Understanding Inference in Bayesian Networks: From Naive Bayes to Gibbs Sampling (with Python Examples)
Inference in Bayesian Networks: From Naive Bayes to Gibbs Sampling In our previous post, we looked at how to represent uncertainty. Now, we look at the engine of the system: Inference . Inference allows us to take observed data (evidence) and calculate the probability of hidden states. Naive Bayes Inference Exact Naive Bayes assumes that features are independent given the class. Despite its "naive" name, it is a workhorse in modern applications. $$P(C \mid o_1, \dots, o_m) \propto P(C) \prod_{i=1}^m P(o_i \mid C)$$ Real-World Application: Spam Filtering When you receive an email containing the words "Offer" and "Free," a Naive Bayes classifier looks at the probability of those words appearing in known Spam vs. Not Spam emails. It assumes the word "Offer" appearing is independent of "Free" being there, allowing for lightning-fas...
