Related papers: Rejoinder to "Support Vector Machines with Applica…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
Reply to arXiv:1903.09201.
Support Vector Machines have been a popular topic for quite some time now, and as they develop, a need for new methods of feature selection arises. This work presents various approaches SVM feature selection developped using new tools such…
Support Vector Machines (SVMs) are popular tools for data mining tasks such as classification, regression, and density estimation. However, original SVM (C-SVM) only considers local information of data points on or over the margin.…
This paper summarizes my doctoral research on evaluation algorithms for HEX-programs, which extend Answer Set Programming with means for interfacing external computations. The focus is on integrating different subprocesses of…
Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector $M$ via the equations $v…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large…
We give a new proof of Theorem 6 in [L. Qiu and X. Zhan, On the span of Hadamard products of vectors, Linear Algebra Appl. 422 (2007) 304--307].
We present a new approach to obtaining photometric redshifts using a kernel learning technique called Support Vector Machines (SVMs). Unlike traditional spectral energy distribution fitting, this technique requires a large and…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described…
We discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms.
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In…
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…
Comments on extensions of Verma modules in the Bernstein-Gelfand-Gelfand Category O.
This paper comments on the published work dealing with robustness and regularization of support vector machines (Journal of Machine Learning Research, vol. 10, pp. 1485-1510, 2009) [arXiv:0803.3490] by H. Xu, etc. They proposed a theorem to…