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.
Study compares exponential and power-law kernels in modeling high-frequency trading data.
New method for spectral and Bergman kernels under local spectral gap condition.
New random feature maps for Laplacian and related kernels.
A new MMD-based test combines kernels for two-sample testing without splitting data.
Explicit formula for Bergman kernel of abelian varieties proved.
Deep neural kernels and Laplace kernel have equivalent RKHS on spheres.
Study evaluates RKHS choices for assessing graph models using KSD tests.
We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry. First, we establish the off-diagonal exponential estimate for the generalized Bergman kernel. As an application, we obtai…
Study asymptotics of extension and orthogonal Bergman kernels for high tensor powers of positive line bundles.
The recently proposed "generalized min-max" (GMM) kernel can be efficiently linearized, with direct applications in large-scale statistical learning and fast near neighbor search. The linearized GMM kernel was extensively compared in with linearized radial basis function (RBF) kernel. On a large number of classificatio…
We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-expo…
Paper studies kernel hyperparameters for clustering, proposing an efficient search method.
Paper introduces kernel deformed exponential families for sparse continuous attention.
In this paper we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchel-Rockafellar duality theory, we give explicit formulation of the dual problem as well as of the related optimality conditions. Moreover, we provide a new computational framework for solving…
Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological summaries, most noticeably the Persistence Diagram, are typically defined in comple…
We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling e…
We apply a fast kernel method for mask-based single-channel speech enhancement. Specifically, our method solves a kernel regression problem associated to a non-smooth kernel function (exponential power kernel) with a highly efficient iterative method (EigenPro). Due to the simplicity of this method, its hyper-parameter…
Unified score and distance-based GoF tests for model adequacy.
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances relying on optimal transport theory - such as the Wasserstein distance between …
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in thei…
New research sets the minimax lower bound for KSD estimation at sqrt(n).
We propose and investigate two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively. The models proposed exhibit jumps clustering features. Models of this kind have been already proposed for the spot price…
Study the Bochner-Schrödinger operator on symplectic manifolds, proving gap existence and asymptotic kernel behavior.
Quantum kernel methods can lead to trivial models due to exponential concentration of kernel values.
We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line b…
A new kernel improves tensor classification accuracy and reduces computation time.
Efficiently accelerates attention calculation for Transformers with relative positional encoding.
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…
Kernel estimator optimally recovers function from noisy exponential Radon transform.
We prove a conjecture about approximating Gaussian Processes on one dimension.
We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual embedding, that avoids computation of the partition function. This technique also allows the develo…
Study on KRR with power-law data, showing better sample complexity.
We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the exponential weights algorithm and bound its regret in this setting. Under conditions on …
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…
We discover scaling laws for kernel regression loss under various learning rate schedules.
New spectral mixture representation for isotropic kernels simplifies random Fourier features.
Study shows Bergman kernel quotient approaches one for punctured surfaces.
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
A new method for kernel tests without data splitting increases power.
Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.
Develops European power option pricing under correlated interest rate and asset processes.
CTT compresses samples to test distributions near-linearly, outperforming existing methods.
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space and the number of data points. To tackle the big data challenge, a quantum SVM a…
Boosts change-point detection power with optimal sub-sampling.
New kernels on symmetric groups enable efficient Gaussian process sampling.
Appropriately designing the proposal kernel of particle filters is an issue of significant importance, since a bad choice may lead to deterioration of the particle sample and, consequently, waste of computational power. In this paper we introduce a novel algorithm adaptively approximating the so-called optimal proposal…
Given two sets of independent samples from unknown distributions and , a two-sample test decides whether to reject the null hypothesis that . Recent attention has focused on kernel two-sample tests as the test statistics are easy to compute, converge fast, and have low bias with their finite sample estimate…
Kernel thinning compresses distributions more effectively than i.i.d. sampling or standard thinning.