{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Robust Pooling\n", "\n", "We illustrate several robust pooling operations. Denote by $\\phi$ the penalty function. Then robust pooling finds the solution to the optimization problem\n", "\n", "$$\n", "y \\in \\text{arg min}_u \\sum_{i=1}^{n} \\phi(u - x_i; \\alpha)\n", "$$\n", "\n", "where $\\alpha$ is a parameter of the penalty function." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# define various penalty functions\n", "\n", "import numpy as np\n", "\n", "phi = {\n", " 'Quadratic': lambda z, alpha: 0.5 * np.power(z, 2.0),\n", " 'Huber': lambda z, alpha: np.where(np.abs(z) <= alpha, 0.5 * np.power(z, 2.0), alpha * np.abs(z) - 0.5 * alpha * alpha),\n", " 'Pseudo-Huber': lambda z, alpha: np.power(alpha, 2.0) * (np.sqrt(1.0 + np.power(z, 2.0) / np.power(alpha, 2.0)) - 1.0),\n", " 'Welsch': lambda z, alpha: 1.0 - np.exp(-0.5 * np.power(z / alpha, 2.0)),\n", " 'Trunc. Quad.': lambda z, alpha: np.minimum(0.5 * np.power(z, 2.0), 0.5 * alpha * alpha)\n", "}" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot the penalty functions\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "alpha = 1.0\n", "z = np.linspace(-5.0, 5.0, num=101)\n", "\n", "for name in sorted(phi.keys()):\n", " plt.plot(z, phi[name](z, alpha))\n", "\n", "plt.title(\"$\\phi(z, a)$\")\n", "plt.legend(sorted(phi.keys()))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By plotting the sum of two penalty functions centered at $x_1 = -2\\alpha$ and $x_2 = 2\\alpha$, respectively, we can observe some of their properties: such as the convexity of Huber, the strong convexity of pseudo-Huber and the non-convexity of Welsch." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot the sum of two penalty functions\n", "\n", "alpha = 1.0\n", "delta = 2.0 * alpha\n", "u = np.linspace(-5.0, 5.0, num=101)\n", "\n", "for name in sorted(phi.keys()):\n", " plt.plot(u, phi[name](u - delta, alpha) + phi[name](u + delta, alpha))\n", "\n", "plt.title(\"$f(x, u) = \\phi(u - x_1, a) + \\phi(u - x_2, a)$\")\n", "plt.legend(sorted(phi.keys()))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot the sum of two penalty functions scaled\n", "\n", "for name in sorted(phi.keys()):\n", " f = phi[name](u - delta, alpha) + phi[name](u + delta, alpha)\n", " plt.plot(u, f / (np.max(f) - np.min(f)))\n", "\n", "plt.title(\"$f(x, u) = \\kappa \\phi(u - x_1, a) + \\kappa \\phi(u - x_2, a)$\")\n", "plt.legend(sorted(phi.keys()), loc='lower right')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "We now explore how the solutions of the sum of two penalty functions vary as a function of its inputs. We fix $x_1$ to zero and varying $x_2$. Our objective (with $\\alpha = 1$) is\n", "$$\n", "f(x, u) = \\phi(u) + \\phi(u - x)\n", "$$\n", "for scalar $x$ and $u$.\n", "\n", "As we vary $x$ we see that the non-convex penalty functions can produce multiple isolated solutions, while the strongly convex quadratic and pseudo-Huber always produce a single solution. Note, however, that for a large number of points (sum of $n >> 2$ penalty functions) the effect from changing a single point would not be as pronounced as we demonstrate here for just two points." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# prepare data for animation and plots\n", "\n", "def find_local_minima(v):\n", " \"\"\"Finds the local minima of a one-dimensional curve and returns their index. In the\n", " case of a plateau (such as for Huber) returns the boundary points of the plateau.\"\"\"\n", " return [i for i in range(1, len(v)-1) if ((v[i] < v[i-1]) and (v[i] <= v[i+1])) or ((v[i] <= v[i-1]) and (v[i] < v[i+1]))]\n", "\n", "\n", "x = np.linspace(-4.0, 4.0, num=100)\n", "u = np.linspace(-5.0, 5.0, num=501)\n", "y = {}\n", "for name in sorted(phi.keys()):\n", " y[name] = [[] for xi in x]\n", "\n", "for i in range(len(x)):\n", " for name in sorted(phi.keys()):\n", " # find (global) minimia of objective function\n", " f = phi[name](u, 1.0) + phi[name](u - x[i], 1.0)\n", " f_min = np.min(f)\n", " y[name][i] = [j for j in find_local_minima(f) if f[j] <= f_min + 1.0e-3]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "%%capture\n", "# animate solution for sum of two penalty functions\n", "\n", "from matplotlib import animation\n", "from IPython.display import HTML\n", "\n", "\n", "def animate(fnum, u, x, y):\n", " plt.clf()\n", "\n", " for a in ax:\n", " a.clear()\n", " \n", " for name in sorted(phi.keys()):\n", " # plot the (normalized) objective\n", " f = phi[name](u, 1.0) + phi[name](u - x[fnum], 1.0)\n", " f = f / np.max(f)\n", " p = ax[0].plot(u, f)\n", "\n", " # indicate minima\n", " for i in y[name][fnum]:\n", " ax[0].plot([u[i], u[i]], [-0.1, f[i]], color=p[0].get_color(), ls='--')\n", " \n", " # plot y (global minima) as a function of x\n", " y_min = [min(u[i]) for i in y[name][:fnum+1]]\n", " y_max = [max(u[i]) for i in y[name][:fnum+1]]\n", " \n", " ax[1].plot(x[:fnum+1], y_min, color=p[0].get_color())\n", " ax[1].plot(x[:fnum+1], y_max, color=p[0].get_color())\n", " \n", " ax[0].set_xlim(u[0], u[-1]); ax[0].set_ylim(-0.1, 1.0)\n", " ax[0].set_xlabel(r\"$u$\"); ax[0].set_ylabel(r\"$f$ (scaled)\")\n", " ax[0].set_title(\"Objective\")\n", " \n", " ax[1].set_xlim(x[0], x[-1]); ax[1].set_ylim(-4.0, 4.0)\n", " ax[1].set_xlabel(r\"$x$\"); ax[1].set_ylabel(r\"$y$\")\n", " ax[1].set_title(\"Solution\")\n", "\n", " return ax\n", "\n", "\n", "fig = plt.figure()\n", "ax = [plt.subplot(1, 2, 1), plt.subplot(1, 2, 2)]\n", "ani = animation.FuncAnimation(fig, animate, fargs=(u, x, y), interval=100, frames=len(x), blit=False, repeat=False)\n", "plt.close(fig)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# display using video or javascript\n", "HTML(ani.to_html5_video())\n", "#HTML(ani.to_jshtml())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now plot the solution sets separately for each penalty function." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cm = plt.rcParams[\"axes.prop_cycle\"].by_key()[\"color\"]\n", "\n", "for indx, name in enumerate(sorted(phi.keys())):\n", " y_min = [min(u[i]) for i in y[name]]\n", " y_max = [max(u[i]) for i in y[name]]\n", "\n", " fig = plt.figure()\n", " plt.plot(x, y_min, color=cm[indx % len(cm)])\n", " plt.plot(x, y_max, color=cm[indx % len(cm)])\n", " for i in range(len(x)):\n", " if len(y[name][i]) > 2:\n", " for uj in [u[jy] for jy in y[name][i] if ((u[jy] != y_min[i]) and (u[jy] != y_max[i]))]:\n", " plt.plot(x[i], uj, color=cm[indx % len(cm)], marker='.')\n", " \n", " if name == \"Huber\":\n", " plt.fill_between(x, y_max, y_min, color=cm[indx % len(cm)])\n", " \n", " plt.xlabel(r\"$x$\"); plt.ylabel(r\"$y$\"); plt.title(name)\n", " \n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }