debugging

examples/statistical_model_prototype.jl

@@ -17,6 +17,10 @@ struct GeneralGaussianMixture{W, M, C}
     covariances::C
 end
 
+struct ScoreModel{P, S}
+    probability_model::P
+    inverse_covariances::S
+end
 
 function determine_statistical_model(trajectory, tree_type::Tree{Val{false},S}; override=false) where {S}
     if typeof(tree_type.arguments) <: NamedTuple
@@ -66,17 +70,17 @@ function determine_statistical_model(trajectory, tree_type::Tree{Val{false},S};
     return embedding, probability_weights, means, partitions
 end
 
-
+##
 # include the lorenz file here
-method = Tree(false, 0.01)
+method = Tree(false, 0.001)
 
 emb, pr, ms, partitions = determine_statistical_model(trajectory, method)
 
 empirical_centers = zeros(size(trajectory)[1], maximum(partitions))
 empirical_covariance = zeros(size(trajectory)[1], size(trajectory)[1], maximum(partitions))
 empirical_count = zeros(Int64, maximum(partitions))
 for (i, state) in ProgressBar(enumerate(eachcol(trajectory)))
-    cell_index = embedding(state)
+    cell_index = emb(state)
     partitions[i] = cell_index
     empirical_count[cell_index] += 1
     empirical_centers[:, cell_index] .+= state
@@ -107,6 +111,14 @@ function rand(Σmodel::GeneralGaussianMixture)
     return rand(MvNormal(Σmodel.means[:, cell_index], Σmodel.covariances[:, :, cell_index]))
 end
 
+function rand(Σmodel::GeneralGaussianMixture, N::Int)
+    samples = zeros(size(Σmodel.means)[1], N)
+    for i in 1:N 
+        samples[:, i] .= rand(Σmodel)
+    end
+    return samples
+end
+
 function mean(δmodel::DeltaFunction)
     ensemble_mean = zeros(size(δmodel.means)[1])
     for i in 1:size(δmodel.means)[2]
@@ -168,4 +180,89 @@ scatter(samples)
 ##
 totcov = cov(trajectory')
 cov(Σmodel)
-cov(δmodel)
+cov(δmodel)
+
+fig = Figure()
+ax = Axis(fig[1, 1])
+density!(ax, samples[1, :], normalization = :pdf, color = (:red, 0.5))
+hist!(ax, trajectory[1, :], normalization = :pdf, color = (:blue, 0.5))
+display(fig)
+
+##
+function ScoreModel(gm::GeneralGaussianMixture)
+    n = size(gm.means)[1]
+    m = size(gm.means)[2]
+    Σinv = zeros(n, n, m)
+    for i in 1:m
+        Σinv[:, :, i] = pinv(gm.covariances[:, :, i])
+    end
+    return ScoreModel(gm, Σinv)
+end
+
+score = ScoreModel(Σmodel)
+
+function (score::ScoreModel)(x)
+    n = size(score.probability_model.means)[1]
+    m = size(score.probability_model.means)[2]
+    score_value = zeros(n)
+    denominator = [0.0]
+    for i in 1:m
+        Δ = score.probability_model.means[:, i] - x
+        Σ⁻¹Δ = score.inverse_covariances[:, :, i] * Δ
+        normalization = sqrt(det(2π * score.probability_model.covariances[:, :, i]))
+        U = exp(-0.5 * Δ' * Σ⁻¹Δ) / normalization
+        weightedU = score.probability_model.weights[i] * U 
+        score_value .+= weightedU * Σ⁻¹Δ
+        denominator .+= weightedU
+    end
+    return score_value / denominator[1]
+end
+
+##
+dt = 0.01
+iterations = 10^6
+
+
+trajectory = zeros(1, iterations)
+trajectory[:, 1] .= [0.0]
+step = RungeKutta4(1)
+for i in ProgressBar(2:iterations)
+    step(linear, trajectory[:, i-1], dt)
+    trajectory[:, i] .= step.xⁿ⁺¹ .+ sqrt(dt) * randn(1)
+end
+
+method = Tree(false, 0.1)
+
+emb, pr, ms, partitions = determine_statistical_model(trajectory, method)
+
+empirical_centers = zeros(size(trajectory)[1], maximum(partitions))
+empirical_covariance = zeros(size(trajectory)[1], size(trajectory)[1], maximum(partitions))
+empirical_count = zeros(Int64, maximum(partitions))
+for (i, state) in ProgressBar(enumerate(eachcol(trajectory)))
+    cell_index = emb(state)
+    partitions[i] = cell_index
+    empirical_count[cell_index] += 1
+    empirical_centers[:, cell_index] .+= state
+    empirical_covariance[:, :, cell_index] .+= state * state'
+end
+# adjust 
+adj_empirical_centers = empirical_centers ./ reshape(empirical_count, 1, length(empirical_count))
+adj_empirical_covariance = empirical_covariance ./ reshape(empirical_count .- 1, 1, 1, length(empirical_count))
+for i in 1:length(probability_weights)
+    adj_empirical_covariance[:, :, i] .-= (adj_empirical_centers[:, i] * adj_empirical_centers[:, i]') * empirical_count[i] / (empirical_count[i] - 1)
+end
+probability_weights = empirical_count / sum(empirical_count)
+
+δmodel = DeltaFunction(probability_weights, adj_empirical_centers)
+Σmodel = GeneralGaussianMixture(probability_weights, adj_empirical_centers, adj_empirical_covariance * 20)
+
+score = ScoreModel(Σmodel)
+
+σemp = cov(trajectory')
+xs = range(-3, 3, length=100)
+scorevals = [score([x])[1] for x in xs]
+fig = Figure()
+ax = Axis(fig[1, 1])
+scatter!(ax, xs, scorevals)
+lines!(ax, xs, -xs / σemp^2, color=:red)
+display(fig)