Related papers: Stochastic complexity of Bayesian networks
Bayesian sociality models provide a scalable and flexible alternative for network analysis, capturing degree heterogeneity through actor-specific parameters while mitigating the identifiability challenges of latent space models. This paper…
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…
Learning the structure of Bayesian networks from data is known to be a computationally challenging, NP-hard problem. The literature has long investigated how to perform structure learning from data containing large numbers of variables,…
Neural networks are powerful function approximators with tremendous potential in learning complex distributions. However, they are prone to overfitting on spurious patterns. Bayesian inference provides a principled way to regularize neural…
In this work we investigate the reasons why Batch Normalization (BN) improves the generalization performance of deep networks. We argue that one major reason, distinguishing it from data-independent normalization methods, is randomness of…
Despite its long history, Bayesian neural networks (BNNs) and variational training remain underused in practice: standard Gaussian posteriors misalign with network geometry, KL terms can be brittle in high dimensions, and implementations…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…
We show how to treat systematic uncertainties using Bayesian deep networks for regression. First, we analyze how these networks separately trace statistical and systematic uncertainties on the momenta of boosted top quarks forming fat jets.…
This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a…
This paper describes and discusses Bayesian Neural Network (BNN). The paper showcases a few different applications of them for classification and regression problems. BNNs are comprised of a Probabilistic Model and a Neural Network. The…
Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…
We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The…
Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and…
Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value…
Bayesian neural networks perform variational inference over the weights however calculation of the posterior distribution remains a challenge. Our work builds on variational inference techniques for bayesian neural networks using the…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…