Related papers: Graphical Models for Discrete and Continuous Data

We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by…

This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…

Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent…

The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…

Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…

Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…

Causal discovery from observational data is challenging, especially with large datasets and complex relationships. Traditional methods often struggle with scalability and capturing global structural information. To overcome these…

Gaussian graphical models are often used to infer gene networks based on microarray expression data. Many scientists, however, have begun using high-throughput sequencing technologies to measure gene expression. As the resulting…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…

We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is…

Associated to each graph G is a Gaussian graphical model. Such models are often used in high-dimensional settings, i.e. where there are relatively few data points compared to the number of variables. The maximum likelihood threshold of a…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…

We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…

Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…

We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a…

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…