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Make suffstats and fit_mle type-generic for Normal{T} #1560

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Make suffstats and fit_mle type-generic for Normal{T} #1560

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debbf4f
Make suffstats and fit_mle type generic for Normal{T}
gdalle May 30, 2022
7443d7b
Merge branch 'JuliaStats:master' into type_generic_normal
gdalle Jun 9, 2023
4b27b30
Type generic partially known Normal
gdalle Jun 9, 2023
27ea06f
Merge branch 'master' into type_generic_normal
gdalle Jan 13, 2024
de449b2
Fix known stats and minimize diff
gdalle Jan 13, 2024
9203e63
Useless diff
gdalle Jan 13, 2024
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124 changes: 71 additions & 53 deletions src/univariate/continuous/normal.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -120,38 +120,41 @@ rand!(rng::AbstractRNG, d::Normal, A::AbstractArray{<:Real}) = A .= muladd.(d.σ

#### Fitting

struct NormalStats <: SufficientStats
s::Float64 # (weighted) sum of x
m::Float64 # (weighted) mean of x
s2::Float64 # (weighted) sum of (x - μ)^2
tw::Float64 # total sample weight
struct NormalStats{T<:Real} <: SufficientStats
s::T # (weighted) sum of x
m::T # (weighted) mean of x
s2::T # (weighted) sum of (x - μ)^2
tw::T # total sample weight
function NormalStats(s::T1, m::T2, s2::T3, tw::T4) where {T1,T2,T3,T4}
T = promote_type(T1, T2, T3, T4)
return new{T}(T(s), T(m), T(s2), T(tw))
end
end

function suffstats(::Type{<:Normal}, x::AbstractArray{T}) where T<:Real
n = length(x)

# compute s
s = zero(T) + zero(T)
s = zero(T)
for i in eachindex(x)
@inbounds s += x[i]
end
m = s / n

# compute s2
s2 = zero(m)
s2 = zero(T)
for i in eachindex(x)
@inbounds s2 += abs2(x[i] - m)
end

NormalStats(s, m, s2, n)
end

function suffstats(::Type{<:Normal}, x::AbstractArray{T}, w::AbstractArray{Float64}) where T<:Real
n = length(x)

function suffstats(::Type{<:Normal}, x::AbstractArray{T1}, w::AbstractArray{T2}) where {T1<:Real,T2<:Real}
T = promote_type(T1, T2)
# compute s
tw = 0.0
s = 0.0 * zero(T)
tw = zero(T)
s = zero(T)
for i in eachindex(x, w)
@inbounds wi = w[i]
@inbounds s += wi * x[i]
Expand All @@ -160,7 +163,7 @@ function suffstats(::Type{<:Normal}, x::AbstractArray{T}, w::AbstractArray{Float
m = s / tw

# compute s2
s2 = zero(m)
s2 = zero(T)
for i in eachindex(x, w)
@inbounds s2 += w[i] * abs2(x[i] - m)
end
Expand All @@ -170,29 +173,35 @@ end

# Cases where μ or σ is known

struct NormalKnownMu <: IncompleteDistribution
μ::Float64
struct NormalKnownMu{T<:Real} <: IncompleteDistribution
μ::T
end

struct NormalKnownMuStats <: SufficientStats
μ::Float64 # known mean
s2::Float64 # (weighted) sum of (x - μ)^2
tw::Float64 # total sample weight
struct NormalKnownMuStats{T<:Real} <: SufficientStats
μ::T # known mean
s2::T # (weighted) sum of (x - μ)^2
tw::T # total sample weight
function NormalKnownMuStats(μ::T1, s2::T2, tw::T3) where {T1,T2,T3}
T = promote_type(T1, T2, T3)
return new{T}(μ, s2, tw)
end
end

function suffstats(g::NormalKnownMu, x::AbstractArray{T}) where T<:Real
function suffstats(g::NormalKnownMu{T0}, x::AbstractArray{T1}) where {T0,T1<:Real}
T = promote_type(T0, T1)
μ = g.μ
s2 = zero(T) + zero(μ)
s2 = zero(T)
for i in eachindex(x)
@inbounds s2 += abs2(x[i] - μ)
end
NormalKnownMuStats(g.μ, s2, length(x))
end

function suffstats(g::NormalKnownMu, x::AbstractArray{T}, w::AbstractArray{Float64}) where T<:Real
function suffstats(g::NormalKnownMu{T0}, x::AbstractArray{T1}, w::AbstractArray{T2}) where {T0,T1<:Real,T2<:Real}
T = promote_type(T0, T1, T2)
μ = g.μ
s2 = 0.0 * abs2(zero(T) - zero(μ))
tw = 0.0
s2 = zero(T)
tw = zero(T)
for i in eachindex(x, w)
@inbounds wi = w[i]
@inbounds s2 += abs2(x[i] - μ) * wi
Expand All @@ -201,69 +210,78 @@ function suffstats(g::NormalKnownMu, x::AbstractArray{T}, w::AbstractArray{Float
NormalKnownMuStats(g.μ, s2, tw)
end

struct NormalKnownSigma <: IncompleteDistribution
σ::Float64

function NormalKnownSigma(σ::Float64)
struct NormalKnownSigma{T<:Real} <: IncompleteDistribution
σ::T
function NormalKnownSigma(σ::T) where {T}
σ > 0 || throw(ArgumentError("σ must be a positive value."))
new(σ)
return new{T}(σ)
end
end

struct NormalKnownSigmaStats <: SufficientStats
σ::Float64 # known std.dev
sx::Float64 # (weighted) sum of x
tw::Float64 # total sample weight
struct NormalKnownSigmaStats{T<:Real} <: SufficientStats
σ::T # known std.dev
sx::T # (weighted) sum of x
tw::T # total sample weight
function NormalKnownSigmaStats(σ::T1, sx::T2, tw::T3) where {T1,T2,T3}
T = promote_type(T1, T2, T3)
return new{T}(σ, sx, tw)
end
end

function suffstats(g::NormalKnownSigma, x::AbstractArray{T}) where T<:Real
NormalKnownSigmaStats(g.σ, sum(x), Float64(length(x)))
function suffstats(g::NormalKnownSigma, x::AbstractArray{<:Real})
NormalKnownSigmaStats(g.σ, sum(x), length(x))
end

function suffstats(g::NormalKnownSigma, x::AbstractArray{T}, w::AbstractArray{T}) where T<:Real
function suffstats(g::NormalKnownSigma, x::AbstractArray{<:Real}, w::AbstractArray{<:Real})
NormalKnownSigmaStats(g.σ, dot(x, w), sum(w))
end

# fit_mle based on sufficient statistics

fit_mle(::Type{<:Normal}, ss::NormalStats) = Normal(ss.m, sqrt(ss.s2 / ss.tw))
fit_mle(::Type{D}, ss::NormalStats) where {D<:Normal} = D(ss.m, sqrt(ss.s2 / ss.tw))
fit_mle(g::NormalKnownMu, ss::NormalKnownMuStats) = Normal(g.μ, sqrt(ss.s2 / ss.tw))
fit_mle(g::NormalKnownSigma, ss::NormalKnownSigmaStats) = Normal(ss.sx / ss.tw, g.σ)

# generic fit_mle methods

function fit_mle(::Type{<:Normal}, x::AbstractArray{T}; mu::Float64=NaN, sigma::Float64=NaN) where T<:Real
if isnan(mu)
if isnan(sigma)
fit_mle(Normal, suffstats(Normal, x))
function fit_mle(
::Type{D}, x::AbstractArray{<:Real};
mu::Union{Nothing,<:Real}=nothing, sigma::Union{Nothing,<:Real}=nothing
) where {D<:Normal}
if isnothing(mu)
if isnothing(sigma)
fit_mle(D, suffstats(Normal, x))
else
g = NormalKnownSigma(sigma)
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We should find a way to preserve/forward the type of D in these cases as well.

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Which eltype should we pick for D though, the one of g or the one of the suffstats?

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I added a conversion in my latest commit, what do you think?

fit_mle(g, suffstats(g, x))
convert(D, fit_mle(g, suffstats(g, x)))
end
else
if isnan(sigma)
if isnothing(sigma)
g = NormalKnownMu(mu)
fit_mle(g, suffstats(g, x))
convert(D, fit_mle(g, suffstats(g, x)))
else
Normal(mu, sigma)
D(mu, sigma)
end
end
end

function fit_mle(::Type{<:Normal}, x::AbstractArray{T}, w::AbstractArray{Float64}; mu::Float64=NaN, sigma::Float64=NaN) where T<:Real
if isnan(mu)
if isnan(sigma)
fit_mle(Normal, suffstats(Normal, x, w))
function fit_mle(
::Type{D}, x::AbstractArray{<:Real}, w::AbstractArray{<:Real};
mu::Union{Nothing,<:Real}=nothing, sigma::Union{Nothing,<:Real}=nothing
) where {D<:Normal}
if isnothing(mu)
if isnothing(sigma)
fit_mle(D, suffstats(Normal, x, w))
else
g = NormalKnownSigma(sigma)
fit_mle(g, suffstats(g, x, w))
convert(D, fit_mle(g, suffstats(g, x, w)))
end
else
if isnan(sigma)
if isnothing(sigma)
g = NormalKnownMu(mu)
fit_mle(g, suffstats(g, x, w))
convert(D, fit_mle(g, suffstats(g, x, w)))
else
Normal(mu, sigma)
D(mu, sigma)
end
end
end
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