Bayesian scoring function Java and JavaScript API for Bayesian Belief Networks

The Bayesian Dirichlet (BD) scoring function is defined as follows.

Click this link to see what each of these terms mean.

For a weekend project, I created a Java and JavaScript API for computing the BD scoring function. The project is open-source with Apache License v2.0. You may download the project from GitHub at https://github.com/vangj/multdir-core.

Let’s see how we may quickly use these APIs to compute the score of a Bayesian Belief Network (BBN). In [Cooper92], a set of data with three variables (X1, X2, X3) was given as follows.

X1	X2	X3
p	a	a
p	p	p
a	a	p
p	p	p
a	a	a
a	p	p
p	p	p
a	a	a
p	p	p
a	a	a

There was also 3 Bayesian network structures (BS) to represent the relationships of the variables as well. Those 3 BS were reported as follows.

• BS1: X1 → X2 → X3
• BS2: X2 ← X1 → X3
• BS3: X1 ← X2 ← X3

In Java, we can use the API to quickly estimate the scores of BS1, BS2, and BS3 as follows.

double bs1 = (new BayesianDirchletBuilder())
		.addKutato(5, 5) //X1
		.addKutato(1, 4) //X2
		.addKutato(4, 1)
		.addKutato(0, 5) //X3
		.addKutato(4, 1)
		.build()
		.get();
double bs2 = (new BayesianDirchletBuilder())
		.addKutato(5, 5) //X1
		.addKutato(1, 4) //X2
		.addKutato(4, 1)
		.addKutato(2, 3) //X3
		.addKutato(4, 1)
		.build()
		.get();
double bs3 = (new BayesianDirchletBuilder())
		.addKutato(1, 4) //X1
		.addKutato(4, 1)
		.addKutato(0, 4) //X2
		.addKutato(5, 1)
		.addKutato(6, 4) //X3
		.build()
		.get();

Likewise, in JavaScript, we can also quickly estimate the scores of these BBNs as follows.

var bs1 = (new BayesianDirichletBuilder())
	.addKutato([5,5])
	.addKutato([1,4])
	.addKutato([4,1])
	.addKutato([0,5])
	.addKutato([4,1])
	.build()
	.get();
var bs2 = (new BayesianDirichletBuilder())
	.addKutato([5,5])
	.addKutato([1,4])
	.addKutato([4,1])
	.addKutato([2,3])
	.addKutato([4,1])
	.build()
	.get();
var bs3 = (new BayesianDirichletBuilder())
	.addKutato([1,4])
	.addKutato([4,1])
	.addKutato([0,4])
	.addKutato([5,1])
	.addKutato([6,4])
	.build()
	.get();

Notice how in both APIs, you only add the counts? Easy.

Also, a working demo of using the JavaScript API to compute the BBN scores is in the repository for this project. Here’s a screenshot. Note that the scores are in log-space. Computing the score using factorials is not practical. In log-space, the lower the score associated with a BBN, the better the BBN.

As always, enjoy and cheers! Sib ntsib dua nawb mog!

References

• [Cooper92] G.F. Cooper and E. Herskovits. A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 9, 309–347 (1992).