Related papers: Short introduction to Nonstandard Analysis
Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin, an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical…
This paper presents an embedding-based approach to detecting variation without relying on prior normalisation or predefined variant lists. The method trains subword embeddings on raw text and groups related forms through combined cosine and…
The program of studying general nonlinear Markov processes was put forward in V. N. Kolokoltsov "Nonlinear Markov Semigroups and Interacting L\'evy Type Processes" (Journ. Stat. Physics 126:3 (2007), 585-642), and was developed by the…
In this short review main issues related to the non-Abelian Stokes theorem have been addressed. The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral…
Autoregressive Large Language Models (LLMs) demonstrate exceptional performance in language understanding and generation. However, their application in text embedding tasks has been relatively slow, along with the analysis of their semantic…
Let $\mathcal{L}$ be a first-order two-sorted language. Let $S$ be some fixed structure. A standard structure is an $\mathcal{L}$-structure of the form $(M,S)$, where $M$ is arbitrary. When $S$ is a compact topological space (and…
Multimodal Language Analysis is a demanding area of research, since it is associated with two requirements: combining different modalities and capturing temporal information. During the last years, several works have been proposed in the…
Generalized linear models are often misspecified due to overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood methods for testing in misspecified models often do not provide satisfactory type-I error…
The basic formalism of a novel scale invarinat nonlinear analysis is presented. A few analytic number theoretic results are derived independent of standard approaches.
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
We determine sufficient structure for an elementary topos to emulate E. Nelson's Internal Set Theory in its internal language, and show that any topos satisfying the internal axiom of choice occurs as a universe of standard objects and…
Nonlinear mixed effects models have become a standard platform for analysis when data is in the form of continuous and repeated measurements of subjects from a population of interest, while temporal profiles of subjects commonly follow a…
It has been widely believed for half a century that there will never exist a nonlinear theory of generalized functions, in any mathematical context. The aim of this text is to show the converse is the case and invite the reader to…
Anomaly detection or more generally outliers detection is one of the most popular and challenging subject in theoretical and applied machine learning. The main challenge is that in general we have access to very few labeled data or no…
Music Structure Analysis (MSA) aims to uncover the high-level organization of musical pieces. State-of-the-art methods are often based on supervised deep learning, but these methods are bottlenecked by the need for heavily annotated data…
The paper overviews and investigates several nonparametric methods of estimating covariograms. It provides a unified approach and notation to compare the main approaches used in applied research. The primary focus is on methods that utilise…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
Recently, the second author, Briseid and Safarik introduced nonstandard Dialectica, a functional interpretation that is capable of eliminating instances of familiar principles of nonstandard arithmetic - including overspill, underspill, and…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
Semi-supervised learning, which has emerged from the beginning of this century, is a new type of learning method between traditional supervised learning and unsupervised learning. The main idea of semi-supervised learning is to introduce…