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Mixtures of Unigrams are one of the simplest and most efficient tools for clustering textual data, as they assume that documents related to the same topic have similar distributions of terms, naturally described by Multinomials. When the…
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…
We introduce a novel exploratory technique, termed biarchetype analysis, which extends archetype analysis to simultaneously identify archetypes of both observations and features. This innovative unsupervised machine learning tool aims to…
The popularity of applying machine learning methods to computational linguistics problems has produced a large supply of trainable natural language processing systems. Most problems of interest have an array of off-the-shelf products or…
Numerous recent techniques for text style transfer characterize their approaches as variants of reinforcement learning and preference optimization. In this work, we consider the relationship between these approaches and a class of…
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
Although considerable effort has been dedicated to improving the solution to the hyperspectral unmixing problem, non-idealities such as complex radiation scattering and endmember variability negatively impact the performance of most…
Most of the world's digital data is currently encoded in a sequential form, and compression methods for sequences have been studied extensively. However, there are many types of non-sequential data for which good compression techniques are…
In a previous article, an `invariant method' to calculate monomial integrals over the U(n) group was introduced. In this paper, we study the more traditional group-theoretical method, and compare its strengths and weaknesses with those of…
Adaptive filters are at the core of many signal processing applications, ranging from acoustic noise supression to echo cancelation, array beamforming, channel equalization, to more recent sensor network applications in surveillance, target…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
A great many tools have been developed for supervised classification, ranging from early methods such as linear discriminant analysis through to modern developments such as neural networks and support vector machines. A large number of…
We are interested in generalizing part of the theory of ultrafilters on omega to larger cardinals. Here we set the scene for further investigations introducing properties of ultrafilters in strong sense dual to being normal.
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
This paper describes a method to find a connection between combinatorial identities and hypergeometric series with a number of examples. Combinatorial identities can often be written as hypergeometric series with unit argument. In a number…
Combinatorial Testing (CT) is a potentially powerful testing technique, whereas its failure revealing ability might be dramatically reduced if it fails to handle constraints in an adequate and efficient manner. To ensure the wider…
Understanding and interpreting how machine learning (ML) models make decisions have been a big challenge. While recent research has proposed various technical approaches to provide some clues as to how an ML model makes individual…
We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations $\mid_M$ and…
The aim of this paper is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. Recently, a number of nonstandard versions of Goedel's system T have been introduced ([2,9,12]), and it was shown in [26] that the…
Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing…