Franke2012.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import special, stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 631,
   "metadata": {},
   "outputs": [],
   "source": [
    "dist_open_under = stats.norm(loc=0, scale=1/3)\n",
    "dist_open_pdf = dist_open_under.pdf\n",
    "dist_open = dist_open_under.rvs\n",
    "\n",
    "dist_closed_under = stats.uniform(0,1)\n",
    "dist_closed = dist_closed_under.rvs\n",
    "\n",
    "myclip_a = 0\n",
    "my_mean, my_std = 0.1, 1/3\n",
    "a = (myclip_a - my_mean) / my_std\n",
    "dist_halfopen_under = stats.truncnorm(a, b=np.inf, loc=my_mean, scale=my_std)\n",
    "dist_halfopen_pdf = dist_halfopen_under.pdf\n",
    "dist_halfopen = dist_halfopen_under.rvs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [],
   "source": [
    "def theoretical_optimal(context_shape):\n",
    "    num_obj, num_props = context_shape\n",
    "    \n",
    "    return np.min([1, (2*num_props)/num_obj])\n",
    "\n",
    "def create_context(context_size, num_properties_type):\n",
    "    \"\"\"\n",
    "    Like in Franke 2012 (On scales, etc.), 1/3 of properties of each type.\n",
    "    Return an array with shape (# objects, # properties)\n",
    "    \"\"\"\n",
    "    size=(context_size, num_properties_type)\n",
    "    context = np.column_stack((\n",
    "        dist_open(size),\n",
    "        dist_closed(size),\n",
    "        dist_halfopen(size)\n",
    "    ))\n",
    "    return context\n",
    "\n",
    "def calculate_salience(context):\n",
    "    \"\"\"\n",
    "    Calculates the salience of every object with respect to each property\n",
    "    \"\"\"\n",
    "    # first and second dimensions are both the objects\n",
    "    tiled_context = np.tile(context, reps=(len(context),1,1))\n",
    "    tiled_context_2 = np.tile(context[:,None,:], reps=(1, len(context), 1))\n",
    "    distances = np.abs(tiled_context - tiled_context_2)\n",
    "    saliences = np.sum(distances, axis=1)\n",
    "    return saliences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.4 0.2 1.8]\n",
      " [0.7 0.3 1.2]\n",
      " [0.5 0.3 1. ]]\n"
     ]
    }
   ],
   "source": [
    "# this is the context from the paper\n",
    "context = np.array([\n",
    "    [0.2, -0.1, 1.3],\n",
    "    [-0.1, 0.0, 0.3],\n",
    "    [0.3, -0.2, 0.5]\n",
    "])\n",
    "\n",
    "print(calculate_salience(context))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {},
   "outputs": [],
   "source": [
    "def communicate(context, salience, designated_object, print_output=False):\n",
    "    \n",
    "    # first decide for each object which signal to send\n",
    "    # the indices of the most salient property for each object (the first part of the potential signal)\n",
    "    most_salient_indices = np.argmax(salience, axis=1)\n",
    "    # the most salient property for each object (can only use np.choice up to 30 rows)\n",
    "    most_salient = context[range(len(most_salient_indices)), most_salient_indices]\n",
    "    # mean value of the properties across objects\n",
    "    median = np.median(context, axis=0)\n",
    "    # this is the polarity of the signal for each potential designated object, i.e. the second part of the message\n",
    "    polarity = (most_salient > median[most_salient_indices]).astype(int)\n",
    "\n",
    "    signal = (most_salient_indices[designated_object], polarity[designated_object])\n",
    "\n",
    "    # saliences of each object wrt the property indicated by the signal\n",
    "    saliences_objects = salience[:,signal[0]]\n",
    "    # degrees of all objects wrt the property indicated by the signal\n",
    "    prop = context[:, signal[0]]\n",
    "    # mask for which objects are compatible with the signal's polarity\n",
    "    indices_compatible_polarity = prop > median[signal[0]] if signal[1] else prop < median[signal[0]]\n",
    "    # find max of saliency among the objects compatible with the polarity\n",
    "    masked_saliences = np.where(indices_compatible_polarity, saliences_objects, 0)\n",
    "    picked = np.argmax(masked_saliences)\n",
    "\n",
    "    if print_output:\n",
    "        display(\"Context\", context)\n",
    "        display(\"salience\", salience)\n",
    "        display(\"most salient\", most_salient)\n",
    "        display(\"most_salient_indices\", most_salient_indices)\n",
    "        display(\"median\", median)\n",
    "        display(\"polarity\", polarity)\n",
    "        display(\"signal\", signal)\n",
    "        display(\"saliences_objects\", saliences_objects)\n",
    "        display(\"prop\", prop)\n",
    "        display(\"compatible\", indices_compatible_polarity)\n",
    "        display(\"masked_saliences\", masked_saliences)\n",
    "        display(\"picked\", picked)\n",
    "        display(\"designated\", designated_object)\n",
    "        print(\"\\n\\n\")\n",
    "    \n",
    "    # returns (whether successful, index property, value of property for object)\n",
    "    return picked == designated_object, signal[0], context[designated_object, signal[0]], "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "def run_single(context_size, num_prop_per_type, num_runs=500):\n",
    "    data = np.empty((num_runs, 3))\n",
    "    for i in range(num_runs):\n",
    "        designated_index = np.random.randint(context_size)\n",
    "        context = create_context(context_size, num_prop_per_type)\n",
    "        salience = calculate_salience(context)\n",
    "        data[i] = communicate(context, salience, designated_index)\n",
    "    return data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plots from the paper\n",
    "\n",
    "## First plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 632,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_properties_per_type_grid, num_objects_grid = np.mgrid[2:21, 2:21]\n",
    "success_rates = np.zeros(shape=(num_objects_grid.flatten().size, 3))\n",
    "for i, (num_properties_per_type, num_objects) in enumerate(\n",
    "        zip(num_properties_per_type_grid.flatten(), num_objects_grid.flatten())):\n",
    "    theo_max = theoretical_optimal((num_objects, num_properties_per_type*3))\n",
    "    success_rate = np.mean(run_single(num_objects, num_properties_per_type).T[0])\n",
    "    success_rates[i] = [num_objects, num_properties_per_type, success_rate/theo_max]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 633,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y, Z = success_rates.T\n",
    "\n",
    "prop_success_results = np.reshape(Z, num_objects_grid.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 634,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 410.976x287.683 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "cm = ax.pcolormesh(\n",
    "    num_properties_per_type_grid,\n",
    "    num_objects_grid, \n",
    "    prop_success_results,\n",
    "#     cmap=\"Greens\"\n",
    ")\n",
    "\n",
    "ax.set_xticks(np.linspace(10, 60, 6)/3)\n",
    "ax.set_xticklabels(np.linspace(10, 60, 6))\n",
    "\n",
    "cb = fig.colorbar(cm)\n",
    "\n",
    "ax.set_xlabel(\"Number of properties\")\n",
    "ax.set_ylabel(\"Context size\")\n",
    "\n",
    "cb.ax.set_ylabel(\"Proportion successful\", rotation=270, labelpad=15)\n",
    "\n",
    "w = 5.708\n",
    "fig.set_size_inches(w, w*0.7)\n",
    "plt.savefig(\"frankeSuccess.png\", dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 602,
   "metadata": {},
   "outputs": [],
   "source": [
    "def second_plot(results, num_properties):    \n",
    "    \n",
    "    successful, prop_index, prop_value = results.T\n",
    "    \n",
    "    open_scale = prop_value[(prop_index < num_properties)]\n",
    "    closed_scale = prop_value[((prop_index >= num_properties) & (prop_index < num_properties*2))]\n",
    "    half_closed_scale = prop_value[(prop_index >= num_properties*2)]\n",
    "    \n",
    "    fig, (ax1, ax2, ax3) = plt.subplots(3, 1)\n",
    "\n",
    "    #### first ax\n",
    "\n",
    "    ax1.hist(open_scale, bins=100, ec=\"black\", density=True)\n",
    "\n",
    "    ax1_2 = ax1.twinx()\n",
    "    xs = np.linspace(-1.5, 1.5, 1000)\n",
    "    ys = dist_open_pdf(xs)\n",
    "    ax1_2.plot(xs, ys, color=\"green\")\n",
    "\n",
    "    #### second ax\n",
    "\n",
    "    ax2.hist(closed_scale, bins=100, ec=\"black\", density=True)\n",
    "\n",
    "    ax2_2 = ax2.twinx()\n",
    "    ax2_2.plot([0,1], [1,1], color=\"green\")\n",
    "\n",
    "    #### third ax\n",
    "\n",
    "    ax3.hist(half_closed_scale, bins=60, ec=\"black\", density=True)\n",
    "\n",
    "    ax3_2 = ax3.twinx()\n",
    "    xs = np.linspace(0, 2.5, 1000)\n",
    "    ys = dist_halfopen_pdf(xs)\n",
    "    ax3_2.plot(xs, ys, color=\"green\")\n",
    "    \n",
    "    for axis in [ax1_2, ax2_2, ax3_2]:\n",
    "        axis.tick_params(axis='y', colors='green')\n",
    "    \n",
    "    ax3.set_xlabel(\"Degrees\")\n",
    "    ax2.set_ylabel(\"Densities\")\n",
    "\n",
    "    fig.subplots_adjust(hspace=0.4)\n",
    "\n",
    "    return fig, (ax1, ax2, ax3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 635,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_properties_per_type = 8\n",
    "context_size = 30\n",
    "results = run_single(context_size, num_properties_per_type, num_runs=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 636,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 410.976x287.683 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = second_plot(results, num_properties_per_type)\n",
    "\n",
    "w = 5.708\n",
    "fig.set_size_inches(w, w*0.7)\n",
    "plt.savefig(\"frankeSamples.png\", dpi=300)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:computational_models] *",
   "language": "python",
   "name": "conda-env-computational_models-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}