arXiv subjects

Lucas Vogels

Publications and source records attributed to Lucas Vogels.

4 recordsLinked to original sources

arXiv2026

Multiple Jump MCMC: A Scalable Algorithm for Bayesian Inference on Binary Model Spaces

This article considers Bayesian model inference on binary model spaces. Binary model spaces are used by a large class of models, including graphical models, variable selection, mixture distributions, and decision trees. Traditional strategies in this field, such as reversible jump or birth-death MCMC algorithms, are still popular, despite suffering from a slow exploration of the model space. In this article, we propose an alternative: the Multiple Jump MCMC algorithm. The algorithm is simple, rejection-free, and remarkably fast. When applied to undirected Gaussian graphical models, it is 100 to 200 times faster than the state-of-the-art, solving models with $500,000$ parameters in less than a minute. We provide theorems showing how accurately our algorithm targets the posterior, and we show how to apply our framework to Gaussian graphical models, Ising models, and variable selection, but note that it applies to most Bayesian posterior inference on binary model spaces.

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arXiv2024

Modeling Alzheimer's Disease: Bayesian Copula Graphical Model from Demographic, Cognitive, and Neuroimaging Data

The early detection of Alzheimer's disease (AD) requires an understanding of the relationships between a wide range of features. Conditional independencies and partial correlations are suitable measures for these relationships, because they can identify the effects of confounding and mediating variables. This article presents a Bayesian approach to Gaussian copula graphical models (GCGMs) in order to estimate these conditional dependencies and partial correlations. This approach has two key advantages. First, it includes binary, discrete, and continuous variables. Second, it quantifies the uncertainty of the estimates. Despite these advantages, Bayesian GCGMs have not been applied to AD research yet. In this study, we design a GCGM to find the conditional dependencies and partial correlations among brain-region specific gray matter volume and glucose uptake, amyloid-beta levels, demographic information, and cognitive test scores. We applied our model to 1022 participants, including healthy and cognitively impaired, across different stages of AD. We found that aging reduces cognition through three indirect pathways: hippocampal volume loss, posterior cingulate cortex (PCC) volume loss, and amyloid-beta accumulation. We found a positive partial correlation between being woman and cognition, but also discovered four indirect pathways that dampen this association in women: lower hippocampal volume, lower PCC volume, more amyloid-beta accumulation, and less education. We found limited relations between brain-region specific glucose uptake and cognition, but discovered that the hippocampus and PCC volumes are related to cognition. These results show that the use of GCGMs offers valuable insights into AD pathogenesis.

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arXiv2023

Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison

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 methods can measure the uncertainty of conditional relationships and include prior information. However, frequentist methods are often preferred due to the computational burden of the Bayesian approach. Over the last decade, Bayesian methods have seen substantial improvements, with some now capable of generating accurate estimates of graphs up to a thousand variables in mere minutes. Despite these advancements, a comprehensive review or empirical comparison of all recent methods has not been conducted. This paper delves into a wide spectrum of Bayesian approaches used for structure learning and evaluates their efficacy through a comprehensive simulation study. We also demonstrate how to apply Bayesian structure learning to a real-world data set and provide directions for future research. This study gives an exhaustive overview of this dynamic field for newcomers, practitioners, and experts.

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arXiv2023

Scalable Bayesian Structure Learning for Gaussian Graphical Models Using Marginal Pseudo-likelihood

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly exploring graph structures and precision matrices. To address this challenge, we perform inference directly on the graph by integrating out the precision matrix. We adopt a marginal pseudo-likelihood approach, eliminating the need to compute intractable normalizing constants and perform computationally intensive precision matrix sampling. Building on this framework, we develop continuous-time (birth-death) and discrete-time (reversible jump) Markov chain Monte Carlo (MCMC) algorithms that efficiently explore the posterior over graph space. We establish theoretical guarantees for posterior contraction, convergence, and graph selection consistency. The algorithms scale to large graph spaces, enabling parallel exploration for graphs with over 1,000 nodes, while providing uncertainty quantification and supporting flexible prior specification over the graph space. Extensive simulations show substantial computational gains over state-of-the-art Bayesian approaches without sacrificing graph recovery accuracy. Applications to human and mouse gene expression datasets demonstrate the ability of our approach to recover biologically meaningful structures and quantify uncertainty in complex networks. An implementation is available in the R package BDgraph.

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