相关论文: Short introduction to Nonstandard Analysis
Limits of agreement with the mean (LOAM) can be used for assessing agreement of continuous measurements made by different observers. Definitions of a LOAM for measuring reproducibility has been introduced under a two-way random effects…
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the classical \emph{O$ (\cdot ) $} and \emph{o$ (\cdot ) $} notation…
This paper consists of a description of the variety of two dimensional associative algebras within the framework of Nonstandard Analysis. By decomposing each algebra in A^2 as sum of a Jordan algebra and a Lie algebra, we calculate the…
This study introduces an iterative Bayesian Robbins--Monro (IBRM) sequence, which unites the classical Robbins--Monro sequence with statistical estimation for faster root-finding under noisy observations. Although the standard…
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;…
In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
Most of the successful and predominant methods for bilingual lexicon induction (BLI) are mapping-based, where a linear mapping function is learned with the assumption that the word embedding spaces of different languages exhibit similar…
Neural abstractive summarization methods often require large quantities of labeled training data. However, labeling large amounts of summarization data is often prohibitive due to time, financial, and expertise constraints, which has…
In order to apply nonstandard methods to questions of algebraic geometry we continue our investigation from "Enlargements of categories" (Theory Appl. Categ. 14 (2005), No. 16, 357--398) and show how important homotopical constructions…
Proprietary and closed APIs are becoming increasingly common to process natural language, and are impacting the practical applications of natural language processing, including few-shot classification. Few-shot classification involves…
In this chapter we present an overview of the main ideas and methods in the fractional integration and cointegration literature. We do not attempt to give a complete survey of this enormous literature, but rather a more introductory…
We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a…
In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important…
With text analysis tools becoming increasingly sophisticated over the last decade, researchers now face a decision of whether to use state-of-the-art models that provide high performance but that can be highly opaque in their operations and…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
Evaluations are critical for understanding the capabilities of large language models (LLMs). Fundamentally, evaluations are experiments; but the literature on evaluations has largely ignored the literature from other sciences on experiment…
The ``Painlev\'e analysis'' is quite often perceived as a collection of tricks reserved to experts. The aim of this course is to demonstrate the contrary and to unveil the simplicity and the beauty of a subject which is in fact the theory…
These lectures are a brief introduction to supersymmetry.
This paper reports on application of bootstrap nonlinear regression method to a design of an experiment dataset with fewer experimental runs. Design with desired properties was augmented and verified using graphical techniques. The…