Related papers: A New Characterization of Probabilities in Bayesia…
Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link…
The clique tree algorithm is the standard method for doing inference in Bayesian networks. It works by manipulating clique potentials - distributions over the variables in a clique. While this approach works well for many networks, it is…
We present a Bayesian nonparametric Poisson factorization model for modeling network data with an unknown and potentially growing number of overlapping communities. The construction is based on completely random measures and allows the…
We study the extent to which wide neural networks may be approximated by Gaussian processes when initialized with random weights. It is a well-established fact that as the width of a network goes to infinity, its law converges to that of a…
Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…
Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…
Recent advances in computing power and the potential to make more realistic assumptions due to increased flexibility have led to the increased prevalence of simulation models in economics. While models of this class, and particularly…
Quasi-Bayesian theory uses convex sets of probability distributions and expected loss to represent preferences about plans. The theory focuses on decision robustness, i.e., the extent to which plans are affected by deviations in subjective…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
Bayesian networks (BNs) are graphical \emph{first-order} probabilistic models that allow for a compact representation of large probability distributions, and for efficient inference, both exact and approximate. We introduce a…
Consider a population of individuals and a network that encodes social connections among them. We are interested in making inference on finite population and super-population estimands that are a function of both individuals' responses and…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
As the information available to lay users through autonomous data sources continues to increase, mediators become important to ensure that the wealth of information available is tapped effectively. A key challenge that these information…
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…
Humans and other animals behave as if we perform fast Bayesian inference underlying decisions and movement control given uncertain sense data. Here we show that a biophysically realistic model of the subthreshold membrane potential of a…
We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. We further demonstrate that this finding allows us to make meaningful estimates of the model uncertainty using…
In this work we make an attempt to understand social networks from a mathematical viewpoint. In the first instance we consider a network where each node representing an individual can connect with a neighbouring node with a certain…
We introduce an information theoretic criterion for Bayesian network structure learning which we call quotient normalized maximum likelihood (qNML). In contrast to the closely related factorized normalized maximum likelihood criterion, qNML…
We propose a general method for distributed Bayesian model choice, using the marginal likelihood, where a data set is split in non-overlapping subsets. These subsets are only accessed locally by individual workers and no data is shared…