Integrated Bayesian Inference Framework: Markov Chain Monte Carlo, Hyperdimensional Computing, Knowledge Graphs and GNNs

Preamble

Bayesian inference stands as a cornerstone in the realm of statistical modelling and machine learning, offering us a robust framework for updating beliefs in light of new evidence. This article dives into an intricate Python-based Bayesian inference framework I created that amalgamates several advanced computational techniques: Markov Chain Monte Carlo (MCMC), Hyperdimensional Computing (HDC), Knowledge Graphs and Graph Neural Networks (GNNs).

I will explore the mathematical underpinnings of each component, dissect the accompanying code with rich snippets and deep explanations, examine practical use cases, highlight the benefits of this integrated approach and elucidate the results obtained from executing the framework.

Introduction

Bayesian inference provides a probabilistic approach to statistical modelling, allowing for the updating of beliefs as new data becomes available. Central to Bayesian methods is Bayes’ Theorem, which relates the posterior probability of a hypothesis to its prior probability and the likelihood of observed data.

In this comprehensive framework, we integrate several advanced techniques to enhance Bayesian inference:

• Markov Chain Monte Carlo (MCMC): Facilitates sampling from complex probability distributions.
• Hyperdimensional Computing (HDC): Offers efficient representation and manipulation of high-dimensional data.
• Knowledge Graphs: Encapsulate rich relational information among data points.
• Graph Neural Networks (GNNs): Leverage the structure of knowledge graphs to learn representations and make predictions.

By synergising these components, the framework aims to perform sophisticated Bayesian inference tasks with improved accuracy and efficiency.

Mathematical Foundations

Understanding the mathematical principles behind each component is crucial for grasping how they interoperate within the framework.

Bayesian Inference