Terms

Terms specify how a node variable is build from its parents.

Usage

Here is how a term can be setup

from bn_testing.terms import Term
import numpy as np

some_term = Term(
    parents=['a', 'b'],
    term_fn=lambda v: np.sqrt(v['a'])*v['b'],
)

Afterwards, the term can be applied on pymc variables and distributions:

import pymc as pm

dist = some_term(
   a=pm.Normal.dist(mu=1, sigma=0.4),
   b=pm.Beta.dist(alpha=0.4, beta=0.2),
 )

Existing terms

Here is a list of terms that ease instantiation for some classes of terms frequently used. Assume that the parents are \(x_1,\ldots,x_n\):

• Linear: A linear term of the form \(\sum_{i=1}^nw_ix_i\)

• Polynomial: A multivariate polynomial, i.e., a sum of the form \(\sum_{j=1}^mc_j\prod_{i=1}^nx_i^{e_{ji}}\)

Arithmetic with terms

Given two terms term_a and term_b, another term can be constructed by applying a basic arithemtic computation. For instance:

term_a + term_b
term_a * term_b
(2 * term_a + 3 * term_b)**10

Note

Composing terms like term_a(term_b) is currently not supported.

Implementing own terms

Typically, new terms can be formed by combining the basic terms.

Here is a small example how a term can be computed:

from bn_testing.terms import Term
import numpy as np

class RootMeanSquared(Term):

   def __init__(self, parents):
       super(OwnTerm, self).__init__(parents=parents)

   def apply(self, parents_mapping):
       parents = self.get_vars_from_dict(parents_mapping)
       return np.sqrt(np.mean(parents**2))

Note

Generally, Terms are generated by Conditionals and the parents are selected at runtime randomly. Terms, however, should be deterministic and any random selections should be done in the calling Conditionals.