Related papers: Sheaves as a Framework for Understanding and Inter…

As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle…

Identification of input data points relevant for the classifier (i.e. serve as the support vector) has recently spurred the interest of researchers for both interpretability as well as dataset debugging. This paper presents an in-depth…

Sheaves are mathematical objects consisting of a base which constitutes a topological space and the data associated with each open set thereof, e.g. continuous functions defined on the open sets. Sheaves have originally been used in…

Deep learning has become popular because of its potential to achieve high accuracy in prediction tasks. However, accuracy is not always the only goal of statistical modelling, especially for models developed as part of scientific research.…

An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…

Human vision greatly benefits from the information about sizes of objects. The role of size in several visual reasoning tasks has been thoroughly explored in human perception and cognition. However, the impact of the information about sizes…

Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and…

In healthcare, making the best possible predictions with complex models (e.g., neural networks, ensembles/stacks of different models) can impact patient welfare. In order to make these complex models explainable, we present DeepSHAP for…

In the present work, we describe a framework for modeling how models can be built that integrates concepts and methods from a wide range of fields. The information schism between the real-world and that which can be gathered and considered…

We propose that the sheaf condition on a presheaf of design spaces provides a mathematical model for multi-view consistency in the architecture of cyber-physical systems (CPS). In model-based systems engineering, multiple engineering views…

The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment…

Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…

Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global…

In this paper, we identify some categorical structures in which one can model predicative formal systems: in other words, predicative analogues of the notion of a topos, with the aim of using sheaf models to interprete predicative formal…

Estimating feature importance is a significant aspect of explaining data-based models. Besides explaining the model itself, an equally relevant question is which features are important in the underlying data generating process. We present a…

Deep Learning models tend to learn correlations of patterns on huge datasets. The bigger these systems are, the more complex are the phenomena they can detect, and the more data they need for this. The use of Artificial Intelligence (AI) is…

Machine learning algorithms often assume that training samples are independent. When data points are connected by a network, the induced dependency between samples is both a challenge, reducing effective sample size, and an opportunity to…

In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the…

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…