Related papers: Union-Free Generic Depth for Non-Standard Data
Graph condensation (GC), which reduces the size of a large-scale graph by synthesizing a small-scale condensed graph as its substitution, has benefited various graph learning tasks. However, existing GC methods rely on centralized data…
In traditional thermodynamical and statistical-mechanical approaches one has (some) detailed knowledge of the principles governing the microdynamics of a system. However in many instances we may not have a Hamiltonian or good information…
Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…
Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…
Standard datasets are frequently used to train and evaluate Machine Learning models. However, the assumed standardness of these datasets leads to a lack of in-depth discussion on how their labels match the derived categories for the…
This work is done as part of a master's thesis project. The increase in the volume of data has given rise to various issues related to the collection, storage, analysis and exploitation of these data in order to create an added value. In…
The development of data-driven approaches for solving differential equations has been followed by a plethora of applications in science and engineering across a multitude of disciplines and remains a central focus of active scientific…
Graph neural networks (GNNs) achieve strong performance on relational data, but real-world graphs are often distributed across organizations that cannot share raw data due to privacy and policy constraints. Existing federated GNN methods…
We define a new category of non-archimedean analytic spaces over a complete discretely valued field, which we call uniformly rigid. It extends the category of rigid spaces, and it can be described in terms of bounded functions on products…
Graph data are ubiquitous in the real world. Graph learning (GL) tries to mine and analyze graph data so that valuable information can be discovered. Existing GL methods are designed for centralized scenarios. However, in practical…
In this article, we expand upon the concepts introduced by David Spivak about the relationship between the category $\mathbf{UM}$ of uber metric spaces and the category $\mathbf{sFuz}$ of fuzzy simplicial sets. We show that fuzzy simplicial…
Graph foundation models have recently attracted significant attention due to its strong generalizability. Although existing methods resort to language models to learn unified semantic representations across domains, they disregard the…
As a mathematically rigorous framework that has amassed a rich theoretical literature, differential privacy is considered by many experts to be the gold standard for privacy-preserving data analysis. Others argue that while differential…
Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…
How to tackle non-iid data is a crucial topic in federated learning. This challenging problem not only affects training process, but also harms performance of clients not participating in training. Existing literature mainly focuses on…
As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional…
Anomaly detection, finding patterns that substantially deviate from those seen previously, is one of the fundamental problems of artificial intelligence. Recently, classification-based methods were shown to achieve superior results on this…
We consider the problem of estimating the difference between two functional undirected graphical models with shared structures. In many applications, data are naturally regarded as high-dimensional random function vectors rather than…
In systems biology, it is becoming increasingly common to measure biochemical entities at different levels of the same biological system. Hence, data fusion problems are abundant in the life sciences. With the availability of a multitude of…
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…