A Review of Bayesian Machine Learning Principles, Methods, and Applications

Bayesian machine learning is a subfield of machine learning that incorporates Bayesian principles and probabilistic models into the learning process. It provides a principled framework for modeling uncertainty, making predictions, and updating beliefs based on observed data. This review article aims to provide an overview of Bayesian machine learning, discussing its foundational concepts, algorithms, and applications. We explore key topics such as Bayesian inference, probabilistic graphical models, Bayesian neural networks, variational inference, Markov chain Monte Carlo methods, and Bayesian optimization. Additionally, we highlight the advantages and challenges of Bayesian machine learning, discuss its application in various domains, and identify future research directions. Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and hyper-parameter tuning. Traditional highdimensional data reduction techniques, such as principal component analysis (PCA), partial least squares (PLS), reduced rank regression (RRR), projection pursuit regression (PPR) are all shown to be shallow learners. Their deep learning counterparts exploit multiple deep layers of data reduction which provide predictive performance gains. Stochastic gradient descent (SGD) training optimisation and Dropout (DO) regularization provide estimation and variable selection. Bayesian regularization is central to finding weights and connections in networks to optimize the predictive bias-variance tradeoff. To illustrate our methodology, we provide an analysis of international bookings on Airbnb. Finally, we conclude with directions for future research