Add rrule for mean

Project.toml

@@ -7,6 +7,7 @@ Cassette = "7057c7e9-c182-5462-911a-8362d720325c"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
 Cassette = "^0.2"

src/ChainRules.jl

@@ -2,6 +2,7 @@ module ChainRules
 
 using Cassette
 using LinearAlgebra
+using Statistics
 using Base.Broadcast: materialize, materialize!, broadcasted, Broadcasted, broadcastable
 
 import NaNMath, SpecialFunctions, LinearAlgebra, LinearAlgebra.BLAS

src/rules/mapreduce.jl

@@ -62,3 +62,25 @@ function rrule(::typeof(sum), ::typeof(abs2), x::AbstractArray{<:Real}; dims=:)
     ∂x = Rule(ȳ -> 2ȳ .* x)
     return y, (DNERule(), ∂x)
 end
+
+#####
+##### `mean`
+#####
+
+_denom(x, dims::Colon) = length(x)
+_denom(x, dims::Integer) = size(x, dims)
+_denom(x, dims) = mapreduce(i->size(x, i), Base.mul_prod, unique(dims), init=1)
+
+# TODO: We have `mean(f, x; dims)` as of 1.3.0-DEV.36
+
+function rrule(::typeof(mean), x::AbstractArray{<:Real}; dims=:)
+    _, dx = rrule(sum, x; dims=dims)
+    n = _denom(x, dims)
+    return mean(x; dims=dims), Rule(ȳ -> dx(ȳ) / n)
+end
+
+function rrule(::typeof(mean), f, x::AbstractArray{<:Real})
+    _, (_, dx) = rrule(sum, f, x)
+    n = _denom(x, :)
+    return mean(f, x), (DNERule(), Rule(ȳ -> dx(ȳ) / n))
+end

test/rules/mapreduce.jl

@@ -64,4 +64,15 @@
             @test x̄_ad ≈ x̄_fd atol=1e-9 rtol=1e-9
         end
     end
+    @testset "mean" begin
+        rng = MersenneTwister(999)
+        n = 9
+        rrule_test(mean, randn(rng), (abs2, nothing), (randn(rng, n), randn(rng, n)))
+        X = randn(rng, n, n)
+        y, dX = rrule(mean, X; dims=1)
+        ȳ = randn(rng, size(y))
+        X̄_ad = dX(ȳ)
+        X̄_fd = j′vp(central_fdm(5, 1), x->mean(x, dims=1), ȳ, X)
+        @test X̄_ad ≈ X̄_fd rtol=1e-9 atol=1e-9
+    end
 end

test/runtests.jl

@@ -1,6 +1,6 @@
 # TODO: more tests!
 
-using ChainRules, Test, FDM, LinearAlgebra, Random
+using ChainRules, Test, FDM, LinearAlgebra, Random, Statistics
 using ChainRules: extern, accumulate, accumulate!, store!, @scalar_rule,
     Wirtinger, wirtinger_primal, wirtinger_conjugate, add_wirtinger, mul_wirtinger,
     Zero, add_zero, mul_zero, One, add_one, mul_one, Casted, cast, add_casted, mul_casted,