Creating Bayesian network structures
The graphical structure of a Bayesian network are stored in objects of class
bn. They can be created in various ways through three
possible representations: the arc set, the adjacency matrix
and them model formula. In addition it's possible to create empty
and random network structures with the empty.graph and
random.graph functions.
Creating an empty network
> library(bnlearn)
> e = empty.graph(LETTERS[1:6])
> e
Randomly generated Bayesian network
model:
[A][B][C][D][E][F]
nodes: 6
arcs: 0
undirected arcs: 0
directed arcs: 0
average markov blanket size: 0.00
average neighbourhood size: 0.00
average branching factor: 0.00
generation algorithm: Empty
Creating a network structure
with a specific arc set
> arc.set = matrix(c("A", "C", "B", "F", "C", "F"),
+ ncol = 2, byrow = TRUE)
> arc.set
[,1] [,2]
[1,] "A" "C"
[2,] "B" "F"
[3,] "C" "F"
> arcs(e) = arc.set
> e
Randomly generated Bayesian network
model:
[A][B][D][E][C|A][F|B:C]
nodes: 6
arcs: 3
undirected arcs: 0
directed arcs: 3
average markov blanket size: 1.33
average neighbourhood size: 1.00
average branching factor: 0.50
generation algorithm: Empty
with a specific adjacency matrix
> adj = matrix(0L, ncol = 6, nrow = 6,
+ dimnames = list(LETTERS[1:6], LETTERS[1:6]))
> adj["A", "C"] = 1L
> adj["B", "F"] = 1L
> adj["C", "F"] = 1L
> adj["D", "E"] = 1L
> adj["A", "E"] = 1L
> adj
A B C D E F
A 0 0 1 0 1 0
B 0 0 0 0 0 1
C 0 0 0 0 0 1
D 0 0 0 0 1 0
E 0 0 0 0 0 0
F 0 0 0 0 0 0
> amat(e) = adj
> e
Randomly generated Bayesian network
model:
[A][B][D][C|A][E|A:D][F|B:C]
nodes: 6
arcs: 5
undirected arcs: 0
directed arcs: 5
average markov blanket size: 2.33
average neighbourhood size: 1.67
average branching factor: 0.83
generation algorithm: Empty
with a specific model formula
There are two ways to do this:- with the
model2networkfunction:> model2network("[A][C][B|A][D|C][F|A:B:C][E|F]") Randomly generated Bayesian network model: [A][C][B|A][D|C][F|A:B:C][E|F] nodes: 6 arcs: 6 undirected arcs: 0 directed arcs: 6 average markov blanket size: 2.67 average neighbourhood size: 2.00 average branching factor: 1.00 generation algorithm: Empty - via direct assignment, as for the arc set or the adjacency matrix:
> modelstring(e) = "[A][C][B|A][D|C][F|A:B:C][E|F]" > e Randomly generated Bayesian network model: [A][C][B|A][D|C][F|A:B:C][E|F] nodes: 6 arcs: 6 undirected arcs: 0 directed arcs: 6 average markov blanket size: 2.67 average neighbourhood size: 2.00 average branching factor: 1.00 generation algorithm: Empty
Creating one or more random network structures
with a specified node ordering
> random.graph(LETTERS[1:6], num = 3)
[[1]]
Randomly generated Bayesian network
model:
[A][B|A][C|A][D|B][E|A:C:D][F|B:C:E]
nodes: 6
arcs: 9
undirected arcs: 0
directed arcs: 9
average markov blanket size: 4.33
average neighbourhood size: 3.00
average branching factor: 1.50
generation algorithm: Full Ordering
arc sampling probability: 0.4
[[2]]
Randomly generated Bayesian network
model:
[A][B][C][D|B][E|A][F|A:E]
nodes: 6
arcs: 4
undirected arcs: 0
directed arcs: 4
average markov blanket size: 1.33
average neighbourhood size: 1.33
average branching factor: 0.67
generation algorithm: Full Ordering
arc sampling probability: 0.4
[[3]]
Randomly generated Bayesian network
model:
[A][B][C][D|A][E|B:C][F|A:B:E]
nodes: 6
arcs: 6
undirected arcs: 0
directed arcs: 6
average markov blanket size: 3.00
average neighbourhood size: 2.00
average branching factor: 1.00
generation algorithm: Full Ordering
arc sampling probability: 0.4
sampling from the space of connected directed acyclic graphs with uniform probability
> random.graph(LETTERS[1:6], num = 2, method = "ic-dag")
[[1]]
Randomly generated Bayesian network
model:
[E][C|E][B|C:E][A|B:E][F|A:B:C:E][D|A:B:C:F]
nodes: 6
arcs: 13
undirected arcs: 0
directed arcs: 13
average markov blanket size: 4.67
average neighbourhood size: 4.33
average branching factor: 2.17
generation algorithm: Ide & Cozman's Multiconnected DAGs
burn in length: 216
maximum in-degree: Inf
maximum out-degree: Inf
maximum degree: Inf
[[2]]
Randomly generated Bayesian network
model:
[E][B|E][C|E][A|B:E][F|A:B:C:E][D|A:B:C:F]
nodes: 6
arcs: 12
undirected arcs: 0
directed arcs: 12
average markov blanket size: 4.67
average neighbourhood size: 4.00
average branching factor: 2.00
generation algorithm: Ide & Cozman's Multiconnected DAGs
burn in length: 216
maximum in-degree: Inf
maximum out-degree: Inf
maximum degree: Inf
sampling from the space of the directed acyclic graphs with uniform probability
> random.graph(LETTERS[1:6], num = 2, method = "melancon")
[[1]]
Randomly generated Bayesian network
model:
[D][E|D][C|D:E][F|C:E][A|C:D:F][B|A:D]
nodes: 6
arcs: 10
undirected arcs: 0
directed arcs: 10
average markov blanket size: 3.67
average neighbourhood size: 3.33
average branching factor: 1.67
generation algorithm: Melancon's Uniform Probability DAGs
burn in length: 216
maximum in-degree: Inf
maximum out-degree: Inf
maximum degree: Inf
[[2]]
Randomly generated Bayesian network
model:
[D][E|D][C|D:E][F|C:E][A|C:D:F][B|A:C:D]
nodes: 6
arcs: 11
undirected arcs: 0
directed arcs: 11
average markov blanket size: 4.00
average neighbourhood size: 3.67
average branching factor: 1.83
generation algorithm: Melancon's Uniform Probability DAGs
burn in length: 216
maximum in-degree: Inf
maximum out-degree: Inf
maximum degree: Inf
