# probGraphicalModels.py - Graphical Models and Belief Networks
# AIFCA Python3 code Version 0.8.0 Documentation at http://aipython.org
# Artificial Intelligence: Foundations of Computational Agents
# http://artint.info
# Copyright David L Poole and Alan K Mackworth 2018.
# This work is licensed under a Creative Commons
# Attribution-NonCommercial-ShareAlike 4.0 International License.
# See: http://creativecommons.org/licenses/by-nc-sa/4.0/deed.en
class Graphical_model(object):
"""The class of graphical models.
A graphical model consists of a set of variables and a set of factors.
List vars is a list of variables
List factors is a list of factors
"""
def __init__(self,vars=None,factors=None):
self.variables = vars
self.factors = factors
class Belief_network(Graphical_model):
"""The class of belief networks."""
def __init__(self,vars=None,factors=None):
"""vars is a list of variables
factors is a list of factors. Here we assume that all of the factors are instances of Prob.
"""
Graphical_model.__init__(self,vars,factors)
assert all(isinstance(f,Prob) for f in factors) if factors else True
from utilities import Displayable
class Inference_method(Displayable):
"""The abstract class of graphical model inference methods"""
def query(self,qvar,obs={}):
raise NotImplementedError("Inference_method query") # abstract method
from variables import Variable
from probFactors import Prob
boolean = [False, True]
A = Variable("A", boolean)
B = Variable("B", boolean)
C = Variable("C", boolean)
f_a = Prob(A,[],[0.4,0.6])
f_b = Prob(B,[A],[0.9,0.1,0.2,0.8])
f_c = Prob(C,[B],[0.5,0.5,0.3,0.7])
bn1 = Belief_network([A,B,C],[f_a,f_b,f_c])
# Bayesian network report of leaving example from
# Poole and Mackworth, Artificial Intelligence, 2010 http://artint.info
# This is Example 6.10 (page 236) shown in Figure 6.1
Al = Variable("Alarm", boolean)
Fi = Variable("Fire", boolean)
Le = Variable("Leaving", boolean)
Re = Variable("Report", boolean)
Sm = Variable("Smoke", boolean)
Ta = Variable("Tamper", boolean)
f_ta = Prob(Ta,[],[0.98,0.02])
f_fi = Prob(Fi,[],[0.99,0.01])
f_sm = Prob(Sm,[Fi],[0.99,0.01,0.1,0.9])
f_al = Prob(Al,[Fi,Ta],[0.9999, 0.0001, 0.15, 0.85, 0.01, 0.99, 0.5, 0.5])
f_lv = Prob(Le,[Al],[0.999, 0.001, 0.12, 0.88])
f_re = Prob(Re,[Le],[0.99, 0.01, 0.25, 0.75])
bn2 = Belief_network([Al,Fi,Le,Re,Sm,Ta],[f_ta,f_fi,f_sm,f_al,f_lv,f_re])
Season = Variable("Season",["summer","winter"])
Sprinkler = Variable("Sprinkler",["on","off"])
Rained = Variable("Rained",boolean)
Grass_wet = Variable("Grass wet",boolean)
Grass_shiny = Variable("Grass shiny",boolean)
Shoes_wet = Variable("Shoes wet",boolean)
f_season = Prob(Season,[],[0.5,0.5])
f_sprinkler = Prob(Sprinkler,[Season],[0.9,0.1,0.05,0.95])
f_rained = Prob(Rained,[Season],[0.7,0.3,0.2,0.8])
f_wet = Prob(Grass_wet,[Sprinkler,Rained], [1,0,0.1,0.9,0.2,0.8,0.02,0.98])
f_shiny = Prob(Grass_shiny, [Grass_wet], [0.95,0.05,0.3,0.7])
f_shoes = Prob(Shoes_wet, [Grass_wet], [0.92,0.08,0.35,0.65])
bn3 = Belief_network([Season, Sprinkler, Rained, Grass_wet, Grass_shiny, Shoes_wet],
[f_season, f_sprinkler, f_rained, f_wet, f_shiny, f_shoes])