Advancing Generative Modelling and Applications with Boltzmann Machines, Restricted Boltzmann Machines, and Sum-Product Networks

Abstract

In the era of advanced machine learning methodologies, generative probabilistic modelling shows great promise for solving real-world problems. This study focuses on Boltzmann Machines (BMs), Restricted Boltzmann Machines (RBMs), and Sum-Product Networks (SPNs), highlighting their abilities to reconstruct complex data distributions and produce meaningful outputs. Notably, BMs and RBMs excel at modelling data distributions, while SPNs utilize hierarchical structures for efficient representation and scalable probabilistic inference. Using the Fashion MNIST dataset as a benchmark, this work demonstrates the models' practicality through reconstructed images, precise predictions, and performance metrics. The findings confirm their applicability in tasks such as image generation, object recognition, and pattern matching. This study provides an empirical assessment of the strengths and limitations of each approach while expanding the potential applications of generative models in machine learning.