Related papers: The Complexity of Bayesian Network Learning: Revis…

Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for…

Deep Neural Networks can generalize despite being significantly overparametrized. Recent research has tried to examine this phenomenon from various view points and to provide bounds on the generalization error or measures predictive of the…

We showed how to use trained neural networks to perform Bayesian reasoning in order to solve tasks outside their initial scope. Deep generative models provide prior knowledge, and classification/regression networks impose constraints. The…

The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are…

This dissertation investigates integer linear programming (ILP) formulation of Bayesian Network structure learning problem. We review the definition and key properties of Bayesian network and explain score metrics used to measure how well…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and…

In practice it is often found that large over-parameterized neural networks generalize better than their smaller counterparts, an observation that appears to conflict with classical notions of function complexity, which typically favor…

Bayesian network (BN) structure discovery algorithms typically either make assumptions about the sparsity of the true underlying network, or are limited by computational constraints to networks with a small number of variables. While these…

We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:…

Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…

Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…

Bayesian nonparametric models offer a flexible and powerful framework for statistical model selection, enabling the adaptation of model complexity to the intricacies of diverse datasets. This survey intends to delve into the significance of…

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the…

Conventional Bayesian Neural Networks (BNNs) are unable to leverage unlabelled data to improve their predictions. To overcome this limitation, we introduce Self-Supervised Bayesian Neural Networks, which use unlabelled data to learn models…

Semi-supervised learning on real-world graphs is frequently challenged by heterophily, where the observed graph is unreliable or label-disassortative. Many existing graph neural networks either rely on a fixed adjacency structure or attempt…

Recent advancements in deep learning have been primarily driven by the use of large models trained on increasingly vast datasets. While neural scaling laws have emerged to predict network performance given a specific level of computational…

A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…

interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest.…