Bayesian Network Joint Probability

Problem

For a binary Bayesian network, each node i has parents parents[i] and conditional probability table cpts[i]. Rows of cpts[i] are indexed by the parent configuration, where the first parent is the least significant bit of the binary index, and columns are the node's probability of being 0 or 1. Return the joint probability of assignment, or 0.0 when shapes are invalid.

Hint

Multiply the conditional probability of each node given its parents' assigned values.

Test cases

case 1

in: [[[],[0]],[[[0.6,0.4]],[[0.9,0.1],[0.2,0.8]]],[0,1]]

expected: 0.06

case 2

in: [[[],[0]],[[[0.6,0.4]],[[0.9,0.1],[0.2,0.8]]],[1,1]]

expected: 0.32000000000000006

case 3

in: [[[],[0]],[[[0.6,0.4]],[[0.9,0.1],[0.2,0.8]]],[1,0]]

expected: 0.08000000000000002

case 4

in: [[[],[],[0,1]],[[[0.5,0.5]],[[0.8,0.2]],[[0.1,0.9],[0.6,0.4],[0.2,0.8],[0.7,0.3]]],[1,0,0]]

expected: 0.24

case 5

in: [[[],[0]],[[[0.6,0.4]],[[0.9,0.1],[0.2,0.8]]],[]]

expected: 0

Starter codePython

def bayesian_network_joint_probability(parents, cpts, assignment):
    # Your code here
    pass

5 test cases · run your code against them in the editor