arXiv research

The paper studies special surfaces with a new type of support function.

Defines spherical type surfaces via support function and classifies them.

Study on convex surfaces in Minkowski space, proving completeness and incompleteness conditions.

The paper studies a flow of convex hypersurfaces expanding by their support and curvature functions.

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…

Reconstructing polytopes with fixed facet directions from support function evaluations.

Proposes an L1-regularized functional SVM for binary classification with functional covariates.

We study the motion of smooth, strictly convex bodies in $\mathbb{R}^n$ expanding in the direction of their normal vector field with speed depending on Gauss curvature and support function.

Suppose that $Ω$ is the open region in $\mathbb{R}^n$ above a Lipschitz graph and let $d$ denote the exterior derivative on $\mathbb{R}^n$. We construct a convolution operator $T$ which preserves support in $\bar{Ω$}, is smoothing of order 1 on the homogeneous function spaces, and is a potential map in the sense that …

Study shows Sobolev functions on non-compact manifolds can't be approximated by smooth compactly supported functions.

Theory for deep neural network approximation of score function and its derivatives.

Neural networks learn the support of the target function through SGD's implicit regularization effect.

We consider the homogeneous and the non-homogeneous convex relaxations for combinatorial penalty functions defined on support sets. Our study identifies key differences in the tightness of the resulting relaxations through the notion of the lower combinatorial envelope of a set-function along with new necessary conditi…

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…

The paper analyzes kNN density estimation's convergence rates under different conditions.

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…

Researchers develop a method to infer reference measures from observed functionals.

Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning. In this paper we dramatically simplify the support func…

Algorithm reduces support of discrete measures by integrating against functions.

A nontrivial smooth steady incompressible Euler flow in three dimensions with compact support is constructed. Another uncommon property of this solution is the dependence between the Bernoulli function and the pressure.

We study the weighted ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We prove support theorems if the manifold and the weight are analytic.

Unified approach to multiclass classification using Gabriel graphs.

Study optimal times to buy and sell stocks using support/resistance lines.

Sparse Gaussian processes with compact kernels for faster inference.

In this paper, we propose a novel asymmetric $ε$-insensitive pinball loss function for quantile estimation. There exists some pinball loss functions which attempt to incorporate the $ε$-insensitive zone approach in it but, they fail to extend the $ε$-insensitive approach for quantile estimation in true sense. The propo…

In this paper, we introduce a novel combined reward cum penalty loss function to handle the regression problem. The proposed combined reward cum penalty loss function penalizes the data points which lie outside the $ε$-tube of the regressor and also assigns reward for the data points which lie inside of the $ε$-tube of…

This study presents a rapid multiple incremental and decremental mechanism based on Weight-Error Curves (WECs) for support-vector analysis. Recursion-free computation is proposed for predicting the Lagrangian multipliers of new samples. This study examines Ridge Support Vector Models, subsequently devising a recursion-…

We develop an integral geometry of stationary Euler equations defining some function $w$ on the Grassmannian of affine lines in the space. This function depends on a putative compactly supported solution $v$ of the system, and we deduce a linear differential equation for $w$. We prove also that the purported annulation…

Least Squares Estimators are suboptimal for 5D convex functions.

Establishes Poincaré's lemma for formal manifolds.

A new line search rule improves support recovery in high-dimensional data.

New regularization method reduces support of empirical risk minimization solutions.

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…

Amortizes MIPS by training neural networks to predict optimal keys.

In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast to this, multiple model enumeration attracts increasing interests in non-standar…

For a convex domain $D$ that is enclosed by the hypersurface $\partial D$ of bounded normal curvature, we prove an angle comparison theorem for angles between $\partial D$ and geodesic rays starting from some fixed point in $D$, and the corresponding angles for hypersurfaces of constant normal curvature. Also, we obtai…

Classification and regression tasks in overparameterized models show different generalization properties.

OKSVM optimizes RBF kernel hyperparameter for SVMs, improving classification performance.

Paper supports robust estimation in regression with heavy-tailed errors.

In this paper, we aim at recovering an undirected weighted graph of $N$ vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix $W$. For instance, this situation arises for stationary signals on graphs or for Markov chains observed at random times. Our approach is based on minimizi…

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

RHPSVM improves SVM performance with robust loss function.

New inequalities for unbounded functions improve denoising score matching.

It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample distribution of SVMs by the bootstrap approach.

A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Support vector machines (SVMs) are well established to estimate location functions …

In this paper we show how to bypass the usual difficulties in the analysis of elliptic integrals that arise when solving period problems for minimal surfaces. The method consists of replacing period problems with ordinary Sturm-Liouville problems involving the support function. We give a practical application by provin…

Study of a flow related to the Orlicz-Minkowski problem for convex hypersurfaces.

Hybrid Bayesian neural networks use function uncertainty for probabilistic inference.