arXiv research

Efficiently handles large support vectors in kernelized online learning.

Researchers calculate the second coefficient in the expansion of a Toeplitz operator.

Dropout increases the generalization of neural networks by expanding the weight space.

Rescaling expansiveness proven for k*-expansive vector fields.

A framework for transformer attention layers derived from SVR.

RPN unifies various models with a reconciled polynomial network.

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…

News items have a significant impact on stock markets but the ways are obscure. Many previous works have aimed at finding accurate stock market forecasting models. In this paper, we use text mining and sentiment analysis on Chinese online financial news, to predict Chinese stock tendency and stock prices based on suppo…

K-StoNet improves neural networks by avoiding local minima and assessing uncertainty.

Develops quantization for non-compact complex manifolds with spectral gap.

This paper gives quantitative global estimates between a time dependent flow on a Riemannian manifold $\left( M\right)$ and the flow of a vector field constructed by truncating the formal Magnus expansion for the logarithm of the flow. As a corollary, we also find quantitative estimates between the composition of the …

SVM generalizes well even with many support vectors in high dimensions.

Sparse Polynomial Chaos expansions improve accuracy and efficiency in simulations.

This paper explores supervised techniques for continuous anomaly detection from biometric touch screen data. A capacitive sensor array used to mimic a touch screen as used to collect touch and swipe gestures from participants. The gestures are recorded over fixed segments of time, with position and force measured for e…

The paper provides non-asymptotic Edgeworth expansions for neural network outputs.

The paper studies the asymptotic expansion of Gaussian integral operators on Riemannian submanifolds.

Application of fuzzy support vector machine in stock price forecast. Support vector machine is a new type of machine learning method proposed in 1990s. It can deal with classification and regression problems very successfully. Due to the excellent learning performance of support vector machine, the technology has becom…

We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive computational model subject to random inputs with an inexpensive-to-evaluate po…

The support vector clustering algorithm is a well-known clustering algorithm based on support vector machines using Gaussian or polynomial kernels. The classical support vector clustering algorithm works well in general, but its performance degrades when applied on big data. In this paper, we have investigated the perf…

We generalize a support vector machine to a support spinor machine by using the mathematical structure of wedge product over vector machine in order to extend field from vector field to spinor field. The separated hyperplane is extended to Kolmogorov space in time series data which allow us to extend a structure of sup…

Support vector machines have attracted much attention in theoretical and in applied statistics. Main topics of recent interest are consistency, learning rates and robustness. In this article, it is shown that support vector machines are qualitatively robust. Since support vector machines can be represented by a functio…

Support Vector Machine (SVM) is an efficient classification approach, which finds a hyperplane to separate data from different classes. This hyperplane is determined by support vectors. In existing SVM formulations, the objective function uses L2 norm or L1 norm on slack variables. The number of support vectors is a me…

BERET improves binary expansion test for multivariate independence.

A new method for support vector regression using a data-driven insensitive parameter.

Let $H_h = h^2 L +V$ where $L$ is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and $V$ is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of $H_h$ as $h \to 0$. As a consequence we get an asymptotic expansion for the …

New symmetry found in colored Alexander polynomial.

Study on recovering supports of multiple sparse vectors from mixed linear measurements.

Sharp Sobolev inequality derived for Riemannian manifolds with bounded Ricci curvature.

The paper studies asymptotic expansions of operators related to Bochner-Schrödinger on Riemannian manifolds.

Study Bergman kernels on Kähler orbifolds with specific properties.

We propose an algorithm for exploring the entire regularization path of asymmetric-cost linear support vector machines. Empirical evidence suggests the predictive power of support vector machines depends on the regularization parameters of the training algorithms. The algorithms exploring the entire regularization path…

Rgtsvm provides a fast and flexible support vector machine (SVM) implementation for the R language. The distinguishing feature of Rgtsvm is that support vector classification and support vector regression tasks are implemented on a graphical processing unit (GPU), allowing the libraries to scale to millions of examples…

SVM and linear regression models coincide in high dimensions.

New algorithms reduce computational burden for principal support vector machines.

Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent researchers reveal that maximizing the margin distribution of whole training dataset ra…

We establish the cancellation of the first $2j$ terms in the diagonal asymptotic expansion of the restriction to the $(0,2j)$-forms of the Bergman kernel associated to the spin${}^c$ Dirac operator on high tensor powers of a positive line bundle twisted by a (non necessarily holomorphic) complex vector bundle, over a c…

LIBTwinSVM offers a free library for efficient Twin Support Vector Machines.

We propose a scheme for recycling Gaussian random vectors into structured matrices to approximate various kernel functions in sublinear time via random embeddings. Our framework includes the Fastfood construction as a special case, but also extends to Circulant, Toeplitz and Hankel matrices, and the broader family of s…

Secure Aggregation protocols allow a collection of mutually distrust parties, each holding a private value, to collaboratively compute the sum of those values without revealing the values themselves. We consider training a deep neural network in the Federated Learning model, using distributed stochastic gradient descen…

Develops geometric Weyl calculus for curved spacetimes.

Support vector data description (SVDD) is a machine learning technique that is used for single-class classification and outlier detection. The idea of SVDD is to find a set of support vectors that defines a boundary around data. When dealing with online or large data, existing batch SVDD methods have to be rerun in eac…

Study asymptotic expansion of graph Laplacian on discretized surfaces, relating spanning trees and cycle-rooted forests.

Bayesian adaptive PCE method improves surrogate modeling and sensitivity analysis.

Investigates point spectra of vector fields and their properties.

Geodesic flows on compact manifolds without conjugate points are shown to have a unique measure of maximal entropy.

New self-similarity for Einstein vacuum equations identified.

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…

Gradient-enhanced GSA uses Poincaré chaos expansions for accurate sensitivity analysis.