Reza Mohammadi

Elias Dubbeldam, Reza Mohammadi, Marit Schoonhoven et al.

Despite recent progress, deep learning methods for tabular data still struggle to compete with traditional tree-based models. A key challenge lies in modeling complex, dataset-specific feature interactions that are central to tabular data. Graph-based tabular deep learning (GTDL) methods aim to address this by representing features and their interactions as graphs. However, existing methods predominantly optimize predictive accuracy, neglecting accurate modeling of the graph structure. This position paper argues that GTDL should move beyond prediction-centric objectives and prioritize the explicit learning and evaluation of feature interactions. Using synthetic datasets with known ground-truth graph structures, we show that existing GTDL methods fail to recover meaningful feature interactions. Moreover, enforcing the true interaction structure improves predictive performance. This highlights the need for GTDL methods to prioritize quantitative evaluation and accurate structural learning. We call for a shift toward structure-aware modeling as a foundation for building GTDL systems that are not only accurate but also interpretable, trustworthy, and grounded in domain understanding.

Reza Mohammadi, Matthew Pratola, Maurits Kaptein

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.

Reza Mohammadi, Helene Massam, Gerard Letac

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.

Reza Mohammadi, Ernst C. Wit

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.