{ "cells": [ { "cell_type": "markdown", "source": [ "# One-Dimensional Cases\n", "\n", "*You are seeing the\n", "notebook output generated by\n", "[Literate.jl](https://github.com/fredrikekre/Literate.jl) from the\n", "[Julia source file](https://github.com/JuliaOptimalTransport/OptimalTransport.jl/blob/master/examples/OneDimension/script.jl).\n", "The rendered HTML can be viewed [in the docs](https://juliaoptimaltransport.github.io/OptimalTransport.jl/dev/examples/OneDimension/).*" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "The 1D case in Optimal Transport is a special case where one can\n", "easily obtain closed form solutions efficiently\n", "when the cost function is convex. In this situation,\n", "one does no need to use Linear Programming solvers\n", "to obtain the exact solution to the problem." ], "metadata": {} }, { "cell_type": "markdown", "source": [ "## Packages\n", "\n", "We load the following packages into our environment:" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "using OptimalTransport\n", "using Distances\n", "using Distributions\n", "using StatsPlots\n", "\n", "using LinearAlgebra\n", "using Random\n", "\n", "Random.seed!(1234);" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "## Continuous Distribution\n", "\n", "In the 1D case, when the source measure $\\mu$ is continuous and the cost function\n", "has the form ``c(x, y) = h(|x - y|)`` where ``h`` is a convex function,\n", "the optimal transport plan is the Monge map\n", "$$\n", "T = F_\\nu^{-1} \\circ F_\\mu\n", "$$\n", "where ``F_\\mu`` is the cumulative distribution function of `μ` and ``F_\\nu^{-1}`` is the\n", "quantile function of `ν`.\n", "In this setting, the optimal transport cost can be computed as\n", "$$\n", "\\int_0^1 c(F_\\mu^{-1}(x), F_\\nu^{-1}(x)) \\mathrm{d}x\n", "$$\n", "where ``F_\\mu^{-1}`` and ``F_\\nu^{-1}`` are the quantile functions of `μ` and `ν`,\n", "respectively.\n", "\n", "We start by defining the distributions." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "μ = Normal(0, 1)\n", "\n", "N = 10\n", "ν = Poisson(N);" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "Nest, we define a cost function." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "c(x, y) = (abs(x - y))^2 # could have used `sqeuclidean` from `Distances.jl`\n", "\n", "T = ot_plan(c, μ, ν);" ], "metadata": {}, "execution_count": 3 }, { "cell_type": "markdown", "source": [ "`T` is the Monge Map. Let's visualize it." ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=3}", "image/png": 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], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "104.72027014853339" }, "metadata": {}, "execution_count": 5 } ], "cell_type": "code", "source": [ "ot_cost(c, μ, ν)" ], "metadata": {}, "execution_count": 5 }, { "cell_type": "markdown", "source": [ "If instead you want the 2-Wasserstein distance (which is the square root\n", "of the optimal transport with the Square Euclidean distatce, then use" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "10.233292243874079" }, "metadata": {}, "execution_count": 6 } ], "cell_type": "code", "source": [ "wasserstein(μ, ν; p=2)" ], "metadata": {}, "execution_count": 6 }, { "cell_type": "markdown", "source": [ "## Finite Discrete Distributions\n", "\n", "If the source and target measures are 1D finite discrete distributions\n", "(sometimes referred as empirical distributions, or as sample distributions),\n", "and if the cost function is convex, then the optimal\n", "transport plan can be written as a sorting algorithm,\n", "where the utmost left probability mass of the source is transported\n", "to the closest probability mass of the target, until everything is transported.\n", "\n", "Define your measures as DiscreteNonParametric, which is a type in Distributions.jl.\n", "Also, let's assume both point masses with equal weights and let's\n", "use the `sqeuclidean` function instead of creating our own cost function." ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "M = 15\n", "μ = DiscreteNonParametric(1.5rand(M), fill(1 / M, M))\n", "\n", "N = 10\n", "ν = DiscreteNonParametric(1.5rand(N) .+ 2, fill(1 / N, N))\n", "\n", "γ = ot_plan(sqeuclidean, μ, ν);" ], "metadata": {}, "execution_count": 7 }, { "cell_type": "markdown", "source": [ "This time γ is a sparse matrix containing the transport plan. Let's visualize the results.\n", "We create a function `curve` just as a helper to draw the transport plan." ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "┌ Warning: Assignment to `p` in soft scope is ambiguous because a global variable by the same name exists: `p` will be treated as a new local. Disambiguate by using `local p` to suppress this warning or `global p` to assign to the existing global variable.\n", "└ @ string:15\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=26}", "image/png": 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length=100)\n", " p = plot!(x, transport.(x); color=:green, label=nothing, alpha=0.5)\n", " end\n", "end\n", "p" ], "metadata": {}, "execution_count": 8 }, { "cell_type": "markdown", "source": [ "Again, the optimal transport cost can be calculated with" ], "metadata": {} }, { "outputs": [ { "output_type": "execute_result", "data": { "text/plain": "3.2925430197981305" }, "metadata": {}, "execution_count": 9 } ], "cell_type": "code", "source": [ "ot_cost(sqeuclidean, μ, ν)" ], "metadata": {}, "execution_count": 9 }, { "cell_type": "markdown", "source": [ "---\n", "\n", "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*" ], "metadata": {} } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.8.0" }, "kernelspec": { "name": "julia-1.8", "display_name": "Julia 1.8.0", "language": "julia" } }, "nbformat": 4 }