Add Willmott index of agreement

src/continuous.jl

@@ -545,3 +545,55 @@ RSquared
 const rsq = RSquared()
 "$RSquaredDoc"
 const rsquared = rsq
+
+# -------------------------------------------------------------------------
+# Willmott index of agreement (d)
+
+# type for measure without argument checks:
+struct _WillmottD end
+
+function (::_WillmottD)(yhat, y)
+    μ = aggregate(y)  # mean
+    # numerator: Σ_i (ŷ_i - y_i)^2
+    num = LPSumLoss(p=2)(yhat, y)
+    # denominator: Σ_i (|ŷ_i - μ| + |y_i - μ|)^2
+    den = multimeasure((yhat, y) -> (abs(yhat - μ) + abs(y - μ))^2; mode=Sum())(yhat, y)
+    return den == 0 ? (num == 0 ? 1.0 : 0.0) : 1 - num/den
+end
+
+WillmottD() = _WillmottD() |> API.robust_measure |> API.fussy_measure
+const WillmottDType = API.FussyMeasure{<:API.RobustMeasure{<:_WillmottD}}
+
+@trait(
+    _WillmottD,
+    consumes_multiple_observations = true,
+    kind_of_proxy = LearnAPI.Point(),
+    observation_scitype = Union{Missing,Infinite},
+    orientation = Score(),
+    human_name = "Willmott index of agreement (d)",
+)
+
+@fix_show WillmottD::WillmottDType
+
+register(WillmottD, "willmott_d")
+
+const WillmottDDoc = docstring(
+    "WillmottD()",
+    scitype=DOC_INFINITE,
+    body=
+"""
+Returns Willmott index of agreement (d)
+
+``d = 1 - \\dfrac{\\sum (ŷ_i - y_i)^2}{\\sum (|ŷ_i - \\bar y| + |y_i - \\bar y|)^2}``,
+
+where ``\\bar y`` is the mean of the targets. The value lies in ``[0,1]`` with higher
+being better.
+
+References: Willmott [(1981)](https://doi.org/10.1080/02723646.1981.10642213)
+""",
+)
+
+"$WillmottDDoc"
+WillmottD
+"$WillmottDDoc"
+const willmott_d = WillmottD()

test/continuous.jl

@@ -31,6 +31,16 @@ rng = srng(666899)
     yhat = rand(rng, 4)
     @test isapprox(log_cosh(yhat, y), mean(log.(cosh.(yhat - y))))
     @test rsq(yhat, y) == 1 - sum((yhat - y).^2)/sum((y .- mean(y)).^2)
+    let
+        num = sum((yhat - y).^2)
+        den = sum((abs.(yhat .- mean(y)) .+ abs.(y .- mean(y))).^2)
+        @test isapprox(willmott_d(yhat, y), den == 0 ? (num == 0 ? 1.0 : 0.0) : 1 - num/den)
+        # additional tests for willmott_d
+        @test willmott_d(yhat, yhat) == 1
+        @test willmott_d(y, y) == 1
+        @test willmott_d(yhat .+ 1, zeros(length(yhat))) == 0  # yhat .+ 1 ensures it's not all zeros
+        @test willmott_d(zeros(4), zeros(4)) == 1
+    end
 
     # a multi-target test where there is a parameter:
     y   = rand(rng, 2, 10)