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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,58 @@ | ||
| pairwise_dot(x) = pairwise(SqEuclidean(), x; dims=2) | ||
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| function pairwise_dot_kai(x) | ||
| n = size(x, 2) | ||
| xixj = x' * x | ||
| xsq = sum(x .^ 2; dims=1) | ||
| return repeat(xsq', 1, n) + repeat(xsq, n, 1) - 2xixj | ||
| end | ||
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| # pairwise_dot(x::CuArray) = pairwise_dot_kai(x) | ||
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| pairwise_dot(x, y) = pairwise(SqEuclidean(), x, y; dims=2) | ||
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| function pairwise_dot_kai(x, y) | ||
| nx = size(x, 2) | ||
| ny = size(y, 2) | ||
| xiyj = x' * y | ||
| xsq = sum(x .^ 2; dims=1) | ||
| ysq = sum(y .^ 2; dims=1) | ||
| return repeat(xsq', 1, ny) .+ repeat(ysq, nx, 1) - 2xiyj | ||
| end | ||
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| # pairwise_dot(x::CuArray, y::CuArray) = pairwise_dot_kai(x, y) | ||
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| gaussian_gram_by_pairwise_dot(pdot; σ=1) = exp.(-pdot ./ 2(σ ^ 2)) | ||
| gaussian_gram(x; σ=1) = gaussian_gram_by_pairwise_dot(pairwise_dot(x); σ=σ) | ||
| gaussian_gram(x, y; σ=1) = gaussian_gram_by_pairwise_dot(pairwise_dot(x, y); σ=σ) | ||
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| function estimate_r_de(x_de, x_nu, get_r_hat=get_r_hat_numerically; σs=[sqrt(median([pdot_dede..., pdot_denu...]))]) | ||
| pdot_dede = pairwise_dot_kai(x_de) | ||
| pdot_denu = pairwise_dot_kai(x_de, x_nu) | ||
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| Kdede = mean([gaussian_gram_by_pairwise_dot(pdot_dede; σ=σ) for σ in σs]) | ||
| Kdenu = mean([gaussian_gram_by_pairwise_dot(pdot_denu; σ=σ) for σ in σs]) | ||
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| return get_r_hat(Kdede, Kdenu) | ||
| end | ||
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| function get_r_hat_numerically(Kdede, Kdenu; positive=true, normalisation=true) | ||
| n_de, n_nu = size(Kdenu) | ||
| model = Model(with_optimizer(Ipopt.Optimizer; print_level=0)) | ||
| @variable(model, r[1:n_de]) | ||
| @objective(model, Min, 1 / n_de ^ 2 * sum(r[i] * Kdede[i,j] * r[j] for i = 1:n_de, j=1:n_de) - 2 / (n_de * n_nu) * sum(r[i] * Kdenu[i,j] for i = 1:n_de, j=1:n_nu)) | ||
| if positive | ||
| @constraint(model, r .>= 0) | ||
| end | ||
| if normalisation | ||
| @constraint(model, 1 / n_de * sum(r) == 1) | ||
| end | ||
| JuMP.optimize!(model) | ||
| return value.(r) | ||
| end | ||
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| function get_r_hat_analytical(Kdede, Kdenu; ϵ=1 / 1_000) | ||
| n_de, n_nu = size(Kdenu) | ||
| return n_de / n_nu * inv(Kdede + ϵ * I) * Kdenu * ones(n_nu) | ||
| end | ||
| ; |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,5 @@ | ||
| using Distances: pairwise, SqEuclidean | ||
| using LinearAlgebra: I | ||
| using JuMP, Ipopt | ||
| include("moment_matching.jl") | ||
| export estimate_r_de, get_r_hat_numerically, get_r_hat_analytical |
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