{ "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": "104.72027014853334" }, "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": "10.233292243874077" }, "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": [ { "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": "1.11.6" }, "kernelspec": { "name": "julia-1.11", "display_name": "Julia 1.11.6", "language": "julia" } }, "nbformat": 4 }