bayes-net

A python implemention for checking D-separation and I-equivalence in Bayesian Networks (BN).

D-separation

Given a Bayesian Network, and several queries in the form of X Y | Z where X, Y are two query nodes and Z is a set of observed nodes, src/dsep.py checks whether X and Y are d-separated given Z and prints True or False.

This mainly follows the "Reachable" procedure in

Koller and Friedman (2009), "Probabilistic Graphical Models: Principles and Techniques" (page 75)

To run the code, try

cd src
python dsep.py < ../tests/dsep/test1.in

Input and Output

dsep.py takes input from stdin as follows:

1. First line:

N M Q ``` where N and `M` are the number of nodes and edges in the BN, respectively, `Q` is the number of D-separation queries that will follow.

2. Next M lines:

A B

Each line denotes a directed edge A -> B in the BN graph.

3. Next Q lines:

A B | C D E ...

Each line denotes a query: whether A and B are d-separated given nodes C D E ...

The output to stdout has Q lines, one line per query, which is True if the two nodes are d-separated or False otherwise.

Example

Run

python dsep.py 

and provides input from stdin as follows:

3 2 2
A B
B C
A C | B
C A |

This constructs a BN with 3 nodes and 2 edges:

A -> B -> C

and asks 2 queries:

(1) Are A and C d-separated given B? (True)

(2) Are C and A d-separated? (False)

So the algorithm will print to stdout as

True
False

I-equivalence

Given two Bayesian Networks (BNs), src/iequiv.py tests whether they are I-equivalent. Following Koller and Friedman (2009), two BNs are I-equivalent if and only if they have the same skeletons and immoralities.

To run the code, try

cd src
python iequv.py < ../tests/iequiv/test1.in

Input and Output

iequiv.py takes input from stdin as follows:

1. First line:

N1 M1

where N1 and M1 are the number of nodes and edges, respectively, in the first Bayesian network.

2. Next M1 lines:

A B

Each line denotes a directed edge A -> B in the BN graph.

3. Next line:

N2 M2

where N2 and M2 are the number of nodes and edges, respectively, in the second Bayesian network.

4. Next M2 lines:

A B

Each line denotes a directed edge A -> B in the BN graph.

The output is printed to stdout: True if two graphs are I-equivalent or False otherwise.

Example

Run

python iequiv.py 

and provides input from stdin as follows:

3 2
A B
B C
3 2
C B
A B

This constructs and compares two BNs:

A -> B -> C
A -> B <- C

and the algorithm prints False to stdout since they are not I-equivalent.

Tests

Several simple test cases are provided in tests/dsep and tests/iequiv. Special thanks to the TAs in CMU 10-708 for the test cases. To run the tests:

cd src
python dsep.py < ../tests/dsep/test1.in
python iequv.py < ../tests/iequiv/test1.in