The Book of Why: The New Science of Cause and Effect

by Judea Pearl

More precisely, I assumed that the network would be hierarchical, with arrows pointing from higher neurons to lower ones, or from “parent nodes” to “child nodes.” Each node would send a message to all its neighbors (both above and below in the hierarchy) about its current degree of belief about the variable it tracked (e.g., “I’m two-thirds certain that this letter is an R”). The recipient would process the message in two different ways, depending on its direction. If the message went from parent to child, the child would update its beliefs using conditional probabilities, like the ones we saw in the teahouse example. If the message went from child to parent, the parent would update its beliefs by multiplying them by a likelihood ratio, as in the mammogram example.