Joint probability in a discrete Bayesian network

Multiply the local tables to get one joint probability

A discrete Bayesian network factorizes the joint distribution into one conditional table per node: P(x) = product_i P(x_i | parents of x_i). This question computes the probability of one full assignment.

Implement joint_probability(x, parents, cpts).

• x is a sequence with one integer value per node.
• parents[i] is a tuple of node indices that are the parents of node i. It is empty for a root.
• cpts[i] is a NumPy array with one axis per parent (in the order given by parents[i]) followed by a last axis for node i. Each row along the last axis sums to 1.
• Return the product of cpts[i][parent values..., x_i] over all nodes, as a float.

Constraints

• len(x), len(parents) and len(cpts) must match. Otherwise raise ValueError.
• A table whose number of axes is not len(parents[i]) + 1 raises ValueError.
• A table whose last-axis rows do not sum to 1 raises ValueError.
• A value outside its axis range raises ValueError.
• Do not modify the inputs.

Hints