate the…

Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…

We study an "inner-product kernel" random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large $n$ and $p$ limit. We provide an interpretation of…