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.
New kernels defined for various spaces, including measures.
Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore the connection between conditional independence measures induced by distances on …
Paper compares Bergman kernel and Masur-Veech measure on Teichmüller space.
A Hilbert space embedding for probability measures has recently been proposed, wherein any probability measure is represented as a mean element in a reproducing kernel Hilbert space (RKHS). Such an embedding has found applications in homogeneity testing, independence testing, dimensionality reduction, etc., with the re…
New quantum kernels avoid overfitting by combining local and global components.
Paper generalizes kernel mean embedding to von Neumann-algebra-valued measures.
Paper solves open question about non-positive kernels by decomposing them into PD kernels.
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures from some set to functions in a reproducing kernel Hilbert space (RKHS) with kernel . The RKHS distance of two mapped measures is a semi-metric over . We study three questions. (I) For a…
We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel , which translates naturally into kernels between histograms or clouds of points. We first cover the case where $\Xcal$ is Euclidian, and focus on kernels which take into account th…
A new kernel for probability measures based on optimal transport.
The paper shows how MMD metrizes weak convergence for certain kernels.
Kernel embeddings separate distinct probability distributions, simplifying testing.
Toeplitz operators linked to submultiplicative filtrations and weighted Bergman kernels.
New conditions ensure MMDs separate and converge to target distributions.
Paper advances sparse regularisation theory for measures with new kernel insights.
New method uses kernel Stein discrepancy for measure transport without strict continuity constraints.
We analyzed optimism in linear and kernel regression models.
We prove that a metric measure space equipped with a Dirichlet form admitting an Euclidean heat kernel is necessarily isometric to the Euclidean space. This helps us providing an alternative proof of Colding's celebrated almost rigidity volume theorem via a quantitative version of our main result. We also discuss the c…
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 mappings. We utilize the Discriminant Information criterion, a measure of class …
A new kernel measures brain network similarities, improving disease classification.
A new measure of dependence for various data types.
Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of usi…
We offer a new, rigorous approach to conditional mean embeddings without operator constraints.
Fourier representation improves KSD for infinite-dimensional data.
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size of the data. Many natural measures of similarity between pairs of samples are not…
A new kernel-based CI test improves on existing methods.
The rate of convergence of weighted kernel herding (WKH) and sequential Bayesian quadrature (SBQ), two kernel-based sampling algorithms for estimating integrals with respect to some target probability measure, is investigated. Under verifiable conditions on the chosen kernel and target measure, we establish a near-geom…
kdiff measures distances for time series and structured data.
This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the norms of the Radon-Nikodym derivatives. We also prove that a logarithmic Sobolev inequality holds …
Study birth-death dynamics for sampling Gibbs measures with nonconvex potentials.
New clustering method using point-set kernel measures similarity.
Improved kernel quadrature with convex weights using subsampling.
Extends Tanimoto kernel to real-valued functions.
A novel kernel-based test detects equality versus singularity of two probability measures.
A new method warps inputs to learn nonstationary kernels efficiently.
In this survey article, we review the relation between heat kernels and path integrals. In particular, we review recent results on the approximation of the Wiener measure on compact manifold by measures on (finite-dimensional) spaces of piece-wise geodesics.
Develops efficient inference for noise heterogeneity in machine learning models.
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 structures in the data. Recently, it was suggested to replace the standard kernel …
Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another meas…
Paper proposes a new method to learn distribution kernels via entropy maximization.
Optimizes kernel density ratios for better predictions and information measures.
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few hyperparameters or the kernel is even data dependent in a much more complicated manner. …
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). A pseudometric on the spac…
In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the orthogonality condition of the atoms, yielding overcomplete dictionaries with an exten…
Paper provides unbiased spectral moment estimates from finite data.
A new method quantizes conditional probability measures using deep learning.
Algorithm finds best Dirac mass approximation of target measure.
In this article, we construct the canonical semipositive current or the canonical measure ( the potential of the canonical semipositive current) on a smooth projective variety of nonnegative Kodaira dimension in terms of a dynamical system of Bergman kernels. This current is considered to be a generalization of a Kä…