Related papers: Customised Structural Elicitation
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, model classes which place equality restrictions on concentrations or partial correlations have previously…
A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand,…
In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A…
Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…
We investigate the application of classification techniques to utility elicitation. In a decision problem, two sets of parameters must generally be elicited: the probabilities and the utilities. While the prior and conditional probabilities…
Learning a Bayesian network structure from data is an NP-hard problem and thus exact algorithms are feasible only for small data sets. Therefore, network structures for larger networks are usually learned with various heuristics. Another…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to…
Despite recent advances in automated machine learning, model selection is still a complex and computationally intensive process. For Gaussian processes (GPs), selecting the kernel is a crucial task, often done manually by the expert.…
Supervised classification is one of the most ubiquitous tasks in machine learning. Generative classifiers based on Bayesian networks are often used because of their interpretability and competitive accuracy. The widely used naive and TAN…
Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the…
We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…
Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying…
An efficient structural identifiability analysis algorithm is developed in this study for a broad range of network structures. The proposed method adopts the Wright's path coefficient method to generate identifiability equations in forms of…
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables.…
The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…
We propose a novel method for modeling data by using structural models based on economic theory as regularizers for statistical models. We show that even if a structural model is misspecified, as long as it is informative about the…