Related papers: Are Bayesian networks typically faithful?
To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…
Quantifying uncertainty in neural networks is a highly relevant problem which is essential to many applications. The two predominant paradigms to tackle this task are Bayesian neural networks (BNNs) and deep ensembles. Despite some…
We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…
A discrete Bayesian network is a directed acyclic graph (DAG) consisting of categorical variables. Two popular approaches for DBN modeling include classification and nonparametric methods. However, both methods often require a large number…
It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise…
Max-linear Bayesian networks have emerged as highly applicable models for causal inference via extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian…
Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
Transmission line outage rates are fundamental to power system reliability analysis. Line outages are infrequent, occurring only about once a year, so outage data are limited. We propose a Bayesian hierarchical model that leverages line…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
A difficult task in modeling with Bayesian networks is the elicitation of numerical parameters of Bayesian networks. A large number of parameters is needed to specify a conditional probability table (CPT) that has a larger parent set. In…
Confidence estimates are often "detection-like" - driven by positive evidence in favour of a decision. This empirical observation has been interpreted as showing that human metacognition is limited by biases or heuristics. Here, we show…
Most empirical studies of complex networks do not return direct, error-free measurements of network structure. Instead, they typically rely on indirect measurements that are often error-prone and unreliable. A fundamental problem in…
We perform accurate numerical experiments with fully-connected (FC) one-hidden layer neural networks trained with a discretized Langevin dynamics on the MNIST and CIFAR10 datasets. Our goal is to empirically determine the regimes of…
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…
Bayesian Belief Networks (BBNs) are a powerful formalism for reasoning under uncertainty but bear some severe limitations: they require a large amount of information before any reasoning process can start, they have limited contradiction…
Bayesian networks are widely used to learn and reason about the dependence structure of discrete variables. However, they are only capable of formally encoding symmetric conditional independence, which in practice is often too strict to…
This paper presents a new approach to generate samples from conditional belief functions for a restricted but non trivial subset of conditional belief functions. It assumes the factorization (decomposition) of a belief function along a…
This article describes a robust algorithm to estimate a conditional probability density f(t|x) as a non-parametric smooth regression function. It is based on a neural network and the Bayesian interpretation of the network output as a…