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This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…
This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
Uncertainty quantification is a crucial step of cosmological mass-mapping that is often ignored. Suggested methods are typically only approximate or make strong assumptions of Gaussianity of the shear field. Probabilistic sampling methods,…
Multilevel models (MLMs) are a central building block of the Bayesian workflow. They enable joint, interpretable modeling of data across hierarchical levels and provide a fully probabilistic quantification of uncertainty. Despite their…
A principled approach to characterize the hidden structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for…
Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…
Bayesian neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
Deep neural networks (DNNs) have achieved state-of-the-art performances in many important domains, including medical diagnosis, security, and autonomous driving. In these domains where safety is highly critical, an erroneous decision can…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…
The iterations of many first-order algorithms, when applied to minimizing common regularized regression functions, often resemble neural network layers with pre-specified weights. This observation has prompted the development of…
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…
Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…
We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Sparse Bayesian learning has promoted many effective frameworks for brain activity decoding, especially for the reconstruction of muscle activity. However, existing sparse Bayesian learning mainly employs Gaussian distribution as error…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…