#bayesian-networks

Question 1: Single choice

mediumAI-checkedProbabilistic & Graphical Models

Naive Bayes fails on XOR data ( $y = x_1 \oplus x_2$ ). A Bayesian network with the edges $y \to x_1$ , $y \to x_2$ and $x_1 \to x_2$ classifies it perfectly. Why?

It models $p(x_2 \mid x_1, y)$ , which can encode $x_2 = x_1 \oplus y$ 1
The extra edge acts like a hidden layer, which makes the model nonlinear2
It smooths the counts for $x_2$ , which breaks the ties of naive Bayes3
It drops the prior $p(y)$ , which pulled every posterior to one half4

Timed test