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Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many hardness results are known. In this paper we propose a provably polynomial-time algorithm…

We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks,…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

In this paper we propose a Bayesian method for estimating architectural parameters of neural networks, namely layer size and network depth. We do this by learning concrete distributions over these parameters. Our results show that regular…

In this article, we propose a new hypothesis testing method for directed acyclic graph (DAG). While there is a rich class of DAG estimation methods, there is a relative paucity of DAG inference solutions. Moreover, the existing methods…

Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such…

Continual Learning is a learning paradigm where learning systems are trained with sequential or streaming tasks. Two notable directions among the recent advances in continual learning with neural networks are ($i$) variational Bayes based…

We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial…

This paper proposes a new general approach based on Bayesian networks to model the human behaviour. This approach represents human behaviour with probabilistic cause-effect relations based on knowledge, but also with conditional…

The random dot product graph is a popular model for network data with extensions that accommodate dynamic (time-varying) networks. However, two significant deficiencies exist in the dynamic random dot product graph literature: (1) no…

Bayesian active learning relies on the precise quantification of predictive uncertainty to explore unknown function landscapes. While Gaussian process surrogates are the standard for such tasks, an underappreciated fact is that their…

Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this paper, we review different structures of deep directed generative models and…

Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to…

Uncertainty plays a key role in real-time machine learning. As a significant shift from standard deep networks, which does not consider any uncertainty formulation during its training or inference, Bayesian deep networks are being currently…

Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstrate the…

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…

Many biological networks include cyclic structures. In such cases, Bayesian networks (BNs), which must be acyclic, are not sound models for structure learning. Dynamic BNs can be used but require relatively large time series data. We…

We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and…