Related papers: Rejoinder: Classifier Technology and the Illusion …
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
We describe a method for predicting a classification of an object given classifications of the objects in the training set, assuming that the pairs object/classification are generated by an i.i.d. process from a continuous probability…
This article presents a re-classification of information seeking (IS) tasks, concepts, and algorithms. The proposed taxonomy provides new dimensions to look into information seeking tasks and methods. The new dimensions include the number…
I provide some comments on Arithmetic Teichmuller Spaces constructed in my paper arXiv:2106.11452.
We survey the classical results of the Dirichlet Approximation Theorem.
New proposed models are often compared to state-of-the-art using statistical significance testing. Literature is scarce for classifier comparison using metrics other than accuracy. We present a survey of statistical methods that can be used…
An introduction and overview of constructive reverse mathematics.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
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…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
We respond to comments on our paper, titled "Instrumental variable estimation of the causal hazard ratio."
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 study rate of convergence of recursive estimation procedures for the general…
The ability of a classifier to take on new information and classes by evolving the classifier without it having to be fully retrained is known as incremental learning. Incremental learning has been successfully applied to many…
A class of determinants is introduced. Different kind of mathematical objects, such as Fibonacci, Lucas, Tchebychev, Hermite, Laguerre, Legendre polynomials, sums and covergents are represented as determinants from this class. A closed…
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
In this short position paper, we introduce tensor completions and artifacts and make the case that they are a useful theoretical framework for understanding certain types of hallucinations and generalizations in language models.
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
Active learning methods increase classification quality by means of user feedback. An important subcategory is active learning for outlier detection with one-class classifiers. While various methods in this category exist, selecting one for…
The material of this work is aimed at mathematics educators, as well as math specialists with a keen interest in progressions. In this paper, we study the subject of arithmetic, geometric, mixed, and harmonic progressions or sequences. Some…