Related papers: The Label Algorithm For Irreducible Decomposition …

This paper attempts multi-label classification by extending the idea of independent binary classification models for each output label, and exploring how the inherent correlation between output labels can be used to improve predictions.…

This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…

In multi-label classification, where the evaluation of predictions is less straightforward than in single-label classification, various meaningful, though different, loss functions have been proposed. Ideally, the learning algorithm should…

Many practical applications of AI in medicine consist of semi-supervised discovery: The investigator aims to identify features of interest at a resolution more fine-grained than that of the available human labels. This is often the scenario…

This is a resubmission of preprint 9401008 , which has some TeXnical errors introduced by the "reform" procedure (designed to avoid precisely these problems!). The original can be formatted by editing out the messages "%% following line…

Despite the rich literature on machine learning fairness, relatively little attention has been paid to remediating complex systems, where the final prediction is the combination of multiple classifiers and where multiple groups are present.…

The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [19]. The exposition is…

Multi-label class-incremental learning (MLCIL) is essential for real-world multi-label applications, allowing models to learn new labels while retaining previously learned knowledge continuously. However, recent MLCIL approaches can only…

We extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, we present an additive…

The aim of Active Learning is to select the most informative samples from an unlabelled set of data. This is useful in cases where the amount of data is large and labelling is expensive, such as in machine vision or medical imaging. Two…

We express the multigraded Betti numbers of an arbitrary monomial ideal in terms of the multigraded Betti numbers of two basic classes of ideals. This decompo- sition has multiple applications. In some concrete cases, we use it to construct…

Semi-supervised learning is a powerful technique for leveraging unlabeled data to improve machine learning models, but it can be affected by the presence of ``informative'' labels, which occur when some classes are more likely to be labeled…

Deep neural networks are highly susceptible to overfitting noisy labels, which leads to degraded performance. Existing methods address this issue by employing manually defined criteria, aiming to achieve optimal partitioning in each…

Multi-label classification is becoming increasingly ubiquitous, but not much attention has been paid to interpretability. In this paper, we develop a multi-label classifier that can be represented as a concise set of simple "if-then" rules,…

\textit{Multiple Instance Learning} (MIL) is concerned with learning from bags of instances, where only bag labels are given and instance labels are unknown. Existent approaches in this field were mainly designed for the bag-level label…

In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…

Let $\mathcal{A}$ be an abelian variety over a number field, with a good reduction at a prime ideal containing a prime number $p$. Denote by ${\rm A}$ an abelian variety over a finite field of characteristic $p$, obtained by the reduction…

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This paper is concerned with list decoding of $2$-interleaved binary alternant codes. The principle of the proposed algorithm is based on a combination of a list decoding algorithm for (interleaved) Reed-Solomon codes and an algorithm for…

Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing "mesoprimary decompositions" determined by their underlying monoid congruences. Monoid congruences (and…