Regression and Bayesian Methods in Modern Preference Elicitation

Linear regression is often considered the workhorse of predictive modeling, yet its application extends beyond straightforward predictive tasks. This article seeks to enrich the dialogue around regression techniques by introducing Probit Linear Regression as an effective tool for modeling preferences. Furthermore, we employ a Bayesian framework to transition from classical to Bayesian Linear Regression, elucidating the intrinsic relationship between cost-based optimization — specifically Binary Cross-Entropy (BCE) loss minimization — and maximum likelihood estimation. In doing so, we aim to demonstrate that regularization can be considered a form of Bayesian prior selection, thereby bridging cost function approaches with probabilistic reasoning. Finally, we will discuss how Bayesian Linear Regression allows not only for point estimates but also provides a distribution over these predictions, offering a richer, uncertainty-aware perspective. <h1>The Bayesian Framework</h1> The Bayes Framework identifies two principal components: the data D and the model w. By specifying the likelihood P(D∣w) and a prior over the model P(w), we aim to find the model that maximizes the posterior P(w∣D), derived via Bayes’ theorem as: <a href="https://towardsdatascience.com/regression-and-bayesian-methods-in-modern-preference-elicitation-39a21435898d">Click Here</a>