Related papers: On $p$-adic Classification

Given a prime number $p$, the study of divisibility properties of a sequence $c(n)$ has two contending approaches: $p$-adic valuations and superconcongruences. The former searches for the highest power of $p$ dividing $c(n)$, for each $n$;…

By imposing conditions upon the index of a self-centralizing subgroup of a group, and upon the index of the center of the group, we are able to classify the Chermak-Delgado lattice of the group. This is our main result. We use this result…

This study concentrates on clustering problems and aims to find compact clusters that are informative regarding the outcome variable. The main goal is partitioning data points so that observations in each cluster are similar and the outcome…

While substantial research has been devoted to optimizing model performance, convergence rates, and communication efficiency, the energy implications of federated learning (FL) within Artificial Intelligence of Things (AIoT) scenarios are…

In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the…

Let $p$ be a prime. We discuss methods of solution of congruences modulo $p^n$ using $p$-adic numbers; these methods are similar to computations with real numbers (local methods). Examples of relations between local and global methods are…

In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…

We consider constraint-based methods for causal structure learning, such as the PC-, FCI-, RFCI- and CCD- algorithms (Spirtes et al. (2000, 1993), Richardson (1996), Colombo et al. (2012), Claassen et al. (2013)). The first step of all…

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the…

This article discusses variants of Weber's class number problem in the spirit of arithmetic topology to connect the results of Sinnott--Kisilevsky and Kionke. Let $p$ be a prime number. We first prove the $p$-adic convergence of class…

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…

Majorly classical Active Learning (AL) approach usually uses statistical theory such as entropy and margin to measure instance utility, however it fails to capture the data distribution information contained in the unlabeled data. This can…

The aim of this paper is to prove conjectures concerning $p$-adic valuations of Stirling numbers of the second kind $S(n,k)$, $n,k\in\mathbb{N}_+$, stated by Amdeberhan, Manna and Moll and Berrizbeitia et al., where $p$ is a prime number.…

Machine learning interatomic potentials (MLIPs) provide an effective approach for accurately and efficiently modeling atomic interactions, expanding the capabilities of atomistic simulations to complex systems. However, a priori feature…

In diverse fields ranging from finance to omics, it is increasingly common that data is distributed and with multiple individual sources (referred to as ``clients'' in some studies). Integrating raw data, although powerful, is often not…

In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…

Model-based clustering is a technique widely used to group a collection of units into mutually exclusive groups. There are, however, situations in which an observation could in principle belong to more than one cluster. In the context of…

Traditional clustering methods often perform clustering with low-level indiscriminative representations and ignore relationships between patterns, resulting in slight achievements in the era of deep learning. To handle this problem, we…

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…

We present a clustering method and provide a theoretical analysis and an explanation to a phenomenon encountered in the applied statistical literature since the 1990's. This phenomenon is the natural adaptability of the order when using a…