A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper proves MS convergence for radially symmetric kernels with large bandwidths.
A new method slices and sums radial kernels faster.
OKSVM optimizes RBF kernel hyperparameter for SVMs, improving classification performance.
The paper develops heat kernel comparison theorems and applies them to spectral geometry.
Stochastic gradient descent optimizes Nyström samples for kernel matrix approximation.
Method learns radial basis function distributions from samples.
New Fourier features improve high-precision approximation in large-scale problems.
Adaptive RBF-KAN improves KANs by dynamically adjusting kernel parameters.
The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in Rm. When we choose the Riesz kernel or the Poisson kernel as the kernel, such centers are called a radial center or an illuminating center, respec…
In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in . Our approach focuses on high dimensions and relies solely on the concentration properties of the components in the mixture. We give several results describing of the structure of kernel matrices …
A new multi-kernel RBFNN design improves performance and speed.
We study the complex geometry of generalized Kepler manifolds, defined in Jordan theoretic terms, introduce Hilbert spaces of holomorphic functions defined by radial measures, and find the complete asymptotic expansion of the corresponding reproducing kernels for Kähler potentials, both in the flat and bounded setting.
New kernels defined for various spaces, including measures.
The paper studies heat behavior on curved spaces without radiality assumption.
New example of manifolds with monotonic heat kernels found.
AEN-RBF kernel improves robustness in Bayesian optimization for complex systems.
In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework dynamically adapts the weights of the participating kernels us…
We study the expressive power of kernel methods and the algorithmic feasibility of multiple kernel learning for a special rich class of kernels. Specifically, we define \emph{Euclidean kernels}, a diverse class that includes most, if not all, families of kernels studied in literature such as polynomial kernels and radi…
Study Brownian motions and heat kernel bounds on Kähler and quaternion Kähler manifolds.
Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our approach relies on radial basis functions (RBFs) to interpolate the inverse map ever…
Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel …
The paper proves a nonlocal version of the Alexandrov Theorem for smooth boundaries.
Proposes LRR and LRLR for improving stock prediction accuracy.
Region-based classification of PolSAR data can be effectively performed by seeking for the assignment that minimizes a distance between prototypes and segments. Silva et al (2013) used stochastic distances between complex multivariate Wishart models which, differently from other measures, are computationally tractable.…
In this note, we concentrate on the sub-Laplace on the nilpotent Lie group of rank two, which is the infinitesimal generator of the diffusion generated by Brownian motions and their Lévy area processes, which is the simple extension of the sub-Laplace on the Heisenberg group . In order …
Consistency of the kernel density estimator requires that the kernel bandwidth tends to zero as the sample size grows. In this paper we investigate the question of whether consistency is possible when the bandwidth is fixed, if we consider a more general class of weighted KDEs. To answer this question in the affirmativ…
Paper improves kernel approximations for better statistical learning.
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical -estimation. We interpret the KDE based on a radial, positive semi-definite ke…
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for other methods the spectral information can be used to estimate the excess risk. An …
The study proves that sets with constant nonlocal curvature are composed of equal balls under certain conditions.
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately, kernel means are faced with scalability issues. A single point evaluation of the …
Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address this problem and reduce the arithmetic and storage cost. However, we observed tha…
Paper develops deep learning for metocean variable extremes.
Improved sample efficiency with normalized RBF kernels in neural networks.
We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present a principled framework to interpret CSK, as well as other deep probabilistic mo…
The GMM (generalized min-max) kernel was recently proposed (Li, 2016) as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted to the (generalized) consistent weighted sampling (GCWS) to convert the GMM ker…
New method uses multiple kernels to improve SVGD performance.
New insights into simple kernel smoothing reveal surprising asymptotics.
We focus on kernel methods for set-valued inputs and their application to Bayesian set optimization, notably combinatorial optimization. We investigate two classes of set kernels that both rely on Reproducing Kernel Hilbert Space embeddings, namely the ``Double Sum'' (DS) kernels recently considered in Bayesian set opt…
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior differential on closed forms with image in the kernel of the codifferential. Any Biot-Sav…
Deep neural nets optimize kernel parameters for non-parametric two-sample tests.
GPs with neural network dual kernels improve reinforcement learning performance.
Researchers prove long-time existence for two landmark Brownian motion.
Novel algorithm identifies nonlinear Granger causal relationships using kernel ridge regression.
The paper generalizes radial curvature bounds on manifolds.
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 distributions to some reference distributions denoted as templates. Our framework exte…
Unified quadrature framework for large-scale kernel machines.
Hermann Schwarz, while studying complex analysis, introduced the geometric interpretation for the Poisson kernel in 1890. We shall see here that the geometric interpretation can be useful to develop a new approach to some old classical problems as well as to obtain several new results, mostly related to hyperbolic geom…