Use ChangesOfVariables and InverseFunctions

Project.toml

@@ -1,13 +1,15 @@
 name = "Bijectors"
 uuid = "76274a88-744f-5084-9051-94815aaf08c4"
-version = "0.9.11"
+version = "0.10.0"
 
 [deps]
 ArgCheck = "dce04be8-c92d-5529-be00-80e4d2c0e197"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Functors = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
+InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
 IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LogExpFunctions = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
@@ -22,9 +24,11 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 [compat]
 ArgCheck = "1, 2"
 ChainRulesCore = "0.10.11, 1"
+ChangesOfVariables = "0.1"
 Compat = "3"
 Distributions = "0.23.3, 0.24, 0.25"
 Functors = "0.1, 0.2"
+InverseFunctions = "0.1"
 IrrationalConstants = "0.1"
 LogExpFunctions = "0.3.3"
 MappedArrays = "0.2.2, 0.3, 0.4"

README.md

@@ -18,13 +18,13 @@ The following table lists mathematical operations for a bijector and the corresp
 
 | Operation                          | Method          | Automatic |
 |:------------------------------------:|:-----------------:|:-----------:|
-| `b ↦ b⁻¹`                                      | `inv(b)`                | ✓         |
+| `b ↦ b⁻¹`                                      | `inverse(b)`                | ✓         |
 | `(b₁, b₂) ↦ (b₁ ∘ b₂)`                         | `b₁ ∘ b₂`               | ✓         |
 | `(b₁, b₂) ↦ [b₁, b₂]`                          | `stack(b₁, b₂)`         | ✓         |
 | `x ↦ b(x)`                                     | `b(x)`                  | ×         |
-| `y ↦ b⁻¹(y)`                                   | `inv(b)(y)`             | ×         |
+| `y ↦ b⁻¹(y)`                                   | `inverse(b)(y)`             | ×         |
 | `x ↦ log｜det J(b, x)｜`                       | `logabsdetjac(b, x)`    | AD        |
-| `x ↦ b(x), log｜det J(b, x)｜`                 | `forward(b, x)`         | ✓         |
+| `x ↦ b(x), log｜det J(b, x)｜`                 | `with_logabsdet_jacobian(b, x)`         | ✓         |
 | `p ↦ q := b_* p`                                | `q = transformed(p, b)` | ✓         |
 | `y ∼ q`                                        | `y = rand(q)`           | ✓         |
 | `p ↦ b` such that `support(b_* p) = ℝᵈ`               | `bijector(p)`           | ✓         |
@@ -123,7 +123,7 @@ true
 What about `invlink`?
 
 ```julia
-julia> b⁻¹ = inv(b)
+julia> b⁻¹ = inverse(b)
 Inverse{Logit{Float64},0}(Logit{Float64}(0.0, 1.0))
 
 julia> b⁻¹(y)
@@ -133,7 +133,7 @@ julia> b⁻¹(y) ≈ invlink(dist, y)
 true
 ```
 
-Pretty neat, huh? `Inverse{Logit}` is also a `Bijector` where we've defined `(ib::Inverse{<:Logit})(y)` as the inverse transformation of `(b::Logit)(x)`. Note that it's not always the case that `inv(b) isa Inverse`, e.g. the inverse of `Exp` is simply `Log` so `inv(Exp()) isa Log` is true.
+Pretty neat, huh? `Inverse{Logit}` is also a `Bijector` where we've defined `(ib::Inverse{<:Logit})(y)` as the inverse transformation of `(b::Logit)(x)`. Note that it's not always the case that `inverse(b) isa Inverse`, e.g. the inverse of `Exp` is simply `Log` so `inverse(Exp()) isa Log` is true.
 
 #### Dimensionality
 One more thing. See the `0` in `Inverse{Logit{Float64}, 0}`? It represents the *dimensionality* of the bijector, in the same sense as for an `AbstractArray` with the exception of `0` which means it expects 0-dim input and output, i.e. `<:Real`. This can also be accessed through `dimension(b)`:
@@ -162,7 +162,7 @@ true
 And since `Composed isa Bijector`:
 
 ```julia
-julia> id_x = inv(id_y)
+julia> id_x = inverse(id_y)
 Composed{Tuple{Inverse{Logit{Float64},0},Logit{Float64}},0}((Inverse{Logit{Float64},0}(Logit{Float64}(0.0, 1.0)), Logit{Float64}(0.0, 1.0)))
 
 julia> id_x(x) ≈ x
@@ -199,9 +199,9 @@ julia> logpdf_forward(td, x)
 -1.123311289915276
 ```
 
-#### `logabsdetjac` and `forward`
+#### `logabsdetjac` and `with_logabsdet_jacobian`
 
-In the computation of both `logpdf` and `logpdf_forward` we need to compute `log(abs(det(jacobian(inv(b), y))))` and `log(abs(det(jacobian(b, x))))`, respectively. This computation is available using the `logabsdetjac` method
+In the computation of both `logpdf` and `logpdf_forward` we need to compute `log(abs(det(jacobian(inverse(b), y))))` and `log(abs(det(jacobian(b, x))))`, respectively. This computation is available using the `logabsdetjac` method
 
 ```julia
 julia> logabsdetjac(b⁻¹, y)
@@ -218,21 +218,21 @@ julia> logabsdetjac(b, x) ≈ -logabsdetjac(b⁻¹, y)
 true
 ```
 
-which is always the case for a differentiable bijection with differentiable inverse. Therefore if you want to compute `logabsdetjac(b⁻¹, y)` and we know that `logabsdetjac(b, b⁻¹(y))` is actually more efficient, we'll return `-logabsdetjac(b, b⁻¹(y))` instead. For some bijectors it might be easy to compute, say, the forward pass `b(x)`, but expensive to compute `b⁻¹(y)`. Because of this you might want to avoid doing anything "backwards", i.e. using `b⁻¹`. This is where `forward` comes to good use:
+which is always the case for a differentiable bijection with differentiable inverse. Therefore if you want to compute `logabsdetjac(b⁻¹, y)` and we know that `logabsdetjac(b, b⁻¹(y))` is actually more efficient, we'll return `-logabsdetjac(b, b⁻¹(y))` instead. For some bijectors it might be easy to compute, say, the forward pass `b(x)`, but expensive to compute `b⁻¹(y)`. Because of this you might want to avoid doing anything "backwards", i.e. using `b⁻¹`. This is where `with_logabsdet_jacobian` comes to good use:
 
 ```julia
-julia> forward(b, x)
-(rv = -0.5369949942509267, logabsdetjac = 1.4575353795716655)
+julia> with_logabsdet_jacobian(b, x)
+(-0.5369949942509267, 1.4575353795716655)
 ```
 
 Similarily
 
 ```julia
-julia> forward(inv(b), y)
-(rv = 0.3688868996596376, logabsdetjac = -1.4575353795716655)
+julia> with_logabsdet_jacobian(inverse(b), y)
+(0.3688868996596376, -1.4575353795716655)
 ```
 
-In fact, the purpose of `forward` is to just _do the right thing_, not necessarily "forward". In this function we'll have access to both the original value `x` and the transformed value `y`, so we can compute `logabsdetjac(b, x)` in either direction. Furthermore, in a lot of cases we can re-use a lot of the computation from `b(x)` in the computation of `logabsdetjac(b, x)`, or vice-versa. `forward(b, x)` will take advantage of such opportunities (if implemented).
+In fact, the purpose of `with_logabsdet_jacobian` is to just _do the right thing_, not necessarily "forward". In this function we'll have access to both the original value `x` and the transformed value `y`, so we can compute `logabsdetjac(b, x)` in either direction. Furthermore, in a lot of cases we can re-use a lot of the computation from `b(x)` in the computation of `logabsdetjac(b, x)`, or vice-versa. `with_logabsdet_jacobian(b, x)` will take advantage of such opportunities (if implemented).
 
 #### Sampling from `TransformedDistribution`
 At this point we've only shown that we can replicate the existing functionality. But we said `TransformedDistribution isa Distribution`, so we also have `rand`:
@@ -241,7 +241,7 @@ At this point we've only shown that we can replicate the existing functionality.
 julia> y = rand(td)              # ∈ ℝ
 0.999166054552483
 
-julia> x = inv(td.transform)(y)  # transform back to interval [0, 1]
+julia> x = inverse(td.transform)(y)  # transform back to interval [0, 1]
 0.7308945834125756
 ```
 
@@ -261,7 +261,7 @@ Beta{Float64}(α=2.0, β=2.0)
 julia> b = bijector(dist)              # (0, 1) → ℝ
 Logit{Float64}(0.0, 1.0)
 
-julia> b⁻¹ = inv(b)                    # ℝ → (0, 1)
+julia> b⁻¹ = inverse(b)                    # ℝ → (0, 1)
 Inverse{Logit{Float64},0}(Logit{Float64}(0.0, 1.0))
 
 julia> td = transformed(Normal(), b⁻¹) # x ∼ 𝓝(0, 1) then b(x) ∈ (0, 1)
@@ -280,7 +280,7 @@ It's worth noting that `support(Beta)` is the _closed_ interval `[0, 1]`, while
 ```julia
 td = transformed(Beta())
 
-inv(td.transform)(rand(td))
+inverse(td.transform)(rand(td))
 ```
 
 will never result in `0` or `1` though any sample arbitrarily close to either `0` or `1` is possible. _Disclaimer: numerical accuracy is limited, so you might still see `0` and `1` if you're lucky._
@@ -335,7 +335,7 @@ julia> # Construct the transform
        bs = bijector.(dists)     # constrained-to-unconstrained bijectors for dists
 (Logit{Float64}(0.0, 1.0), Log{0}(), SimplexBijector{true}())
 
-julia> ibs = inv.(bs)            # invert, so we get unconstrained-to-constrained
+julia> ibs = inverse.(bs)            # invert, so we get unconstrained-to-constrained
 (Inverse{Logit{Float64},0}(Logit{Float64}(0.0, 1.0)), Exp{0}(), Inverse{SimplexBijector{true},1}(SimplexBijector{true}()))
 
 julia> sb = Stacked(ibs, ranges) # => Stacked <: Bijector
@@ -411,7 +411,7 @@ Similarily to the multivariate ADVI example, we could use `Stacked` to get a _bo
 ```julia
 julia> d = MvNormal(zeros(2), ones(2));
 
-julia> ibs = inv.(bijector.((InverseGamma(2, 3), Beta())));
+julia> ibs = inverse.(bijector.((InverseGamma(2, 3), Beta())));
 
 julia> sb = stack(ibs...) # == Stacked(ibs) == Stacked(ibs, [i:i for i = 1:length(ibs)]
 Stacked{Tuple{Exp{0},Inverse{Logit{Float64},0}},2}((Exp{0}(), Inverse{Logit{Float64},0}(Logit{Float64}(0.0, 1.0))), (1:1, 2:2))
@@ -481,7 +481,7 @@ julia> Flux.params(flow)
 Params([[-1.05099; 0.502079] (tracked), [-0.216248; -0.706424] (tracked), [-4.33747] (tracked)])
 ```
 
-Another useful function is the `forward(d::Distribution)` method. It is similar to `forward(b::Bijector)` in the sense that it does a forward pass of the entire process "sample then transform" and returns all the most useful quantities in process using the most efficent computation path.
+Another useful function is the `forward(d::Distribution)` method. It is similar to `with_logabsdet_jacobian(b::Bijector, x)` in the sense that it does a forward pass of the entire process "sample then transform" and returns all the most useful quantities in process using the most efficent computation path.
 
 ```julia
 julia> x, y, logjac, logpdf_y = forward(flow) # sample + transform and returns all the useful quantities in one pass
@@ -542,41 +542,43 @@ Logit{Float64}(0.0, 1.0)
 julia> b(0.6)
 0.4054651081081642
 
-julia> inv(b)(y)
+julia> inverse(b)(y)
 Tracked 2-element Array{Float64,1}:
  0.3078149833748082
  0.72380041667891  
 
 julia> logabsdetjac(b, 0.6)
 1.4271163556401458
 
-julia> logabsdetjac(inv(b), y) # defaults to `- logabsdetjac(b, inv(b)(x))`
+julia> logabsdetjac(inverse(b), y) # defaults to `- logabsdetjac(b, inverse(b)(x))`
 Tracked 2-element Array{Float64,1}:
  -1.546158373866469 
  -1.6098711387913573
 
-julia> forward(b, 0.6)         # defaults to `(rv=b(x), logabsdetjac=logabsdetjac(b, x))`
-(rv = 0.4054651081081642, logabsdetjac = 1.4271163556401458)
+julia> with_logabsdet_jacobian(b, 0.6)         # defaults to `(b(x), logabsdetjac(b, x))`
+(0.4054651081081642, 1.4271163556401458)
 ```
 
-For further efficiency, one could manually implement `forward(b::Logit, x)`:
+For further efficiency, one could manually implement `with_logabsdet_jacobian(b::Logit, x)`:
 
 ```julia
-julia> import Bijectors: forward, Logit
+julia> using Bijectors: Logit
 
-julia> function forward(b::Logit{<:Real}, x)
+julia> import Bijectors: with_logabsdet_jacobian
+
+julia> function with_logabsdet_jacobian(b::Logit{<:Real}, x)
            totally_worth_saving = @. (x - b.a) / (b.b - b.a)  # spoiler: it's probably not
            y = logit.(totally_worth_saving)
            logjac = @. - log((b.b - x) * totally_worth_saving)
-           return (rv=y, logabsdetjac = logjac)
+           return (y, logjac)
        end
 forward (generic function with 16 methods)
 
-julia> forward(b, 0.6)
-(rv = 0.4054651081081642, logabsdetjac = 1.4271163556401458)
+julia> with_logabsdet_jacobian(b, 0.6)
+(0.4054651081081642, 1.4271163556401458)
 
-julia> @which forward(b, 0.6)
-forward(b::Logit{#s4} where #s4<:Real, x) in Main at REPL[43]:2
+julia> @which with_logabsdet_jacobian(b, 0.6)
+with_logabsdet_jacobian(b::Logit{#s4} where #s4<:Real, x) in Main at REPL[43]:2
 ```
 
 As you can see it's a very contrived example, but you get the idea.
@@ -613,10 +615,10 @@ julia> logabsdetjac(b_ad, 0.6)
 julia> y = b_ad(0.6)
 0.4054651081081642
 
-julia> inv(b_ad)(y)
+julia> inverse(b_ad)(y)
 0.6
 
-julia> logabsdetjac(inv(b_ad), y)
+julia> logabsdetjac(inverse(b_ad), y)
 -1.4271163556401458
 ```
 
@@ -665,7 +667,7 @@ help?> Bijectors.Composed
 
   A Bijector representing composition of bijectors. composel and composer results in a Composed for which application occurs from left-to-right and right-to-left, respectively.
 
-  Note that all the alternative ways of constructing a Composed returns a Tuple of bijectors. This ensures type-stability of implementations of all relating methdos, e.g. inv.
+  Note that all the alternative ways of constructing a Composed returns a Tuple of bijectors. This ensures type-stability of implementations of all relating methods, e.g. inverse.
 
   If you want to use an Array as the container instead you can do
 
@@ -713,9 +715,9 @@ The distribution interface consists of:
 #### Methods
 The following methods are implemented by all subtypes of `Bijector`, this also includes bijectors such as `Composed`.
 - `(b::Bijector)(x)`: implements the transform of the `Bijector`
-- `inv(b::Bijector)`: returns the inverse of `b`, i.e. `ib::Bijector` s.t. `(ib ∘ b)(x) ≈ x`. In most cases this is `Inverse{<:Bijector}`.
+- `inverse(b::Bijector)`: returns the inverse of `b`, i.e. `ib::Bijector` s.t. `(ib ∘ b)(x) ≈ x`. In most cases this is `Inverse{<:Bijector}`.
 - `logabsdetjac(b::Bijector, x)`: computes log(abs(det(jacobian(b, x)))).
-- `forward(b::Bijector, x)`: returns named tuple `(rv=b(x), logabsdetjac=logabsdetjac(b, x))` in the most efficient manner.
+- `with_logabsdet_jacobian(b::Bijector, x)`: returns the tuple `(b(x), logabsdetjac(b, x))` in the most efficient manner.
 - `∘`, `composel`, `composer`: convenient and type-safe constructors for `Composed`. `composel(bs...)` composes s.t. the resulting composition is evaluated left-to-right, while `composer(bs...)` is evaluated right-to-left. `∘` is right-to-left, as excepted from standard mathematical notation.
 - `jacobian(b::Bijector, x)` [OPTIONAL]: returns the Jacobian of the transformation. In some cases the analytical Jacobian has been implemented for efficiency.
 - `dimension(b::Bijector)`: returns the dimensionality of `b`.
@@ -725,7 +727,7 @@ For `TransformedDistribution`, together with default implementations for `Distri
 - `bijector(d::Distribution)`: returns the default constrained-to-unconstrained bijector for `d`
 - `transformed(d::Distribution)`, `transformed(d::Distribution, b::Bijector)`: constructs a `TransformedDistribution` from `d` and `b`.
 - `logpdf_forward(d::Distribution, x)`, `logpdf_forward(d::Distribution, x, logjac)`: computes the `logpdf(td, td.transform(x))` using the forward pass, which is potentially faster depending on the transform at hand.
-- `forward(d::Distribution)`: returns `(x = rand(dist), y = b(x), logabsdetjac = logabsdetjac(b, x), logpdf = logpdf_forward(td, x))` where `b = td.transform`. This combines sampling from base distribution and transforming into one function. The intention is that this entire process should be performed in the most efficient manner, e.g. the `logabsdetjac(b, x)` call might instead be implemented as `- logabsdetjac(inv(b), b(x))` depending on which is most efficient.
+- `forward(d::Distribution)`: returns `(x = rand(dist), y = b(x), logabsdetjac = logabsdetjac(b, x), logpdf = logpdf_forward(td, x))` where `b = td.transform`. This combines sampling from base distribution and transforming into one function. The intention is that this entire process should be performed in the most efficient manner, e.g. the `logabsdetjac(b, x)` call might instead be implemented as `- logabsdetjac(inverse(b), b(x))` depending on which is most efficient.
 
 # Bibliography
 1. Rezende, D. J., & Mohamed, S. (2015). Variational Inference With Normalizing Flows. [arXiv:1505.05770](https://arxiv.org/abs/1505.05770v6).

src/Bijectors.jl

@@ -35,6 +35,9 @@ using MappedArrays
 using Base.Iterators: drop
 using LinearAlgebra: AbstractTriangular
 
+import ChangesOfVariables: with_logabsdet_jacobian
+import InverseFunctions: inverse
+
 import ChainRulesCore
 import Functors
 import IrrationalConstants
@@ -51,6 +54,8 @@ export  TransformDistribution,
         logpdf_with_trans,
         isclosedform,
         transform,
+        with_logabsdet_jacobian,
+        inverse,
         forward,
         logabsdetjac,
         logabsdetjacinv,
@@ -121,7 +126,7 @@ end
 # Distributions
 
 link(d::Distribution, x) = bijector(d)(x)
-invlink(d::Distribution, y) = inv(bijector(d))(y)
+invlink(d::Distribution, y) = inverse(bijector(d))(y)
 function logpdf_with_trans(d::Distribution, x, transform::Bool)
     if ispd(d)
         return pd_logpdf_with_trans(d, x, transform)
@@ -188,14 +193,14 @@ function invlink(
     y::AbstractVecOrMat{<:Real},
     ::Val{proj}=Val(true),
 ) where {proj}
-    return inv(SimplexBijector{proj}())(y)
+    return inverse(SimplexBijector{proj}())(y)
 end
 function invlink_jacobian(
     d::Dirichlet,
     y::AbstractVector{<:Real},
     ::Val{proj}=Val(true),
 ) where {proj}
-    return jacobian(inv(SimplexBijector{proj}()), y)
+    return jacobian(inverse(SimplexBijector{proj}()), y)
 end
 
 ## Matrix
@@ -249,6 +254,13 @@ include("utils.jl")
 include("interface.jl")
 include("chainrules.jl")
 
+Base.@deprecate forward(b::AbstractBijector, x) NamedTuple{(:rv,:logabsdetjac)}(with_logabsdet_jacobian(b, x))
+
+@noinline function Base.inv(b::AbstractBijector)
+    Base.depwarn("`Base.inv(b::AbstractBijector)` is deprecated, use `inverse(b)` instead.", :inv)
+    inverse(b)
+end
+
 # Broadcasting here breaks Tracker for some reason
 maporbroadcast(f, x::AbstractArray{<:Any, N}...) where {N} = map(f, x...)
 maporbroadcast(f, x::AbstractArray...) = f.(x...)