Use a faster implementation of AliasTables (#1848)

* switch to AliasTables.jl

* retune heuristic

* add test for #832

* add more tests

* move alias table import and tighten from using to import

* Back out multinomial heuristic adjustment at @adienes's request

* Update test/univariate/discrete/categorical.jl (style)

Co-authored-by: David Widmann <[email protected]>

---------

Co-authored-by: David Widmann <[email protected]>

Project.toml

@@ -4,6 +4,7 @@ authors = ["JuliaStats"]
 version = "0.25.107"
 
 [deps]
+AliasTables = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
@@ -30,6 +31,7 @@ DistributionsDensityInterfaceExt = "DensityInterface"
 DistributionsTestExt = "Test"
 
 [compat]
+AliasTables = "1"
 Aqua = "0.8"
 Calculus = "0.5"
 ChainRulesCore = "1"

src/Distributions.jl

@@ -27,6 +27,8 @@ import PDMats: dim, PDMat, invquad
 using SpecialFunctions
 using Base.MathConstants: eulergamma
 
+import AliasTables
+
 export
     # re-export Statistics
     mean, median, quantile, std, var, cov, cor,

src/samplers/aliastable.jl

@@ -1,22 +1,7 @@
 struct AliasTable <: Sampleable{Univariate,Discrete}
-    accept::Vector{Float64}
-    alias::Vector{Int}
+    at::AliasTables.AliasTable{UInt64, Int}
+    AliasTable(probs::AbstractVector{<:Real}) = new(AliasTables.AliasTable(probs))
 end
-ncategories(s::AliasTable) = length(s.alias)
-
-function AliasTable(probs::AbstractVector)
-    n = length(probs)
-    n > 0 || throw(ArgumentError("The input probability vector is empty."))
-    accp = Vector{Float64}(undef, n)
-    alias = Vector{Int}(undef, n)
-    StatsBase.make_alias_table!(probs, 1.0, accp, alias)
-    AliasTable(accp, alias)
-end
-
-function rand(rng::AbstractRNG, s::AliasTable)
-    i = rand(rng, 1:length(s.alias)) % Int
-    # using `ifelse` improves performance here: github.com/JuliaStats/Distributions.jl/pull/1831/
-    ifelse(rand(rng) < s.accept[i],  i, s.alias[i])
-end
-
+ncategories(s::AliasTable) = length(s.at)
+rand(rng::AbstractRNG, s::AliasTable) = rand(rng, s.at)
 show(io::IO, s::AliasTable) = @printf(io, "AliasTable with %d entries", ncategories(s))

test/samplers.jl

@@ -31,9 +31,11 @@ import Distributions:
         @testset "p=$p" for p in Any[[1.0], [0.3, 0.7], [0.2, 0.3, 0.4, 0.1]]
             test_samples(S(p), Categorical(p), n_tsamples)
             test_samples(S(p), Categorical(p), n_tsamples, rng=rng)
+            @test ncategories(S(p)) == length(p)
         end
     end
 
+    @test string(AliasTable(Float16[1,2,3])) == "AliasTable with 3 entries"
 
     ## Binomial samplers
 

test/univariate/discrete/categorical.jl

@@ -93,9 +93,9 @@ end
 end
 
 @testset "reproducibility across julia versions" begin
-    d= Categorical([0.1, 0.2, 0.7])
+    d = Categorical([0.1, 0.2, 0.7])
     rng = StableRNGs.StableRNG(600)
-    @test rand(rng, d, 10) == [2, 1, 3, 3, 2, 3, 3, 3, 3, 3]
+    @test rand(rng, d, 10) == [3, 1, 1, 2, 3, 2, 3, 3, 2, 3]
 end
 
 @testset "comparisons" begin
@@ -124,4 +124,17 @@ end
     @test Categorical([0.5, 0.5]) ≈ Categorical([0.5f0, 0.5f0])
 end
 
+@testset "issue #832" begin
+    priorities = collect(Float64, 1:1000)
+    priorities[1:50] .= 1e8
+
+    at = Distributions.AliasTable(priorities)
+    iat = rand(at, 16)
+
+    # failure rate of a single sample is sum(51:1000)/50e8 = 9.9845e-5
+    # failure rate of 4 out of 16 samples is 1-cdf(Binomial(16, 9.9845e-5), 3) = 1.8074430840897548e-13
+    # this test should randomly fail with a probability of 1.8074430840897548e-13
+    @test count(==(1e8), priorities[iat]) >= 13
+end
+
 end