Mini-Symposium: Bayesian Structural Learning

Abstract: 
Bayesian Structural Learning captures methods that can uncover potentially hidden structures in complex stochastic systems and heterogenous data. The term Bayesian emphasizes the aim to not only learn structure from the data but also to quantify uncertainties of e.g., predictive distributions or competing models.  This mini symposium brings together researchers targeting this methodological space that is fundamental to modern Bayesian learning. Presentations will highlight this along advancements in distributional modeling, variable selection, and the identification of dependencies along with scalable inference. The need for such methods will be further illustrated in applications from science, engineering and economics.

Confirmed Speakers: 

Speaker: Emanuele Aliverti (University of Padova)
Title: Approximate Bayesian inference for semiparametric ordinal regression
Abstract: Ordinal categorical variables, such as Likert-scale responses, are widely used across many applied scientific fields. In several applications, it is of interest to characterize how their distribution depends on one or more covariates through flexible smooth effects. Under a Bayesian framework, this can be addressed using additive cumulative probit models with penalized regression splines. When the sample size is large, however, posterior inference based on Markov chain Monte Carlo becomes computationally demanding, motivating the use of scalable deterministic approximations. In this talk, we consider two approaches based on Variational Inference: a partially factorized mean-field approximation and an Expectation Propagation routine. We discuss their construction, computational properties, and empirical performance, showing that they provide fast and accurate alternatives to MCMC. The proposed algorithms are illustrated using data from a large 2022 survey measuring public trust in science and scientists.

Speaker: Nicolas Bianco (KIT)
Title: Global shrinkage and local variable selection in spatially varying coefficient models
Abstract: Spatial regression models often assume constant coefficients, implying fixed covariate effects across space. However, in many applications, these effects and their importance vary by location. We propose a novel prior structure for Bayesian spatial regression models with varying coefficients, integrating global shrinkage and local variable selection. Each coefficient is modeled as a Gaussian process, allowing spatial variation. The global shrinkage mechanism concentrates the process around a single value, helping to determine whether a coefficient should vary or remain constant. Simultaneously, local selection identifies whether coefficients are zero or non-zero at specific locations, enabling refined spatial modeling. To support practical implementation, we introduce a prior scaling approach based on marginal prior properties. We analyze the properties of the induced marginal process and provide empirical results demonstrating the model’s effectiveness. Our approach enhances predictive performance and interpretability, offering deeper insights into spatially varying relationships between variables.

Speaker: Isadora Antoniano Villalobos (Uni Venice)
Title: Coherent Bayesian estimation of intensity duration frequency curves
Abstract: Intensity-duration-frequency (IDF) curves are an essential tool for characterizing the frequency of extreme rainfall events and assessing flood risk. These curves describe the expected frequency of extreme rainfall over different accumulation durations and are subject to shape constraints to ensure coherent estimates of exceedance probabilities across durations. Most existing methods for estimating IDF curves either assume that rainfall accumulations at different durations are independent or rely on pairwise likelihood approximations and computationally intensive procedures to account for the full extremal dependence structure. We propose a first-order Markov dependence model for IDF curves that incorporates dependence between intensities observed at discrete durations through duration-dependent bivariate generalized extreme value distributions, while preserving the coherence of the estimated quantile curves. Bayesian inference allows us to incorporate prior knowledge about the parameters of the IDF models and to provide a direct assessment of uncertainty in the estimation of high quantiles. 

Speaker: Deborah Sulem (Universita della Svizzera Italiana)
Title: Bayesian estimation of high-dimensional Gaussian graphical models
Abstract: Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the data, and parameter estimates. However, computational demands have limited their application when the number of variables is large, which prompted the use of pseudo-Bayesian approaches. We propose fully Bayesian algorithms that provably scale to high dimensions when the data-generating precision matrix is sparse, at a similar cost to the best pseudo-Bayesian methods.

Speaker: Dootika Vats (Indian Institute of Technology, Kanpur)
Title: Proximal Hamiltonian Monte Carlo
Abstract: Modern Bayesian models often have non-differentiable posteriors. This is a direct consequence of employing a non-differentiable sparsity inducing prior in the model. As a result, sampling even from efficient gradient-based Markov chain Monte Carlo (MCMC) methods becomes difficult. We circumvent this problem by proposing a Proximal Hamiltonian Monte Carlo (p-HMC) algorithm, which uses tools like proximal mappings and Moreau-Yosida (MY) envelopes within Hamiltonian dynamics. A chief contribution of this work is that we also provide conditions for geometric ergodicity of the underlying HMC chain and a methodology to obtain a suitable choice for the regularization parameter in the MY envelope. We demonstrate the effectiveness of the sampler for a few examples.

Speaker: Gregor Zens  
Title: Scalable Variable Selection and Model Averaging for Latent Regression Models Using Approximate Variational Bayes
Abstract: We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. The framework addresses three interrelated challenges: intractable marginal likelihoods, exponentially large model spaces, and high computational costs in large samples. We introduce a novel integrated likelihood approximation based on mean-field variational posterior approximations and study its asymptotic model-selection properties. To further reduce the computational burden, we develop an approximate variational Bayes scheme that fixes the latent outcomes across models at initial estimates obtained under a baseline null model. This simple approximation often yields model-selection behavior close to that of the full variational Bayes procedure while requiring only a fraction of the computational cost. Extensive numerical studies - including probit, tobit, semiparametric count data models, and Poisson log-normal regression - show accurate inference and substantial speedups, often reducing run-times from days to hours with comparable accuracy. Real-data applications further demonstrate the practical value of the proposed methods for scalable Bayesian inference under model uncertainty.