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.
Deep networks are shown to be equivalent to a new type of kernel chain.
Study Markov chain gradient descent in Hilbert spaces for quadratic loss.
Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of this technique is conducted for the previously unconsidered setting where samples…
Kernel-based methods improve policy evaluation in MRP models.
Kernel thinning compresses distributions more effectively than i.i.d. sampling or standard thinning.
We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a reproducing kernel Hilbert space. We here focus on modelling nonlinear covariance s…
In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of semi-inner-products, we can obtain the explicit representations of the dual (nor…
Study online learning in RKHS with dependent processes, focusing on \(β\)- and \(φ\)-mixing.
Kernel methods are studied in a mean field limit for high-dimensional data.
This paper extends mirror descent to Banach spaces with reproducing kernels.
We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence constructed via Stein's method using functions from a Reproducing Kernel Hilbert Space. O…
We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of smoother RKHS that we call diffusion spaces. We illustrate the general results with…
We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back operation involving the tautological universal bundle and the classifying morphism o…
Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy measures that provably determine the convergence of a sample to its target dist…
Derives properties of heat kernel for Rumin complex on Heisenberg groups.
Paper characterizes embeddability of function spaces into -type RKBS via metric entropy.
A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert space (RKHS), such that the feature space covariance of the samples informs the…
Paper introduces RKHM and KME for richer data analysis.
Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified…
The paper uses Banach spaces to analyze neural networks.
The study uses reproducing kernels to model bond discount curves.
The paper improves probabilistic herding methods using Gibbs distributions.
Paper proposes a method for early stopping in regression using reproducing kernels.
The paper develops a uniform function estimator in RKHS for regression.
The paper develops methods to handle missing data using regularized M-estimation in reproducing kernel Hilbert space.
New method for learning with non-Euclidean data using decomposable kernels.
Study of regularized least squares in RKKS with indefinite kernels.
This study connects Gaussian processes and RKHS, bridging two machine learning communities.
Motivated by multi-task machine learning with Banach spaces, we propose the notion of vector-valued reproducing kernel Banach spaces (RKBS). Basic properties of the spaces and the associated reproducing kernels are investigated. We also present feature map constructions and several concrete examples of vector-valued RK…
This note explains when neural networks can be seen as Gaussian processes.
Study on how sampling works for complex data functions.
Develops vector-valued RKBS for neural networks and operators.
Deep neural networks define suitable reproducing kernel Banach spaces.
Recently, there has been emerging interest in constructing reproducing kernel Banach spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling reconstruction, sparse approximation and functional analysis. Existing constructions include the reflexive RKBS via a bilinear form, the semi-inner-p…
Prefix consistency improves model reliability by weighting answers based on their reproducibility.
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding t…
Paper explores RKHS properties for derivative and integral operators.
Gradient Langevin dynamics (GLD) and stochastic GLD (SGLD) have attracted considerable attention lately, as a way to provide convergence guarantees in a non-convex setting. However, the known rates grow exponentially with the dimension of the space. In this work, we provide a convergence analysis of GLD and SGLD when t…
Kernel interpolation is inconsistent for norms with smoothness above a constant.
New approach to supervised learning in RKHS and vvRKHS using -algebras.
In this paper we propose a bivariate generalization of a weighted indexed semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to repr…
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.
Extends Gaussian process theory to Banach spaces.
The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We propose two power-law kernels by generalizing Gaussian and Laplacian kernels. Th…
We attempt to set a mathematical foundation of immunology and amino acid chains. To measure the similarities of these chains, a kernel on strings is defined using only the sequence of the chains and a good amino acid substitution matrix (e.g. BLOSUM62). The kernel is used in learning machines to predict binding affinit…
Subsampling reduces computational cost in supervised learning in reproducing kernel Hilbert spaces.
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with reproducing kernel Hilbert -module (RKHM), which is another generalization of…
New method trains Markov kernels for efficient sampling.