3.2 Binomial Distribution

We can also model a binomial distribution as an TML KB. If we change the initial coin TML KB from Section 2.1 and add a weight w to the value Heads of attribute Side, our .tml file is updated as follows:

class FlipSequence {
Side Heads 1.0, Tails;
}

Note that if no weight is given to an attribute, the default is a weight of 0.0. An equivalent update to the .tml file is:

class FlipSequence {
Side Heads 1.0, Tails 0.0;
}

we have a binomial distribution with $n$ being the number of flips (in our case 10) and $p = \frac{1}{1 + e^{-w}}$ , where $w$ is the weight of the unit clause (in our case 1). We can verify this by running probabilistic inference:

al -i binomial_coin.tml -o binomial_coin.result -e coin.db -q Side(Flip)

The marginal probabilities for values of Heads returned will be $\frac{1}{1 + e^{-1}} = 0.73$ .