Related papers: A Characterization of the Dirichlet Distribution w…
As machine learning systems get widely adopted for high-stake decisions, quantifying uncertainty over predictions becomes crucial. While modern neural networks are making remarkable gains in terms of predictive accuracy, characterizing…
Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…
Mechanistic network models can capture salient characteristics of empirical networks using a small set of domain-specific, interpretable mechanisms. Yet inference remains challenging because the likelihood is often intractable. We show…
Humans can learn languages from remarkably little experience. Developing computational models that explain this ability has been a major challenge in cognitive science. Bayesian models that build in strong inductive biases - factors that…
Modeling the distribution of natural images is a landmark problem in unsupervised learning. This task requires an image model that is at once expressive, tractable and scalable. We present a deep neural network that sequentially predicts…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise.…
In this paper, we first develop a new family of conjugate prior distributions for the cell parameters of discrete graphical models Markov with respect to a set P of moral directed acyclic graphs with skeleton a given decomposable graph G.…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…
Variational autoencoders and Helmholtz machines use a recognition network (encoder) to approximate the posterior distribution of a generative model (decoder). In this paper we study the necessary and sufficient properties of a recognition…
In open set learning, a model must be able to generalize to novel classes when it encounters a sample that does not belong to any of the classes it has seen before. Open set learning poses a realistic learning scenario that is receiving…
Evidential Deep Learning (EDL) is a popular framework for uncertainty-aware classification that models predictive uncertainty via Dirichlet distributions parameterized by neural networks. Despite its popularity, its theoretical foundations…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
We present a growing dimension asymptotic formalism. The perspective in this paper is classification theory and we show that it can accommodate probabilistic networks classifiers, including naive Bayes model and its augmented version. When…
Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements…
It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to…
Incorporating domain knowledge into the modeling process is an effective way to improve learning accuracy. However, as it is provided by humans, domain knowledge can only be specified with some degree of uncertainty. We propose to…