refactor rewrite the documentation for the global interfaces

src/AdvancedVI.jl

@@ -27,40 +27,42 @@ using StatsBase
 
 # derivatives
 """
-    value_and_gradient!(
-        ad::ADTypes.AbstractADType,
-        f,
-        θ::AbstractVector{<:Real},
-        out::DiffResults.MutableDiffResult
-    )
-
-Evaluate the value and gradient of a function `f` at `θ` using the automatic differentiation backend `ad`.
-The result is stored in `out`. 
-The function `f` must return a scalar value.
-The gradient is stored in `out` as a vector of the same length as `θ`.
+    value_and_gradient!(ad, f, θ, out)
+
+Evaluate the value and gradient of a function `f` at `θ` using the automatic differentiation backend `ad` and store the result in `out`.
+
+# Arguments
+- `ad::ADTypes.AbstractADType`: Automatic differentiation backend. 
+- `f`: Function subject to differentiation.
+- `θ`: The point to evaluate the gradient.
+- `out::DiffResults.MutableDiffResult`: Buffer to contain the output gradient and function value.
 """
 function value_and_gradient! end
 
 # estimators
 """
     AbstractVariationalObjective
 
-An VI algorithm supported by `AdvancedVI` should implement a subtype of  `AbstractVariationalObjective`.
-Furthermore, it should implement the functions `estimate_gradient`.
+Abstract type for the VI algorithms supported by `AdvancedVI`.
+
+# Implementations
+To be supported by `AdvancedVI`, a VI algorithm must implement `AbstractVariationalObjective`.
+Also, it should provide gradients by implementing the function `estimate_gradient!`.
 If the estimator is stateful, it can implement `init` to initialize the state.
 """
 abstract type AbstractVariationalObjective end
 
 """
-    init(
-        rng::Random.AbstractRNG,
-        obj::AbstractVariationalObjective,
-        λ::AbstractVector,
-        restructure
-    )
+    init(rng, obj, λ, restructure)
 
 Initialize a state of the variational objective `obj` given the initial variational parameters `λ`.
 This function needs to be implemented only if `obj` is stateful.
+
+# Arguments
+- `rng::Random.AbstractRNG`: Random number generator.
+- `obj::AbstractVariationalObjective`: Variational objective.
+- `λ`: Initial variational parameters.
+- `restructure`: Function that reconstructs the variational approximation from `λ`.
 """
 init(
     ::Random.AbstractRNG,
@@ -70,25 +72,24 @@ init(
 ) = nothing
 
 """
-    estimate_gradient!(
-        rng         ::Random.AbstractRNG,
-        obj         ::AbstractVariationalObjective,
-        adbackend   ::ADTypes.AbstractADType,
-        out         ::DiffResults.MutableDiffResult
-        prob,
-        λ,
-        restructure,
-        obj_state,
-    )
-
-Estimate (possibly stochastic) gradients of the objective `obj` targeting `prob` with respect to the variational parameters `λ` using the automatic differentiation backend `adbackend`.
-The estimated objective value and gradient are then stored in `out`.
-If the objective is stateful, `obj_state` is its previous state, otherwise, it is `nothing`.
+    estimate_gradient!(rng, obj, adbackend, out, prob, λ, restructure, obj_state)
+
+Estimate (possibly stochastic) gradients of the variational objective `obj` targeting `prob` with respect to the variational parameters `λ`
+
+# Arguments
+- `rng::Random.AbstractRNG`: Random number generator.
+- `obj::AbstractVariationalObjective`: Variational objective.
+- `adbackend::ADTypes.AbstractADType`: Automatic differentiation backend. 
+- `out::DiffResults.MutableDiffResult`: Buffer containing the objective value and gradient estimates. 
+- `prob`: The target log-joint likelihood implementing the `LogDensityProblem` interface.
+- `λ`: Variational parameters to evaluate the gradient on.
+- `restructure`: Function that reconstructs the variational approximation from `λ`.
+- `obj_state`: Previous state of the objective.
 
 # Returns
-- `out`: The `MutableDiffResult` containing the objective value and gradient estimates.
-- `obj_state`: The updated state of the objective estimator.
-- `stat`: Statistics and logs generated during estimation. (Type: `<: NamedTuple`)
+- `out::MutableDiffResult`: Buffer containing the objective value and gradient estimates.
+- `obj_state`: The updated state of the objective.
+- `stat::NamedTuple`: Statistics and logs generated during estimation.
 """
 function estimate_gradient! end