The "Geometry" of Naïve bayes: Teaching probabilities by "Drawing" them

Educational data mining (EDM) is an emerging discipline that studies methods for exploring the data that come from educational environments. This chapter focuses on students that are studying foundations of machine learning (ML) and, in particular, probabilistic models for classification. Interactive ML (IML) is a relatively new area of ML where interaction with users allows ML models to be updated fast and very accurately. In IML, even nonexpert users can solve ML problems with minimum effort by means of intuitive visualization tools. The chapter presents a geometric interpretation of one of the most used probabilistic classifiers in the literature: the Naive Bayes (NB) classifier. Bayesian decision theory is based on quantifying the tradeoffs between classification decisions and the costs that accompany such decisions. It allows us to formally define risk-based decision-making, assign costs to these decisions, and find the decision that minimizes the risks with that particular action.