Variable ordering for exact inference. (#153)

* Add ordering code.

* Update CI.

* Update CI: `actions/cache@v4`.

* Julia 1.6 -> 1.8.

* Use Julia 1.8 in documentation workflow.

Author: samuelsonric

.github/workflows/CI.yml

@@ -16,8 +16,8 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - "1"   # Earliest
-          - "1.6" # Latest
+          - "1"   # Latest
+          - "1.8" # Earliest
         os:
           - ubuntu-latest
           - windows-latest
@@ -26,14 +26,14 @@ jobs:
           - x64
     steps:
       # check out the project and install Julia
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v4
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.version }}
           arch: ${{ matrix.arch }}
 
       # using a cache can speed up execution times
-      - uses: actions/cache@v2
+      - uses: actions/cache@v4
         env:
           cache-name: cache-artifacts
         with:
@@ -57,4 +57,4 @@ jobs:
         with:
           file: ./lcov.info
           flags: unittests
-          name: codecov-umbrella
+          name: codecov-umbrella

.github/workflows/Documentation.yml

@@ -14,7 +14,7 @@ jobs:
       - uses: actions/checkout@v2
       - uses: julia-actions/setup-julia@latest
         with:
-          version: '1.6'
+          version: '1.8'
       - name: Install LuaLatex
         run: sudo apt-get update && sudo apt-get install texlive-full --fix-missing && sudo apt-get install texlive-latex-extra && sudo mktexlsr && sudo updmap-sys
       - name: Install dependencies

Project.toml

@@ -3,6 +3,7 @@ uuid = "ba4760a4-c768-5bed-964b-cf806dc591cb"
 version = "3.4.1"
 
 [deps]
+CliqueTrees = "60701a23-6482-424a-84db-faee86b9b1f8"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
@@ -25,14 +26,15 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 
 [compat]
+CliqueTrees = "0.5.2"
 DataFrames = "0.22,1.0,1.1"
 DataStructures = "0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18"
 Discretizers = "3.0"
 Distributions = "0.17,0.18,0.19,0.20,0.21,0.22,0.23,0.24,0.25"
 Documenter = "0.26, 0.27"
 GraphPlot = "0.5"
-IterTools = "1.3"
 Graphs = "1.0"
+IterTools = "1.3"
 LightXML = "0.8,0.9"
 NBInclude = "2.0"
 Parameters = "0.10,0.11,0.12"
@@ -41,7 +43,7 @@ Reexport = "0.2, 1.0"
 Requires = "1.0.1"
 SpecialFunctions = "0.8,0.10,1.0,1.1,1.2,2"
 StatsBase = "0.25,0.26,0.27,0.28,0.29,0.30,0.31,0.32,0.33"
-julia = "1"
+julia = "1.8"
 
 [extras]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/BayesNets.jl

@@ -16,6 +16,7 @@ include(joinpath("CPDs", "cpds.jl"))
 @reexport using BayesNets.CPDs.ProbabilisticGraphicalModels
 
 import Base: *, /, +, -
+import CliqueTrees
 import DataStructures: PriorityQueue, peek
 import BayesNets.CPDs.ProbabilisticGraphicalModels: markov_blanket, is_independent, infer
 import StatsBase: sample, Weights

src/Inference/exact.jl

@@ -9,7 +9,9 @@ function infer(im::ExactInference, inf::InferenceState{BN}) where {BN<:DiscreteB
     nodes = names(bn)
     query = inf.query
     evidence = inf.evidence
-    hidden = setdiff(nodes, vcat(query, keys(evidence)))
+
+    # hidden = setdiff(nodes, vcat(query, keys(evidence)))
+    hidden = elimination_order(bn, query, evidence)
 
     factors = map(n -> Factor(bn, n, evidence), nodes)
 
@@ -31,3 +33,52 @@ function infer(im::ExactInference, inf::InferenceState{BN}) where {BN<:DiscreteB
 end
 infer(inf::InferenceState{BN}) where {BN<:DiscreteBayesNet} = infer(ExactInference(), inf)
 infer(bn::BN, query::NodeNameUnion; evidence::Assignment=Assignment()) where {BN<:DiscreteBayesNet} = infer(ExactInference(), InferenceState(bn, query, evidence))
+
+function elimination_order(bn::BayesNet, query::AbstractVector, evidence::AbstractDict)
+    order = Symbol[]
+    index = Dict{Symbol, Int}()
+
+    for v in names(bn)
+        if !haskey(evidence, v)
+            push!(order, v)
+            index[v] = length(order)
+        end
+    end
+
+    # construct reduced graph
+    matrix = spzeros(Int, length(order), length(order))
+
+    for v in order
+        i = index[v]
+        push!(rowvals(matrix), i)
+        push!(nonzeros(matrix), 1)
+
+        for w in children(bn, v)
+            if haskey(index, w)
+                j = index[w]
+                push!(rowvals(matrix), j)
+                push!(nonzeros(matrix), 1)
+            end
+        end
+
+        matrix.colptr[i + 1] = length(rowvals(matrix)) + 1
+    end
+
+    # moralize graph
+    matrix = matrix' * matrix
+
+    # make query variables a clique
+    n = length(query)
+    clique = Vector{Int}(undef, n)
+
+    for j in 1:n
+        clique[j] = index[query[j]]
+    end
+
+    matrix[clique, clique] .= 1
+    # alg = CliqueTrees.MF()  # minimum fill heuristic
+    alg = CliqueTrees.MMD() # minimum degree heuristic
+    # alg = CliqueTrees.MCS() # maximum cardinality search
+    perm, _ = CliqueTrees.permutation(matrix; alg=CliqueTrees.CompositeRotations(clique, alg))
+    return order[perm[1:end - n]]
+end