/
reversediff.jl
185 lines (172 loc) · 6.65 KB
/
reversediff.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
module ReverseDiffCompat
using ..ReverseDiff: ReverseDiff, @grad, value, track, TrackedReal, TrackedVector,
TrackedMatrix, TrackedArray
using Requires, LinearAlgebra
using ..Bijectors: Log, SimplexBijector, maphcat, simplex_link_jacobian,
simplex_invlink_jacobian, simplex_logabsdetjac_gradient, ADBijector,
ReverseDiffAD, Inverse
import ..Bijectors: _eps, logabsdetjac, _logabsdetjac_scale, _simplex_bijector,
_simplex_inv_bijector, replace_diag, jacobian, getpd, lower,
_inv_link_chol_lkj, _link_chol_lkj
using Compat: eachcol
using Distributions: LocationScale
# AD implementations
function jacobian(
b::Union{<:ADBijector{<:ReverseDiffAD}, Inverse{<:ADBijector{<:ReverseDiffAD}}},
x::Real
)
return ReverseDiff.gradient(x -> b(x[1]), [x])[1]
end
function jacobian(
b::Union{<:ADBijector{<:ReverseDiffAD}, Inverse{<:ADBijector{<:ReverseDiffAD}}},
x::AbstractVector{<:Real}
)
return ReverseDiff.jacobian(b, x)
end
_eps(::Type{<:TrackedReal{T}}) where {T} = _eps(T)
function Base.minimum(d::LocationScale{<:TrackedReal})
m = minimum(d.ρ)
if isfinite(m)
return d.μ + d.σ * m
else
return m
end
end
function Base.maximum(d::LocationScale{<:TrackedReal})
m = maximum(d.ρ)
if isfinite(m)
return d.μ + d.σ * m
else
return m
end
end
logabsdetjac(b::Log{1}, x::Union{TrackedVector, TrackedMatrix}) = track(logabsdetjac, b, x)
@grad function logabsdetjac(b::Log{1}, x::AbstractVector)
return -sum(log, value(x)), Δ -> (nothing, -Δ ./ value(x))
end
@grad function logabsdetjac(b::Log{1}, x::AbstractMatrix)
return -vec(sum(log, value(x); dims = 1)), Δ -> (nothing, .- Δ' ./ value(x))
end
function _logabsdetjac_scale(a::TrackedReal, x::Real, ::Val{0})
return track(_logabsdetjac_scale, a, value(x), Val(0))
end
@grad function _logabsdetjac_scale(a::Real, x::Real, v::Val{0})
return _logabsdetjac_scale(value(a), value(x), Val(0)), Δ -> (inv(value(a)) .* Δ, nothing, nothing)
end
# Need to treat `AbstractVector` and `AbstractMatrix` separately due to ambiguity errors
function _logabsdetjac_scale(a::TrackedReal, x::AbstractVector, ::Val{0})
return track(_logabsdetjac_scale, a, value(x), Val(0))
end
@grad function _logabsdetjac_scale(a::Real, x::AbstractVector, v::Val{0})
da = value(a)
J = fill(inv.(da), length(x))
return _logabsdetjac_scale(da, value(x), Val(0)), Δ -> (transpose(J) * Δ, nothing, nothing)
end
function _logabsdetjac_scale(a::TrackedReal, x::AbstractMatrix, ::Val{0})
return track(_logabsdetjac_scale, a, value(x), Val(0))
end
@grad function _logabsdetjac_scale(a::Real, x::AbstractMatrix, v::Val{0})
da = value(a)
J = fill(size(x, 1) / da, size(x, 2))
return _logabsdetjac_scale(da, value(x), Val(0)), Δ -> (transpose(J) * Δ, nothing, nothing)
end
# adjoints for 1-dim and 2-dim `Scale` using `AbstractVector`
function _logabsdetjac_scale(a::TrackedVector, x::AbstractVector, ::Val{1})
return track(_logabsdetjac_scale, a, value(x), Val(1))
end
@grad function _logabsdetjac_scale(a::TrackedVector, x::AbstractVector, v::Val{1})
# ∂ᵢ (∑ⱼ log|aⱼ|) = ∑ⱼ δᵢⱼ ∂ᵢ log|aⱼ|
# = ∂ᵢ log |aᵢ|
# = (1 / aᵢ) ∂ᵢ aᵢ
# = (1 / aᵢ)
da = value(a)
J = inv.(da)
return _logabsdetjac_scale(da, value(x), Val(1)), Δ -> (J .* Δ, nothing, nothing)
end
function _logabsdetjac_scale(a::TrackedVector, x::AbstractMatrix, ::Val{1})
return track(_logabsdetjac_scale, a, value(x), Val(1))
end
@grad function _logabsdetjac_scale(a::TrackedVector, x::AbstractMatrix, v::Val{1})
da = value(a)
Jᵀ = repeat(inv.(da), 1, size(x, 2))
return _logabsdetjac_scale(da, value(x), Val(1)), Δ -> (Jᵀ * Δ, nothing, nothing)
end
function _simplex_bijector(X::Union{TrackedVector, TrackedMatrix}, b::SimplexBijector{1})
return track(_simplex_bijector, X, b)
end
@grad function _simplex_bijector(Y::AbstractVector, b::SimplexBijector{1})
Yd = value(Y)
return _simplex_bijector(Yd, b), Δ -> (simplex_link_jacobian(Yd)' * Δ, nothing)
end
@grad function _simplex_bijector(Y::AbstractMatrix, b::SimplexBijector{1})
Yd = value(Y)
return _simplex_bijector(Yd, b), Δ -> begin
maphcat(eachcol(Yd), eachcol(Δ)) do c1, c2
simplex_link_jacobian(c1)' * c2
end, nothing
end
end
function _simplex_inv_bijector(X::Union{TrackedVector, TrackedMatrix}, b::SimplexBijector{1})
return track(_simplex_inv_bijector, X, b)
end
@grad function _simplex_inv_bijector(Y::AbstractVector, b::SimplexBijector{1})
Yd = value(Y)
return _simplex_inv_bijector(Yd, b), Δ -> (simplex_invlink_jacobian(Yd)' * Δ, nothing)
end
@grad function _simplex_inv_bijector(Y::AbstractMatrix, b::SimplexBijector{1})
Yd = value(Y)
return _simplex_inv_bijector(Yd, b), Δ -> begin
maphcat(eachcol(Yd), eachcol(Δ)) do c1, c2
simplex_invlink_jacobian(c1)' * c2
end, nothing
end
end
replace_diag(::typeof(log), X::TrackedMatrix) = track(replace_diag, log, X)
@grad function replace_diag(::typeof(log), X)
Xd = value(X)
f(i, j) = i == j ? log(Xd[i, j]) : Xd[i, j]
out = f.(1:size(Xd, 1), (1:size(Xd, 2))')
out, ∇ -> begin
g(i, j) = i == j ? ∇[i, j]/Xd[i, j] : ∇[i, j]
return (nothing, g.(1:size(Xd, 1), (1:size(Xd, 2))'))
end
end
replace_diag(::typeof(exp), X::TrackedMatrix) = track(replace_diag, exp, X)
@grad function replace_diag(::typeof(exp), X)
Xd = value(X)
f(i, j) = ifelse(i == j, exp(Xd[i, j]), Xd[i, j])
out = f.(1:size(Xd, 1), (1:size(Xd, 2))')
out, ∇ -> begin
g(i, j) = ifelse(i == j, ∇[i, j]*exp(Xd[i, j]), ∇[i, j])
return (nothing, g.(1:size(Xd, 1), (1:size(Xd, 2))'))
end
end
logabsdetjac(b::SimplexBijector{1}, x::Union{TrackedVector, TrackedMatrix}) = track(logabsdetjac, b, x)
@grad function logabsdetjac(b::SimplexBijector{1}, x::AbstractVector)
xd = value(x)
return logabsdetjac(b, xd), Δ -> begin
(nothing, simplex_logabsdetjac_gradient(xd) * Δ)
end
end
@grad function logabsdetjac(b::SimplexBijector{1}, x::AbstractMatrix)
xd = value(x)
return logabsdetjac(b, xd), Δ -> begin
(nothing, maphcat(eachcol(xd), Δ) do c, g
simplex_logabsdetjac_gradient(c) * g
end)
end
end
getpd(X::TrackedMatrix) = track(getpd, X)
@grad function getpd(X::AbstractMatrix)
Xd = value(X)
return LowerTriangular(Xd) * LowerTriangular(Xd)', Δ -> begin
Xl = LowerTriangular(Xd)
return (LowerTriangular(Δ' * Xl + Δ * Xl),)
end
end
lower(A::TrackedMatrix) = track(lower, A)
@grad function lower(A::AbstractMatrix)
Ad = value(A)
return lower(Ad), Δ -> (lower(Δ),)
end
end