Bayes Nets

To install, run Pkg.add("BayesNets"). Visualization of Network structure is provided by the TikzGraphs package. Installation requirements (e.g., PGF/Tikz and pdf2svg) are provided here.



In [1]:

    
using BayesNets

Representation



In [2]:

    
b = BayesNet([:B, :S, :E, :D, :C])
addEdges!(b, [(:B, :E), (:S, :E), (:E, :D), (:E, :C)])









    Out[2]:



In [3]:

    
srand(0) # seed the random number generator to 0
setCPD!(b, :B, CPDs.Bernoulli(0.1))
setCPD!(b, :S, CPDs.Bernoulli(0.5))
setCPD!(b, :E, CPDs.Bernoulli([:B, :S], randBernoulliDict(2)))
setCPD!(b, :D, CPDs.Bernoulli([:E], randBernoulliDict(1)))
setCPD!(b, :C, CPDs.Bernoulli([:E], randBernoulliDict(1)));



In [4]:

    
parents(b, :E)









    Out[4]:





2-element Array{Symbol,1}:
 :B
 :S



In [5]:

    
domain(b, :C)









    Out[5]:





DiscreteDomain(Bool[false,true])

Tables and Operations (for discrete variables)



In [6]:

    
table(b, :D)









    Out[6]:




E D p
1 false false 0.72
2 true false 0.79
3 false true 0.28
4 true true 0.21



In [7]:

    
table(b, :B)









    Out[7]:




B p
1 false 0.9
2 true 0.1



In [8]:

    
bt = table(b, :B)
st = table(b, :S)
et = table(b, :E)
tt = bt * et * st









    Out[8]:




B S E p
1 false false false 0.08100000000000003
2 false false true 0.369
3 true false false 0.004999999999999999
4 true false true 0.045000000000000005
5 false true false 0.3735
6 false true true 0.07650000000000001
7 true true false 0.04100000000000001
8 true true true 0.009



In [9]:

    
tt = sumout(tt, [:B, :S])









    Out[9]:




E p
1 false 0.5005000000000001
2 true 0.4995

Computing Probability of Assignment



In [10]:

    
a = [
    :B=>0,
    :S=>1,
    :E=>0,
    :D=>1,
    :C=>1
]
prob(b, a)









    Out[10]:





0.005229000000000001

Sampling



In [11]:

    
rand(b)









    Out[11]:





Dict{Any,Any} with 5 entries:
  :D => false
  :B => false
  :C => false
  :E => false
  :S => true



In [12]:

    
srand(0)
randTable(b, numSamples=5)









    Out[12]:




B C D E S
1 false false false true false
2 true false false true true
3 false false true true false
4 false false false false false
5 true false true false true



In [13]:

    
srand(0)
t = randTable(b, numSamples=10, consistentWith=[:B=>true, :C=>false])









    Out[13]:




B C D E S
1 true false false true true
2 true false true false true
3 true false true true true



In [14]:

    
t = randTable(b, numSamples=100, consistentWith=[:B=>true, :C=>false])
estimate(t)









    Out[14]:




B C D E S p
1 true false false false true 0.5
2 true false false true false 0.25
3 true false false true true 0.25

Structure Learning



In [15]:

    
b = BayesNet([:A, :B, :C])
addEdge!(b, :A, :B)
setCPD!(b, :A, CPDs.Bernoulli(0.5))
setCPD!(b, :B, CPDs.Bernoulli(m->(m[:A] ? 0.5 : 0.45)))
setCPD!(b, :C, CPDs.Bernoulli(0.5))
b









    Out[15]:



In [16]:

    
d = randTable(b, numSamples = 5)









    Out[16]:




A B C
1 false true true
2 true true true
3 true true false
4 true true true
5 true true false



In [17]:

    
count(b, d)









    Out[17]:




A count
1 false 1
2 true 4
A B count
1 false true 1
2 true true 4
C count
1 true 3
2 false 2



In [18]:

    
logBayesScore(b, d)









    Out[18]:





-9.798127036878302



In [19]:

    
b = BayesNet([:A, :B, :C])









    Out[19]:



In [20]:

    
logBayesScore(b, d)









    Out[20]:





-9.287301413112312

	B	S	E	p
1	false	false	false	0.08100000000000003
2	false	false	true	0.369
3	true	false	false	0.004999999999999999
4	true	false	true	0.045000000000000005
5	false	true	false	0.3735
6	false	true	true	0.07650000000000001
7	true	true	false	0.04100000000000001
8	true	true	true	0.009