Abductive inference plays a critical role in solving problems involving uncertain information and multiple competing hypotheses. In the Bayesian network framework, abductive inference involves generating the configuration of target variables that best explains the observed evidence. Furthermore, research has shown that these configurations should be precise and concise. However, the search space for potential explanations can be vast, particularly in more complex networks, requiring efficient search algorithms to traverse this space and find optimal configurations. This aligns with the challenges in explainable artificial intelligence, where researchers aim to provide relevant and meaningful explanations in a computationally efficient manner. Previous work has focused on developing several search algorithms, such as forward, backward, tabu, and reverse jump MCMC algorithms. Algorithms like the forward search algorithm still involve exhaustive searching as it does not prune the neighbourhood of potential solutions. To address this, we propose incorporating a statistical neighbourhood selection method, such as the graphical Lasso (Least Absolute Shrinkage and Selection Operator), with the forward search algorithm to prune the search space. The graphical Lasso’s penalty term encourages sparsity, helping to prune less relevant variables, thereby improving computational efficiency. By reducing the set of instantiations, the forward-gLasso algorithm provides explanations focusing on the most relevant dependencies. We evaluate the performance and computational efficiency of the forward-gLasso algorithm on a set of benchmark Bayesian networks and compare it to the forward search algorithm.