Factor out homoscadasticity check in elbo

src/SparseVariationalApproximationModule.jl

@@ -306,26 +306,16 @@ Statistics. PMLR, 2015.
 """
 function AbstractGPs.elbo(
     sva::SparseVariationalApproximation,
-    fx::FiniteGP{<:AbstractGP,<:AbstractVector,<:Union{Diagonal{<:Real,<:Fill},ScalMat}},
+    fx::FiniteGP,
     y::AbstractVector{<:Real};
     num_data=length(y),
     quadrature=DefaultExpectationMethod(),
 )
-    σ² = fx.Σy[1]
+    σ² = _get_homoscedastic_noise(fx.Σy)
     lik = GaussianLikelihood(σ²)
     return elbo(sva, LatentFiniteGP(fx, lik), y; num_data, quadrature)
 end
 
-function AbstractGPs.elbo(
-    ::SparseVariationalApproximation, ::FiniteGP, ::AbstractVector; kwargs...
-)
-    return error(
-        "The observation noise fx.Σy must be homoscedastic.\n",
-        "To avoid this error, construct fx using: f = GP(kernel); fx = f(x, σ²)",
-        ", where σ² is a positive Real.",
-    )
-end
-
 """
     elbo(
         sva::SparseVariationalApproximation,
@@ -372,4 +362,13 @@ function _prior_kl(sva::SparseVariationalApproximation{NonCentered})
     return (trace_term + m_ε'm_ε - length(m_ε) - logdet(C_ε)) / 2
 end
 
+_get_homoscedastic_noise(Σy::Union{Diagonal{<:Real,<:Fill},ScalMat}) = Σy[1]
+function _get_homoscedastic_noise(_)
+    return error(
+        "The observation noise fx.Σy must be homoscedastic.\n",
+        "To avoid this error, construct fx using: f = GP(kernel); fx = f(x, σ²)",
+        ", where σ² is a positive Real.\n"
+    )
+end
+
 end