{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "entities = {'self', 'addressee', 'other'}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1 entity referent\n", "* self (\"me\")\n", "* addressee (\"you here\")\n", "* other (\"somebody else\")\n", "\n", "### 2+ entity referent\n", "* self, addressee (\"me and you here\" / inclusive we)\n", "* self, other (\"me and somebody else\" / exclusive we)\n", "* addressee, addressee (\"the two or more of you here\")\n", "* addressee, other (\"one of you here and somebody else\")\n", "* other, other (\"the two or more of them\")\n", "\n", "### 3+ entity referent\n", "* self, addressee, addressee (\"me and the two or more of you here\")\n", "* self, addressee, other (\"me, one of you here, and somebody else\")\n", "* self, other, other (\"me and two or more other people\")\n", "* addressee, addressee, other (\"the two or more of you and somebody else\")\n", "* addressee, other, other (\"one of you and two or more other people\")\n", "\n", "### 4+ entity referent\n", "* self, addressee, addressee, other (\"me, the two or more of you here, and somebody else\")\n", "* self, addressee, other, other (\"me, one of you here, and two or more other people\")\n", "* addressee, addressee, other, other (\"the two or more of you here and two or more other people\")\n", "\n", "### 5+ entity referent\n", "* self, addressee, addressee, other, other (\"me, the two or more of you here, and two or more other people\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are 17 possible markers if there's no distinction between 2 entities of the same type and 3+ entities of the same type.\n", "* a dual or trial entity number could be added to have a 3-way distinction between e.g. [other, other] and [other, other, other]\n", "* another entity category besides self, addressee, and other could be added (invisible/divine entities)\n", "* multiple self referents could be included (choral we)\n", "\n", "Also, what about the issue of mis-identifying the cue as \"self\" rather than \"addressee\" (kids calling themselves \"you\")?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from itertools import combinations, combinations_with_replacement\n", "\n", "referents = []\n", "\n", "for i in xrange(1, len(entities) * 2):\n", " for combo in combinations_with_replacement(entities, i):\n", " \n", " # choral we is impossible\n", " if combo.count('self') > 1:\n", " continue\n", " \n", " # only singular vs plural\n", " if combo.count('addressee') > 2:\n", " continue\n", " \n", " if combo.count('other') > 2:\n", " continue\n", " \n", " # compound cues\n", " referent = list(combo)\n", " \n", " for j in xrange(2, len(combo) + 1):\n", " for compound in combinations(combo, j):\n", " \n", " if compound not in referent:\n", " referent.append(compound)\n", " \n", " referents.append(referent)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "17" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(referents)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[['addressee'],\n", " ['self'],\n", " ['other'],\n", " ['addressee', 'addressee', ('addressee', 'addressee')],\n", " ['addressee', 'self', ('addressee', 'self')],\n", " ['addressee', 'other', ('addressee', 'other')],\n", " ['self', 'other', ('self', 'other')],\n", " ['other', 'other', ('other', 'other')],\n", " ['addressee',\n", " 'addressee',\n", " 'self',\n", " ('addressee', 'addressee'),\n", " ('addressee', 'self'),\n", " ('addressee', 'addressee', 'self')],\n", " ['addressee',\n", " 'addressee',\n", " 'other',\n", " ('addressee', 'addressee'),\n", " ('addressee', 'other'),\n", " ('addressee', 'addressee', 'other')],\n", " ['addressee',\n", " 'self',\n", " 'other',\n", " ('addressee', 'self'),\n", " ('addressee', 'other'),\n", " ('self', 'other'),\n", " ('addressee', 'self', 'other')],\n", " ['addressee',\n", " 'other',\n", " 'other',\n", " ('addressee', 'other'),\n", " ('other', 'other'),\n", " ('addressee', 'other', 'other')],\n", " ['self',\n", " 'other',\n", " 'other',\n", " ('self', 'other'),\n", " ('other', 'other'),\n", " ('self', 'other', 'other')],\n", " ['addressee',\n", " 'addressee',\n", " 'self',\n", " 'other',\n", " ('addressee', 'addressee'),\n", " ('addressee', 'self'),\n", " ('addressee', 'other'),\n", " ('self', 'other'),\n", " ('addressee', 'addressee', 'self'),\n", " ('addressee', 'addressee', 'other'),\n", " ('addressee', 'self', 'other'),\n", " ('addressee', 'addressee', 'self', 'other')],\n", " ['addressee',\n", " 'addressee',\n", " 'other',\n", " 'other',\n", " ('addressee', 'addressee'),\n", " ('addressee', 'other'),\n", " ('other', 'other'),\n", " ('addressee', 'addressee', 'other'),\n", " ('addressee', 'other', 'other'),\n", " ('addressee', 'addressee', 'other', 'other')],\n", " ['addressee',\n", " 'self',\n", " 'other',\n", " 'other',\n", " ('addressee', 'self'),\n", " ('addressee', 'other'),\n", " ('self', 'other'),\n", " ('other', 'other'),\n", " ('addressee', 'self', 'other'),\n", " ('addressee', 'other', 'other'),\n", " ('self', 'other', 'other'),\n", " ('addressee', 'self', 'other', 'other')],\n", " ['addressee',\n", " 'addressee',\n", " 'self',\n", " 'other',\n", " 'other',\n", " ('addressee', 'addressee'),\n", " ('addressee', 'self'),\n", " ('addressee', 'other'),\n", " ('self', 'other'),\n", " ('other', 'other'),\n", " ('addressee', 'addressee', 'self'),\n", " ('addressee', 'addressee', 'other'),\n", " ('addressee', 'self', 'other'),\n", " ('addressee', 'other', 'other'),\n", " ('self', 'other', 'other'),\n", " ('addressee', 'addressee', 'self', 'other'),\n", " ('addressee', 'addressee', 'other', 'other'),\n", " ('addressee', 'self', 'other', 'other'),\n", " ('addressee', 'addressee', 'self', 'other', 'other')]]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "referents" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Spoken English collapses these to 6 possibilities: I, you, s/he, we, you guys, they" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def english(referents):\n", " # first-person\n", " if 'self' in referents:\n", " \n", " if 'addressee' in referents: # inclusive we\n", " # doesn't matter who else is being referred to\n", " return 'we'\n", " \n", " if 'other' in referents: # exclusive we\n", " # doesn't matter who else is being referred to\n", " return 'we' \n", " \n", " return 'I'\n", " \n", " # second-person, if the speaker isn't included\n", " elif 'addressee' in referents:\n", " \n", " if referents.count('addressee') > 1: # inclusive you\n", " return 'you guys'\n", " \n", " if 'other' in referents: # exclusive you\n", " return 'you guys'\n", " \n", " return 'you'\n", " \n", " # third-person, if the addressee isn't included either\n", " elif 'other' in referents:\n", " \n", " if referents.count('other') > 1:\n", " return 'they'\n", " \n", " return 's/he'" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'we'" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "english(['self', 'addressee'])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'we'" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "english(['self', 'other'])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'you guys'" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "english(['addressee', 'other'])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'you guys'" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "english(['addressee', 'addressee']) # also ('addressee', 'addressee') compound" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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CuesOutcomes
0 [addressee] you
1 [self] I
2 [other] s/he
3 [addressee, addressee, (addressee, addressee)] you guys
4 [addressee, self, (addressee, self)] we
5 [addressee, other, (addressee, other)] you guys
6 [self, other, (self, other)] we
7 [other, other, (other, other)] they
8 [addressee, addressee, self, (addressee, addre... we
9 [addressee, addressee, other, (addressee, addr... you guys
10 [addressee, self, other, (addressee, self), (a... we
11 [addressee, other, other, (addressee, other), ... you guys
12 [self, other, other, (self, other), (other, ot... we
13 [addressee, addressee, self, other, (addressee... we
14 [addressee, addressee, other, other, (addresse... you guys
15 [addressee, self, other, other, (addressee, se... we
16 [addressee, addressee, self, other, other, (ad... we
\n", "

17 rows × 2 columns

\n", "
" ], "text/plain": [ " Cues Outcomes\n", "0 [addressee] you\n", "1 [self] I\n", "2 [other] s/he\n", "3 [addressee, addressee, (addressee, addressee)] you guys\n", "4 [addressee, self, (addressee, self)] we\n", "5 [addressee, other, (addressee, other)] you guys\n", "6 [self, other, (self, other)] we\n", "7 [other, other, (other, other)] they\n", "8 [addressee, addressee, self, (addressee, addre... we\n", "9 [addressee, addressee, other, (addressee, addr... you guys\n", "10 [addressee, self, other, (addressee, self), (a... we\n", "11 [addressee, other, other, (addressee, other), ... you guys\n", "12 [self, other, other, (self, other), (other, ot... we\n", "13 [addressee, addressee, self, other, (addressee... we\n", "14 [addressee, addressee, other, other, (addresse... you guys\n", "15 [addressee, self, other, other, (addressee, se... we\n", "16 [addressee, addressee, self, other, other, (ad... we\n", "\n", "[17 rows x 2 columns]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas\n", "\n", "data = pandas.DataFrame()\n", "\n", "data['Cues'] = referents\n", "data['Outcomes'] = [english(referent) for referent in referents]\n", "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume that the distribution of referent sets is uniform, which is probably not true." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy\n", "\n", "def sampler(p):\n", " \n", " def uniform():\n", " return numpy.random.choice(p)\n", " \n", " return uniform\n", "\n", "referent_sampler = sampler(len(data))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import ndl\n", "\n", "def activation(W):\n", " return pandas.DataFrame([ndl.activation(c, W) for c in data.Cues], index=data.index)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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Is/hetheyweyouyou guys
0 -0.000848-0.004426-0.010796 0.094586 0.051966 0.115364
1 0.038021-0.004950-0.012859 0.244965-0.003339-0.044676
2 -0.000927 0.055316 0.066743 0.114067-0.002913 0.074110
3 -0.001350-0.006548-0.015506 0.147016 0.048047 0.193614
4 0.036280-0.010656-0.027279 0.482914 0.044615 0.028538
5 -0.002198 0.044708 0.041887 0.229084 0.045385 0.275810
6 0.036122 0.043941 0.038201 0.528713-0.007516-0.007599
7 -0.001687 0.048333 0.142420 0.160588-0.004411 0.100827
8 0.035268-0.013435-0.033228 0.616866 0.038504 0.078863
9 -0.002760 0.039354 0.030369 0.304269 0.039766 0.394813
10 0.033516 0.029490 0.003721 0.845571 0.034954 0.119107
11-0.003384 0.035624 0.107613 0.277364 0.041903 0.337897
12 0.034578 0.034353 0.102137 0.654354-0.009695-0.001124
13 0.032382 0.021968-0.011912 1.048176 0.026274 0.188487
14-0.004007 0.029325 0.091090 0.359332 0.035411 0.474638
15 0.031102 0.017140 0.053163 0.995321 0.029755 0.143911
16 0.029846 0.008438 0.030560 1.225235 0.019831 0.220925
\n", "

17 rows × 6 columns

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" ], "text/plain": [ " I s/he they we you you guys\n", "0 -0.000848 -0.004426 -0.010796 0.094586 0.051966 0.115364\n", "1 0.038021 -0.004950 -0.012859 0.244965 -0.003339 -0.044676\n", "2 -0.000927 0.055316 0.066743 0.114067 -0.002913 0.074110\n", "3 -0.001350 -0.006548 -0.015506 0.147016 0.048047 0.193614\n", "4 0.036280 -0.010656 -0.027279 0.482914 0.044615 0.028538\n", "5 -0.002198 0.044708 0.041887 0.229084 0.045385 0.275810\n", "6 0.036122 0.043941 0.038201 0.528713 -0.007516 -0.007599\n", "7 -0.001687 0.048333 0.142420 0.160588 -0.004411 0.100827\n", "8 0.035268 -0.013435 -0.033228 0.616866 0.038504 0.078863\n", "9 -0.002760 0.039354 0.030369 0.304269 0.039766 0.394813\n", "10 0.033516 0.029490 0.003721 0.845571 0.034954 0.119107\n", "11 -0.003384 0.035624 0.107613 0.277364 0.041903 0.337897\n", "12 0.034578 0.034353 0.102137 0.654354 -0.009695 -0.001124\n", "13 0.032382 0.021968 -0.011912 1.048176 0.026274 0.188487\n", "14 -0.004007 0.029325 0.091090 0.359332 0.035411 0.474638\n", "15 0.031102 0.017140 0.053163 0.995321 0.029755 0.143911\n", "16 0.029846 0.008438 0.030560 1.225235 0.019831 0.220925\n", "\n", "[17 rows x 6 columns]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "W = ndl.rw(data, M=100, distribution=referent_sampler)\n", "A = activation(W)\n", "A" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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TruthPredictionAccurate?
0 you you guys False
1 I we False
2 s/he we False
3 you guys you guys True
4 we we True
5 you guys you guys True
6 we we True
7 they we False
8 we we True
9 you guys you guys True
10 we we True
11 you guys you guys True
12 we we True
13 we we True
14 you guys you guys True
15 we we True
16 we we True
\n", "

17 rows × 3 columns

\n", "
" ], "text/plain": [ " Truth Prediction Accurate?\n", "0 you you guys False\n", "1 I we False\n", "2 s/he we False\n", "3 you guys you guys True\n", "4 we we True\n", "5 you guys you guys True\n", "6 we we True\n", "7 they we False\n", "8 we we True\n", "9 you guys you guys True\n", "10 we we True\n", "11 you guys you guys True\n", "12 we we True\n", "13 we we True\n", "14 you guys you guys True\n", "15 we we True\n", "16 we we True\n", "\n", "[17 rows x 3 columns]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pandas.DataFrame([data['Outcomes'], A.idxmax(1), A.idxmax(1) == data['Outcomes']], \n", " index = ['Truth', 'Prediction', 'Accurate?']).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With 100 trials, the learner is getting a lot of them right, but just by predicting 'you guys' or 'we' (if self is a referent) all of the time, since those cover most of the referent sets." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import sim" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "english_learning = sim.Simulation(english, data, referent_sampler, 2000)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEKCAYAAADzQPVvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X9cVGWiP/DPAEMqqPgTcWYKZVBAEDDUrKwxLdCraLol\n", "dis1KrbCbKvVbXe/K+7dTNq8rSvVpVY37YfYZgp2ZXS1piwVMhF/gAoKOoyIQqKC2sDwfP9wz+3s\n", 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"plt.plot(range(1, len(trajectory) + 1), trajectory, '-')\n", "plt.xlabel('Trial Number')" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%load_ext rpy2.ipython\n", "\n", "%Rpush trajectory" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAeAAAAHgCAIAAADytinCAAAgAElEQVR4nO3da3Bb55kn+OdccACC\n", "JEgCpARRogTJgi5EJDuWnebFVpy040hmNLGrpz094+rxbOTtJNtVcnZTU7VT5drwQ2prq2trK/Km\n", "qiu9UnWne7VJZ6ZGGbNlO9O5WTcybcuJZZG6QKIAUqIgUABlgARxO+fsh8c6gsGLAQokXoH/3wfW\n", "wcE5wMMXB3+8eHGAVzJNkwAAQDxytQsAAID5IaABAASFgAYAEBQCGgBAUAhoAABBIaABAASFgAYA\n", "EBQCGgBAUAhoAABBIaABAASlVvbm+vv7+/v7i1YODAycO3eOiA4dOuR2u+ddAwAARSrWgw4Gg3Oj\n", "mddHo9H+/v6XX375+PHj864BAIC5KhbQsVisv7+/o6Nj7vpAIEBEfr9/fHx83jWWZDI5dc/s7Gyl\n", "agMAeBhVbIijq6troas8Hg8vWPE9dw175513JiYmeHn37t1PPvlkuWUoiiLLci6XK3fHZSLLsmEY\n", 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"ggplot(trajectory, aes(trial, learned)) + \n", " geom_point(alpha=0.25) + \n", " stat_smooth() +\n", " coord_cartesian(ylim=c(0,1))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.2" } }, "nbformat": 4, "nbformat_minor": 0 }