Related papers: Practically Perfect
We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…
In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…
Safe and reliable disclosure of information from confidential data is a challenging statistical problem. A common approach considers the generation of synthetic data, to be disclosed instead of the original data. Efficient approaches ought…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the "true" solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and…
In this short paper, following the most recent advances in complex network theory, a new approach to number theory with potential applications to other fields is proposed. The model by Garcia-Perez, Serrano and Boguna, introduces an…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…
Bayesian interpretations of neural processing require that biological mechanisms represent and operate upon probability distributions in accordance with Bayes' theorem. Many have speculated that synaptic failure constitutes a mechanism of…
We characterize some asymptotic properties of edge exchangeable random graphs in terms of the measure used to generate them. In particular, we give a necessary and sufficient condition for eventual forever connectedness, a sufficient…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
We are living in the big data era, as current technologies and networks allow for the easy and routine collection of data sets in different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive for…
Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…
We develop the necessary theory in computational algebraic geometry to place Bayesian networks into the realm of algebraic statistics. We present an algebra{statistics dictionary focused on statistical modeling. In particular, we link the…
We describe expectation propagation for approximate inference in dynamic Bayesian networks as a natural extension of Pearl s exact belief propagation.Expectation propagation IS a greedy algorithm, converges IN many practical cases, but NOT…
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…
Bayesian neural networks attempt to combine the strong predictive performance of neural networks with formal quantification of uncertainty associated with the predictive output in the Bayesian framework. However, it remains unclear how to…
Bayesian inference can quantify uncertainty in the predictions of neural networks using posterior distributions for model parameters and network output. By looking at these posterior distributions, one can separate the origin of uncertainty…
Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact…