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##### | ||
##### Wasserstein distance | ||
##### | ||
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function pysearchsorted(a,b;side="left") | ||
if side == "left" | ||
return searchsortedfirst.(Ref(a),b) .- 1 | ||
else | ||
return searchsortedlast.(Ref(a),b) | ||
end | ||
end | ||
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function _cdf_distance(p, u_values, v_values, u_weights=nothing, v_weights=nothing) | ||
_validate_distribution!(u_values, u_weights) | ||
_validate_distribution!(v_values, v_weights) | ||
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u_sorter = sortperm(u_values) | ||
v_sorter = sortperm(v_values) | ||
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all_values = vcat(u_values, v_values) | ||
sort!(all_values) | ||
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# Compute the differences between pairs of successive values of u and v. | ||
deltas = diff(all_values) | ||
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# Get the respective positions of the values of u and v among the values of | ||
# both distributions. | ||
u_cdf_indices = pysearchsorted(u_values[u_sorter],all_values[1:end-1], side="right") | ||
v_cdf_indices = pysearchsorted(v_values[v_sorter],all_values[1:end-1], side="right") | ||
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# Calculate the CDFs of u and v using their weights, if specified. | ||
if u_weights == nothing | ||
u_cdf = (u_cdf_indices) / length(u_values) | ||
else | ||
u_sorted_cumweights = vcat([0], cumsum(u_weights[u_sorter])) | ||
u_cdf = u_sorted_cumweights[u_cdf_indices] / u_sorted_cumweights[end] | ||
end | ||
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if v_weights == nothing | ||
v_cdf = (v_cdf_indices) / length(v_values) | ||
else | ||
v_sorted_cumweights = vcat([0], cumsum(v_weights[v_sorter])) | ||
v_cdf = v_sorted_cumweights[v_cdf_indices] / v_sorted_cumweights[end] | ||
end | ||
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# Compute the value of the integral based on the CDFs. | ||
if p == 1 | ||
return sum(abs.(u_cdf - v_cdf) .* deltas) | ||
end | ||
if p == 2 | ||
return sqrt(sum((u_cdf - v_cdf).^2 .* deltas)) | ||
end | ||
return sum(abs.(u_cdf - v_cdf).^p .* deltas)^(1/p) | ||
end | ||
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function _validate_distribution!(vals, weights) | ||
# Validate the value array. | ||
length(vals) == 0 && throw(ValueError("Distribution can't be empty.")) | ||
# Validate the weight array, if specified. | ||
if weights ≠ nothing | ||
if length(weights) != length(vals) | ||
throw(ValueError("Value and weight array-likes for the same | ||
empirical distribution must be of the same size.")) | ||
end | ||
any(weights .< 0) && throw(ValueError("All weights must be non-negative.")) | ||
if !(0 < sum(weights) < Inf) | ||
throw(ValueError("Weight array-like sum must be positive and | ||
finite. Set as None for an equal distribution of | ||
weight.")) | ||
end | ||
end | ||
return nothing | ||
end | ||
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function wasserstein_distance(u_values, v_values, u_weights=nothing, v_weights=nothing) | ||
return _cdf_distance(1, u_values, v_values, u_weights, v_weights) | ||
end |