copy of old

Project.toml

@@ -3,6 +3,11 @@ uuid = "e1fe09cc-5134-44c2-a941-50f4cd97986a"
 authors = ["David Métivier <[email protected]> and contributors"]
 version = "0.1.0"
 
+[deps]
+ArgCheck = "dce04be8-c92d-5529-be00-80e4d2c0e197"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+
 [compat]
 julia = "1"
 

README.md

@@ -1 +1,47 @@
 # ExpectationMaximization
+
+This package provides a simple implementation of the Expectation Maximization algorithm used to fit mixture models.
+Due to [Julia](https://julialang.org/) amazing [multiple dispatch](https://www.youtube.com/watch?v=kc9HwsxE1OY) systems and the [Distributions](https://juliastats.org/Distributions.jl/stable/) package, the code is very generic i.e., mixture of all common distributions should be supported.
+
+## Example
+
+```julia
+using Distributions
+using ExpectationMaximization
+```
+
+### Model
+
+```julia
+N = 50000
+θ₁ = 10
+θ₂ = 5
+α = 0.2
+β = 0.3
+# Mixture Model here one can put any classical distributions
+mix_true = MixtureModel([Exponential(θ₁), Gamma(α, θ₂)], [β, 1 - β]) 
+
+# Generate N samples from the mixture
+y = rand(mix_true, N) 
+```
+
+### Inference
+
+```julia
+# Initial guess
+mix_mle = fit_mle(mix_guess, y; display = :iter, tol = 1e-3, robust = false, infos = false)
+
+# Fit the MLE with the EM algorithm
+mix_mle = fit_mle(mix_guess, y; display = :iter, tol = 1e-3, robust = false, infos = false)
+```
+
+### Verify results
+
+```julia
+rtol = 5e-2
+p = params(mix_mle)[1] # (θ₁, (α, θ₂))
+isapprox(β, probs(mix_mle)[1]; rtol = rtol)
+isapprox(θ₁, p[1]...; rtol = rtol)
+isapprox(α, p[2][1]; rtol = rtol)
+isapprox(θ₂, p[2][2]; rtol = rtol)
+```

src/fit_em.jl

@@ -0,0 +1,157 @@
+"""
+fit_mle(mix::MixtureModel, y; display = :none, maxiter = 100, tol = 1e-3, robust = false)
+
+fit_em use Expectation Maximization (EM) algorithm to maximize the Loglikelihood (fit) the mixture to an i.i.d sample `y`.
+The `mix` agrument is a mixture that is used to initilize the EM algorithm.
+"""
+function fit_mle(mix::MixtureModel, y::AbstractVector; display = :none, maxiter = 1000, tol = 1e-3, robust = false, infos = false)
+
+    @argcheck display in [:none, :iter, :final]
+    @argcheck maxiter >= 0
+
+    N, K = length(y), ncomponents(mix)
+    history = Dict("converged" => false, "iterations" => 0, "logtots" => zeros(0))
+
+    # Allocate memory for in-place updates
+
+    LL = zeros(N, K)
+    γ = similar(LL)
+    c = zeros(N)
+    # types = typeof.(components(mix))
+
+    # Initial parameters
+    α = copy(probs(mix))
+    dists = copy(components(mix))
+
+    # E-step
+    # evaluate likelihood for each type k
+    for k = 1:K
+        LL[:, k] = log(α[k]) .+ logpdf(dists[k], y)
+    end
+    robust && replace!(LL, -Inf => nextfloat(-Inf), Inf => log(prevfloat(Inf)))
+    # get posterior of each category
+    c[:] = logsumexp(LL, dims = 2)
+    γ[:, :] = exp.(LL .- c)
+
+    # Loglikelihood
+    logtot = sum(c)
+    (display == :iter) && println("Iteration 0: logtot = $logtot")
+
+    for it = 1:maxiter
+
+        # M-step
+        # with γ, maximize (update) the parameters
+        α[:] = mean(γ, dims = 1)
+        dists[:] = [fit_mle(dists[k], y, γ[:, k]) for k = 1:K]
+
+        # E-step
+        # evaluate likelihood for each type k
+        for k = 1:K
+            LL[:, k] = log(α[k]) .+ logpdf(dists[k], y)
+        end
+        robust && replace!(LL, -Inf => nextfloat(-Inf), Inf => log(prevfloat(Inf)))
+        # get posterior of each category
+        c[:] = logsumexp(LL, dims = 2)
+        γ[:, :] = exp.(LL .- c)
+
+        # Loglikelihood
+        logtotp = sum(c)
+        (display == :iter) && println("Iteration $it: logtot = $logtotp")
+
+        push!(history["logtots"], logtotp)
+        history["iterations"] += 1
+
+        if abs(logtotp - logtot) < tol
+            (display in [:iter, :final]) &&
+                println("EM converged in $it iterations, logtot = $logtotp")
+            history["converged"] = true
+            break
+        end
+
+        logtot = logtotp
+    end
+
+    if !history["converged"]
+        if display in [:iter, :final]
+            println("EM has not converged after $(history["iterations"]) iterations, logtot = $logtot")
+        end
+    end
+
+    return infos ? (MixtureModel(dists, α), history) : MixtureModel(dists, α)
+end
+
+function fit_mle(mix::MixtureModel, y::AbstractMatrix; display = :none, maxiter = 1000, tol = 1e-3, robust = false, infos = false)
+
+    @argcheck display in [:none, :iter, :final]
+    @argcheck maxiter >= 0
+
+    N, K = size(y, 2), ncomponents(mix)
+    history = Dict("converged" => false, "iterations" => 0, "logtots" => zeros(0))
+
+    # Allocate memory for in-place updates
+
+    LL = zeros(N, K)
+    γ = similar(LL)
+    c = zeros(N)
+    # types = typeof.(components(mix))
+
+    # Initial parameters
+    α = copy(probs(mix))
+    dists = copy(components(mix))
+
+    # E-step
+    # evaluate likelihood for each type k
+    for k = 1:K
+        LL[:, k] = log(α[k]) .+ logpdf(dists[k], y)
+    end
+    robust && replace!(LL, -Inf => nextfloat(-Inf), Inf => log(prevfloat(Inf)))
+    # get posterior of each category
+    c[:] = logsumexp(LL, dims = 2)
+    γ[:, :] = exp.(LL .- c)
+
+    # Loglikelihood
+    logtot = sum(c)
+    (display == :iter) && println("Iteration 0: logtot = $logtot")
+
+    for it = 1:maxiter
+
+        # M-step
+        # with γ in hand, maximize (update) the parameters
+        α[:] = mean(γ, dims = 1)
+        dists[:] = [fit_mle(dists[k], y, γ[:, k]) for k = 1:K]
+
+        # E-step
+        # evaluate likelihood for each type k
+        for k = 1:K
+            LL[:, k] = log(α[k]) .+ logpdf(dists[k], y)
+        end
+        robust && replace!(LL, -Inf => nextfloat(-Inf), Inf => log(prevfloat(Inf)))
+        # get posterior of each category
+        c[:] = logsumexp(LL, dims = 2)
+        γ[:, :] = exp.(LL .- c)
+
+        # Loglikelihood
+        logtotp = sum(c)
+        (display == :iter) && println("Iteration $it: logtot = $logtotp")
+
+        push!(history["logtots"], logtotp)
+        history["iterations"] += 1
+
+        if abs(logtotp - logtot) < tol
+            (display in [:iter, :final]) &&
+                println("EM converged in $it iterations, logtot = $logtotp")
+            history["converged"] = true
+            break
+        end
+
+        logtot = logtotp
+    end
+
+    if !history["converged"]
+        if display in [:iter, :final]
+            println("EM has not converged after $(history["iterations"]) iterations, logtot = $logtot")
+        end
+    end
+
+    return infos ? (MixtureModel(dists, α), history) : MixtureModel(dists, α)
+end

src/fit_mle_product_distributions.jl

@@ -0,0 +1,31 @@
+#! What is the convention and or the most efficient way to store these multidim arrays: samples from column/row correspond to one distributions?
+#! Here we choose row correspond to one distributions and number of row is the number of realization
+#! It seems to be the convention
+#TODO Only work for distributions with known fit_mle (cannot be product_distribution of mixture because of the typeof)
+"""
+Simply extend the `fit_mle` function to multivariate Product distributions.
+"""
+function fit_mle(g::Product, x::AbstractMatrix)
+    S = size(x, 1) # row convention
+    vec_g = g.v
+    @argcheck S == length(vec_g)
+    return product_distribution([fit_mle(typeof(vec_g[s]), y) for (s, y) in enumerate(eachrow(x))])
+end
+
+function fit_mle(g::Product, x::AbstractMatrix, γ::AbstractVector)
+    S = size(x, 1) # row convention
+    vec_g = g.v
+    @argcheck S == length(vec_g)
+    return product_distribution([fit_mle(typeof(vec_g[s]), y, γ) for (s, y) in enumerate(eachrow(x))])
+end
+
+"""
+Now `fit_mle(Bernoulli(0.2), x)` is accepted in addition of `fit_mle(Bernoulli, x)` this allows compatibility with how `fit_mle(g::Product)` and `fit_mle(g::MixtureModel)` are written.
+"""
+function fit_mle(g::Distribution{Univariate,Discrete}, args...)
+    fit_mle(typeof(g), args...)
+end
+
+function fit_mle(g::Distribution{Univariate,Continuous}, args...)
+    fit_mle(typeof(g), args...)
+end

test/runtests.jl

@@ -1,6 +1,22 @@
 using ExpectationMaximization
+using Distributions
 using Test
 
 @testset "ExpectationMaximization.jl" begin
-    # Write your tests here.
+    N = 50000
+    θ₁ = 10
+    θ₂ = 5
+    α = 0.2
+    β = 0.3
+    rtol = 5e-2
+    mix_true = MixtureModel([Exponential(θ₁), Gamma(α, θ₂)], [β, 1 - β])
+    y = rand(mix_true, N)
+    mix_guess = MixtureModel([Exponential(1), Gamma(0.5, 1)], [0.5, 1 - 0.5])
+    mix_mle = fit_mle(mix_guess, y; display = :iter, tol = 1e-3, robust = false, infos = false)
+
+    p = params(mix_mle)[1]
+    @test isapprox(β, probs(mix_mle)[1]; rtol = rtol)
+    @test isapprox(θ₁, p[1]...; rtol = rtol)
+    @test isapprox(α, p[2][1]; rtol = rtol)
+    @test isapprox(θ₂, p[2][2]; rtol = rtol)
 end