Related papers: Spectral Bayesian Network Theory
In this study, a Bayesian Network (BN) is considered to represent a nuclear plant mechanical system degradation. It describes a causal representation of the phenomena involved in the degradation process. Inference from such a BN needs to…
In this report, we will be interested at Dynamic Bayesian Network (DBNs) as a model that tries to incorporate temporal dimension with uncertainty. We start with basics of DBN where we especially focus in Inference and Learning concepts and…
Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…
We introduce new geometric objects called spectral networks. Spectral networks are networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensional N=2 theories coupled to…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian belief networks. By imposing additional assumptions about the nature of the probabilistic models represented in the belief networks, we derive…
Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough…
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…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…
Neural networks have achieved remarkable performance across various problem domains, but their widespread applicability is hindered by inherent limitations such as overconfidence in predictions, lack of interpretability, and vulnerability…
In this work, we demonstrate the Empirical Bayes approach to learning a Dynamic Bayesian Network. By starting with several point estimates of structure and weights, we can use a data-driven prior to subsequently obtain a model to quantify…
This paper investigates two prominent probabilistic neural modeling paradigms: Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression. While BNNs incorporate epistemic uncertainty by…
We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks,…
The structure of a Bayesian network encodes most of the information about the probability distribution of the data, which is uniquely identified given some general distributional assumptions. Therefore it's important to study the…
Graphical models or networks describe the statistical dependence among multiple variables and are widely used in biology (e.g., gene regulatory networks). Under appropriate assumptions, directed edges may represent causal relationships. A…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
The goal of this brief pedagogical article is to show that Binary Decision Diagrams are a special kind of Bayesian Net. This observation is obvious to workers in these two fields, but it might not be too obvious to others.
Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using…
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…
Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this paper, we review different structures of deep directed generative models and…
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's…