arXiv subjects

Reza Mohammadi

Publications and source records attributed to Reza Mohammadi.

11 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.

stat.ME↗

arXiv2026

The Role of Feature Interactions in Graph-based Tabular Deep Learning

Accurate predictions on tabular data rely on capturing complex, dataset-specific feature interactions. Attention-based methods and graph neural networks, referred to as graph-based tabular deep learning (GTDL), aim to improve predictions by modeling these interactions as a graph. In this work, we analyze how these methods model the feature interactions. Current GTDL approaches primarily focus on optimizing predictive accuracy, often neglecting the accurate modeling of the underlying graph structure. Using synthetic datasets with known ground-truth graph structures, we find that current GTDL methods fail to recover meaningful feature interactions, as their edge recovery is close to random. This suggests that the attention mechanism and message-passing schemes used in GTDL do not effectively capture feature interactions. Furthermore, when we impose the true interaction structure, we find that the predictive accuracy improves. This highlights the need for GTDL methods to prioritize accurate modeling of the graph structure, as it leads to better predictions.

cs.LG↗

arXiv2025

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.

stat.ME↗

arXiv2025

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.

stat.AP↗

arXiv2024

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.

stat.ME↗

arXiv2024

Bayesian Structural Learning with Parametric Marginals for Count Data: An Application to Microbiota Systems

High dimensional and heterogeneous count data are collected in various applied fields. In this paper, we look closely at high-resolution sequencing data on the microbiome, which have enabled researchers to study the genomes of entire microbial communities. Revealing the underlying interactions between these communities is of vital importance to learn how microbes influence human health. To perform structural learning from multivariate count data such as these, we develop a novel Gaussian copula graphical model with two key elements. Firstly, we employ parametric regression to characterize the marginal distributions. This step is crucial for accommodating the impact of external covariates. Neglecting this adjustment could potentially introduce distortions in the inference of the underlying network of dependences. Secondly, we advance a Bayesian structure learning framework, based on a computationally efficient search algorithm that is suited to high dimensionality. The approach returns simultaneous inference of the marginal effects and of the dependence structure, including graph uncertainty estimates. A simulation study and a real data analysis of microbiome data highlight the applicability of the proposed approach at inferring networks from multivariate count data in general, and its relevance to microbiome analyses in particular. The proposed method is implemented in the R package BDgraph.

stat.ME↗

arXiv2021

Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models

Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wishart. With this prior, the transition probabilities in the search algorithms necessitate evaluating the ratios of the prior normalizing constants of G-Wishart. In moderate to high-dimensions, this ratio is often approximated using sampling-based methods as computationally expensive updates in the search algorithm. Calculating this ratio so far has been a major computational bottleneck. We overcome this issue by representing a search algorithm in which the ratio of normalizing constant is carried out by an explicit closed-form approximation. Using this approximation within our search algorithm yields significant improvement in the scalability of structure learning without sacrificing structure learning accuracy. We study the conditions under which the approximation is valid. We also evaluate the efficacy of our method with simulation studies. We show that the new search algorithm with our approximation outperforms state-of-the-art methods in both computational efficiency and accuracy. The implementation of our work is available in the R package BDgraph.

math.ST↗

arXiv2020

Continuous-Time Birth-Death MCMC for Bayesian Regression Tree Models

Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree models according to their posterior probabilities. The critical component of such an MCMC algorithm is to construct good Metropolis-Hastings steps for updating the tree topology. However, such algorithms frequently suffering from local mode stickiness and poor mixing. As a result, the algorithms are slow to converge. Hitherto, authors have primarily used discrete-time birth/death mechanisms for Bayesian (sums of) regression tree models to explore the model space. These algorithms are efficient only if the acceptance rate is high which is not always the case. Here we overcome this issue by developing a new search algorithm which is based on a continuous-time birth-death Markov process. This search algorithm explores the model space by jumping between parameter spaces corresponding to different tree structures. In the proposed algorithm, the moves between models are always accepted which can dramatically improve the convergence and mixing properties of the MCMC algorithm. We provide theoretical support of the algorithm for Bayesian regression tree models and demonstrate its performance.

stat.ML↗

arXiv2020

Dewetted Au nanoparticles on TiO$_2$ surfaces -- Evidence of a size-independent plasmonic photo-electrochemical response

Flat TiO$_2$ layers are deposited by magnetron sputtering on Ti/Si wafers. The TiO$_2$ surfaces are then sputter-coated with thin Au films of a nominal thickness of 0.5-10 nm that are converted by solid-state dewetting into Au nanoparticles of tuneable size and spacing; the Au nanoparticle size can be tuned over a broad range, i.e. ca. 3-200 nm. The Au-decorated TiO$_2$ surfaces enable plasmonic photo-electrochemical water splitting under visible light illumination (450-750 nm). The water splitting performance reaches a maximum for TiO$_2$ layers decorated with ~ 30 nm-sized Au particles. As expected, optical absorption measurements show a red shift of the plasmonic extinction band with increasing the Au nanoparticle size. However, the plasmonic photocurrent is found to peak at ~ 600 nm regardless of the size of the Au nanoparticles, i.e. the plasmonic photocurrent band position is size-independent. Such a remarkable observation can be ascribed to a hot electron injection cut-off effect.

physics.app-ph↗

arXiv2020

Gaussian graphical models reveal inter-modal and inter-regional conditional dependencies of brain alterations in Alzheimer's disease

Alzheimer's disease (AD) is characterized by a sequence of pathological changes, which are commonly assessed in vivo using MRI and PET. Currently, the most approaches to analyze statistical associations between brain regions rely on Pearson correlation. However, these are prone to spurious correlations arising from uninformative shared variance. Notably, there are no appropriate multivariate statistical models available that can easily integrate dozens of variables derived from such data, being able to use the additional information provided from the combination of data sources. Gaussian graphical models (GGMs) can estimate the conditional dependency from given data, which is expected to reflect the underlying causal relationships. We applied GGMs to assess multimodal regional brain alterations in AD. We obtained data from N=972 subjects from the Alzheimer's Disease Neuroimaging Initiative. The mean amyloid load (AV45-PET), glucose metabolism (FDG-PET), and gray matter volume (MRI) were calculated. GGMs were estimated using a Bayesian framework for the combined multimodal data to obtain conditional dependency networks. Conditional dependency matrices were much sparser (10% density) than Pearson correlation matrices (50% density). Within modalities, conditional dependency networks yielded clusters connecting anatomically adjacent regions. For associations between different modalities, only few region-specific connections remained. Graph-theoretical network statistics were significantly altered between groups, with a biphasic u-shape trajectory. GGMs removed shared variance among multimodal measures of regional brain alterations in MCI and AD, and yielded sparser matrices compared to Pearson correlation networks. Therefore, GGMs may be used as alternative to thresholding-approaches typically applied to correlation networks to obtain the most informative relations between variables.

q-bio.NC↗

arXiv2019

BDgraph: An R Package for Bayesian Structure Learning in Graphical Models

Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce the R package BDgraph which performs Bayesian structure learning for general undirected graphical models (decomposable and non-decomposable) with continuous, discrete, and mixed variables. The package efficiently implements recent improvements in the Bayesian literature, including that of Mohammadi and Wit (2015) and Dobra and Mohammadi (2018). To speed up computations, the computationally intensive tasks have been implemented in C++ and interfaced with R, and the package has parallel computing capabilities. In addition, the package contains several functions for simulation and visualization, as well as several multivariate datasets taken from the literature and used to describe the package capabilities. The paper includes a brief overview of the statistical methods which have been implemented in the package. The main part of the paper explains how to use the package. Furthermore, we illustrate the package's functionality in both real and artificial examples.

stat.ML↗