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Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of…
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Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Causal inference in multivariate time series is challenging due to the fact that the sampling rate may not be as fast as the timescale of the causal interactions. In this context, we can view our observed series as a subsampled version of…
While inference-time scaling has significantly enhanced generative quality in large language and diffusion models, its application to vector-quantized (VQ) visual autoregressive modeling (VAR) remains unexplored. We introduce VAR-Scaling,…
Joint modeling of multiview graphs with a common set of nodes between views and auxiliary predictors is an essential, yet less explored, area in statistical methodology. Traditional approaches often treat graphs in different views as…
In contemporary neuroscience, a key area of interest is dynamic effective connectivity, which is crucial for understanding the dynamic interactions and causal relationships between different brain regions. Dynamic effective connectivity can…
Chain Event Graphs (CEGs) are a widely applicable class of probabilistic graphical model that can represent context-specific independence statements and asymmetric unfoldings of events in an easily interpretable way. Existing model…
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…
Regression Discontinuity Design (RDD) is a popular framework for estimating a causal effect in settings where treatment is assigned if an observed covariate exceeds a fixed threshold. We consider estimation and inference in the common…
We present Visual AutoRegressive modeling (VAR), a new generation paradigm that redefines the autoregressive learning on images as coarse-to-fine "next-scale prediction" or "next-resolution prediction", diverging from the standard…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
High-dimensional data with hundreds of thousands of observations are becoming commonplace in many disciplines. The analysis of such data poses many computational challenges, especially when the observations are correlated over time and/or…
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…
While artificial neural networks excel in unsupervised learning of non-sparse structure, classical statistical regression techniques offer better interpretability, in particular when sparseness is enforced by $\ell_1$ regularization,…
Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…
High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…