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This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori…

The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and…

Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the…

We consider learning from labeled data collected across multiple environments, where the data distribution may vary across these environments. This problem is commonly approached from a causal perspective, seeking invariant representations…

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,…

Graph Laplacian learning, also known as network topology inference, is a problem of great interest to multiple communities. In Gaussian graphical models (GM), graph learning amounts to endowing covariance selection with the Laplacian…

Despite much research targeted at enabling conventional machine learning models to continually learn tasks and data distributions sequentially without forgetting the knowledge acquired, little effort has been devoted to account for more…

We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

Developments in deep generative models have allowed for tractable learning of high-dimensional data distributions. While the employed learning procedures typically assume that training data is drawn i.i.d. from the distribution of interest,…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

Trend filtering is a modern approach to nonparametric regression that is more adaptive to local smoothness than splines or similar basis procedures. Existing analyses of trend filtering focus on estimating a function corrupted by…

This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical…

We first consider the sequential detection of transient signals by generalizing the moving average chart to exponential family and study the false detection probability (FDP) and power of detection (POD) in the steady state. Then windowed…

Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can…

Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm…

We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…

Standard meta-learning for representation learning aims to find a common representation to be shared across multiple tasks. The effectiveness of these methods is often limited when the nuances of the tasks' distribution cannot be captured…

In emotion recognition, it is difficult to recognize human's emotional states using just a single modality. Besides, the annotation of physiological emotional data is particularly expensive. These two aspects make the building of effective…

Advances in neural variational inference have facilitated the learning of powerful directed graphical models with continuous latent variables, such as variational autoencoders. The hope is that such models will learn to represent rich,…