Related papers: Gaussian Process Networks
In this paper we extend existing Bayesian methods for variable selection in Gaussian process regression, to select both the regression terms and the active covariates in the spatial correlation structure. We then use the estimated posterior…
While much work has explored probabilistic graphical models for independent data, less attention has been paid to time series. The goal in this setting is to determine conditional independence relations between entire time series, which for…
Structural learning of directed acyclic graphs (DAGs) or Bayesian networks has been studied extensively under the assumption that data are independent. We propose a new Gaussian DAG model for dependent data which assumes the observations…
Learning the structure of Bayesian networks from data provides insights into underlying processes and the causal relationships that generate the data, but its usefulness depends on the homogeneity of the data population, a condition often…
Bayesian neural networks (BNNs) have recently gained popularity due to their ability to quantify model uncertainty. However, specifying a prior for BNNs that captures relevant domain knowledge is often extremely challenging. In this work,…
In this paper, we study the problem of structure learning for Bayesian networks in which nodes take discrete values. The problem is NP-hard in general but we show that under certain conditions we can recover the true structure of a Bayesian…
Probabilistic circuits (PCs) are a prominent representation of probability distributions with tractable inference. While parameter learning in PCs is rigorously studied, structure learning is often more based on heuristics than on…
There is a brief description of the probabilistic causal graph model for representing, reasoning with, and learning causal structure using Bayesian networks. It is then argued that this model is closely related to how humans reason with and…
Accounting for the complexity of psychological theories requires methods that can predict not only changes in the means of latent variables -- such as personality factors, creativity, or intelligence -- but also changes in their variances.…
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…
In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
This study proposes the first Bayesian approach for learning high-dimensional linear Bayesian networks. The proposed approach iteratively estimates each element of the topological ordering from backward and its parent using the inverse of a…
Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…
Sum-product networks (SPNs) are flexible density estimators and have received significant attention due to their attractive inference properties. While parameter learning in SPNs is well developed, structure learning leaves something to be…
In Bayesian structure learning, we are interested in inferring a distribution over the directed acyclic graph (DAG) structure of Bayesian networks, from data. Defining such a distribution is very challenging, due to the combinatorially…
Bayesian networks are graphical models to represent the probabilistic relationships between variables in the Bayesian framework. The knowledge of all variables can be updated using new information about some of the variables. We show that…
We introduce a principled approach for unsupervised structure learning of deep neural networks. We propose a new interpretation for depth and inter-layer connectivity where conditional independencies in the input distribution are encoded…
Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…