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We consider the general problem of modeling temporal data with long-range dependencies, wherein new observations are fully or partially predictable based on temporally-distant, past observations. A sufficiently powerful temporal model…

Graph Convolutional Network (GCN) has experienced great success in graph analysis tasks. It works by smoothing the node features across the graph. The current GCN models overwhelmingly assume that the node feature information is complete.…

Artificial Intelligence (AI) has recently shown its capabilities for almost every field of life. Machine Learning, which is a subset of AI, is a `HOT' topic for researchers. Machine Learning outperforms other classical forecasting…

Conformal prediction has become increasingly popular for quantifying the uncertainty associated with machine learning models. Recent work in graph uncertainty quantification has built upon this approach for conformal graph prediction. The…

Graph Convolutional Neural Networks (GCNs) has been generally accepted to be an effective tool for node representations learning. An interesting way to understand GCNs is to think of them as a message passing mechanism where each node…

Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the…

Fuzzy systems (FSs) have enjoyed wide applications in various fields, including pattern recognition, intelligent control, data mining and bioinformatics, which is attributed to the strong interpretation and learning ability. In traditional…

The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true…

Contrastive divergence (CD) is a promising method of inference in high dimensional distributions with intractable normalizing constants, however, the theoretical foundations justifying its use are somewhat shaky. This document proposes a…

The dependency of the generalization error of neural networks on model and dataset size is of critical importance both in practice and for understanding the theory of neural networks. Nevertheless, the functional form of this dependency…

The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…

Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…

Graph Neural Networks (GNNs) are powerful models that can manage complex data sources and their interconnection links. One of GNNs' main drawbacks is their lack of interpretability, which limits their application in sensitive fields. In…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

Graph Foundation Models (GFMs) are emerging as a significant research topic in the graph domain, aiming to develop graph models trained on extensive and diverse data to enhance their applicability across various tasks and domains.…

Complex network theory has been applied to solving practical problems from different domains. In this paper, we present a general framework for complex network applications. The keys of a successful application are a thorough understanding…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

Motivated by the Model-Based Design process for Cyber-Physical Systems, we consider issues in conformance testing of systems. Conformance is a quantitative notion of similarity between the output trajectories of systems, which considers…

Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…

By interpreting a traffic scene as a graph of interacting vehicles, we gain a flexible abstract representation which allows us to apply Graph Neural Network (GNN) models for traffic prediction. These naturally take interaction between…