Related papers: Probabilistic Graphical Models: A Concise Tutorial

Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…

We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…

Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…

A variety of real-world tasks involve the classification of images into pre-determined categories. Designing image classification algorithms that exhibit robustness to acquisition noise and image distortions, particularly when the available…

Graphs are common mathematical structures that are visual and intuitive. They constitute a natural and seamless way for system modelling in science, engineering and beyond, including computer science, biology, business process modelling,…

Graphs are ubiquitous in encoding relational information of real-world objects in many domains. Graph generation, whose purpose is to generate new graphs from a distribution similar to the observed graphs, has received increasing attention…

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…

In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…

Recently, several methods have leveraged deep generative modeling to produce example-based explanations of image classifiers. Despite producing visually stunning results, these methods are largely disconnected from classical explainability…

We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…

Graph Neural Networks (GNNs), neural network architectures targeted to learning representations of graphs, have become a popular learning model for prediction tasks on nodes, graphs and configurations of points, with wide success in…

We introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of…

We propose probabilistic task modelling -- a generative probabilistic model for collections of tasks used in meta-learning. The proposed model combines variational auto-encoding and latent Dirichlet allocation to model each task as a…

Particle physics is a branch of science aiming at discovering the fundamental laws of matter and forces. Graph neural networks are trainable functions which operate on graphs---sets of elements and their pairwise relations---and are a…

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on…

We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For…

Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…