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Recent years have witnessed strong empirical performance of over-parameterized neural networks on various tasks and many advances in the theory, e.g. the universal approximation and provable convergence to global minimum. In this paper, we…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

We study Bayesian hypernetworks: a framework for approximate Bayesian inference in neural networks. A Bayesian hypernetwork $\h$ is a neural network which learns to transform a simple noise distribution, $p(\vec\epsilon) = \N(\vec 0,\mat…

The aim of this work is to enable inference of deep networks that retain high accuracy for the least possible model complexity, with the latter deduced from the data during inference. To this end, we revisit deep networks that comprise…

In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and…

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…

The goal of this thesis is to develop the optimisation and generalisation theoretic foundations of learning in artificial neural networks. On optimisation, a new theoretical framework is proposed for deriving architecture-dependent…

Progress in neuroscience has provided unprecedented opportunities to advance our understanding of brain alterations and their correspondence to phenotypic profiles. With data collected from various imaging techniques, studies have…

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…

Neural nets have become popular to accelerate parameter inferences, especially for the upcoming generation of galaxy surveys in cosmology. As neural nets are approximative by nature, a recurrent question has been how to propagate the neural…

Bayesian networks are powerful statistical models to study the probabilistic relationships among set random variables with major applications in disease modeling and prediction. Here, we propose a continuous time Bayesian network with…

Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…

Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…

Neural networks have achieved remarkable performance across various problem domains, but their widespread applicability is hindered by inherent limitations such as overconfidence in predictions, lack of interpretability, and vulnerability…

Directed networks are conveniently represented as graphs in which ordered edges encode interactions between vertices. Despite their wide availability, there is a shortage of statistical models amenable for inference, specially when…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of…

Differential Networks (DNs), tools that encapsulate interactions within intricate systems, are brought under the Bayesian lens in this research. A novel na{\i}ve Bayesian adaptive graphical elastic net (BAE) prior is introduced to estimate…

One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…