Description

BayesianNetwork should support some form of network structure learning based on input data. A simple method would be a greedy algorithm that selects nodes and edges based on mutual information.

Approach

1. User loads input data and defines max degree network, i.e. the max number of parents that any node can have in the network.
2. Select first node randomly from the available columns in the input data.
3. For all remaining nodes: select each node that has the highest mutual information with (some of) the existing nodes in the network, bounded by the max degree network.
4. Calculate the conditional probabilities of all the nodes in the network and instantiate BayesianNetwork

When multiplying two factors with similar indices, pandas will wrongly assume that the indices should be aligned.

Example:

fAC = Factor(
    [0.6, 0.4], 
    {'A': ['a1', 'a0'], 'C': ['x1', 'x0']}
)

fAB = Factor(
    [0.6, 0.4], 
    {'A': ['a1', 'a0'], 'B': ['x1', 'x0']}
)

fAC * fAB 
# --> factor(A,C) or factor(A,B), depending on the order of multiplication.
# Pandas will wrongly assume that indices of B and C are the same thing and will happily
# multiply the columns :-(.

Currently parameter learning with incomplete data is not (properly) supported and needs to be implemented.

Inference performance can be improved by pruning a BN's graph before performing variable elimination.

See also 6b. Inference by Variable Elimination II (Chapter 6) on YouTube.

Inference performance can be improved by properly sorting the list of variables before performing variable elimination.

See also 6a. Inference by Variable Elimination I (Chapter 6) on YouTube.