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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…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

Gaussian Processes (GPs) provide a convenient framework for specifying function-space priors, making them a natural choice for modeling uncertainty. In contrast, Bayesian Neural Networks (BNNs) offer greater scalability and extendability…

Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…

Bayesian optimization (BO) has become a popular strategy for global optimization of expensive real-world functions. Contrary to a common expectation that BO is suited to optimizing black-box functions, it actually requires domain knowledge…

We propose a network structure discovery model for continuous observations that generalizes linear causal models by incorporating a Gaussian process (GP) prior on a network-independent component, and random sparsity and weight matrices as…

Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…

Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good…

Sparse regression problems, where the goal is to identify a small set of relevant predictors, often require modeling not only main effects but also meaningful interactions through other variables. While the pliable lasso has emerged as a…

Deep learning techniques play an increasingly important role in industrial and research environments due to their outstanding results. However, the large number of hyper-parameters to be set may lead to errors if they are set manually. The…

We develop a novel full-Bayesian approach for multiple correlated precision matrices, called multiple Graphical Horseshoe (mGHS). The proposed approach relies on a novel multivariate shrinkage prior based on the Horseshoe prior that borrows…

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…

We address the problem of semi-supervised learning in relational networks, networks in which nodes are entities and links are the relationships or interactions between them. Typically this problem is confounded with the problem of…

Recent CNN-based methods for image deraining have achieved excellent performance in terms of reconstruction error as well as visual quality. However, these methods are limited in the sense that they can be trained only on fully labeled…

We consider the problem of estimation and structure learning of high dimensional signals via a normal sequence model, where the underlying parameter vector is piecewise constant, or has a block structure. We develop a Bayesian fusion…

We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates…

Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…

Generative adversarial networks (GANs) can implicitly learn rich distributions over images, audio, and data which are hard to model with an explicit likelihood. We present a practical Bayesian formulation for unsupervised and…

Sparse modeling for signal processing and machine learning has been at the focus of scientific research for over two decades. Among others, supervised sparsity-aware learning comprises two major paths paved by: a) discriminative methods and…