Which algorithm utilizes Bayes' theorem for classification tasks?

The selection of the Bayesian classifier is based on its foundational use of Bayes' theorem for classification tasks. Bayes' theorem provides a mathematical framework for updating the probability of a hypothesis as more evidence becomes available. In the context of classification, the Bayesian classifier calculates the posterior probability of each class given a set of features, thus allowing it to make informed predictions about which class an instance belongs to.

The Bayesian classifier is particularly effective in situations where the underlying distribution of the data can be assumed to follow a certain probabilistic model. This approach allows it to incorporate prior knowledge (prior probability) and make predictions even with limited data, leveraging the concepts of independence among features in many practical applications.

Each of the other algorithms listed employs different strategies or mathematical frameworks for classification. Decision tree classifiers split data based on feature values in a tree-like structure; support vector machines find hyperplanes that best separate classes; and k-nearest neighbors classify based on the majority class among the nearest data points. None of these methods fundamentally rely on Bayes' theorem, which is the defining characteristic of the Bayesian classifier.