Entropy Estimation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a16146a9",
   "metadata": {},
   "source": [
    "# Estimating the Entropy of Linguistic Distributions\n",
    "\n",
    "[insert intro here]\n",
    "\n",
    "- **Paper**: [Estimating the Entropy of Linguistic Distributions](https://aclanthology.org/2022.acl-short.20) (Arora et al., ACL 2022)\n",
    "- **Code**: https://github.com/rycolab/entropy-estimation\n",
    "\n",
    "## Setup\n",
    "\n",
    "Make sure you have a fairly recent Python version (I am on Python 3.9.12). Run the following:\n",
    "\n",
    "```\n",
    "https://github.com/rycolab/entropy-estimation.git\n",
    "pip install -e .\n",
    "```\n",
    "\n",
    "This will install the entropy package with the necessary dependencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "0451a42b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import entropy\n",
    "from collections import Counter, defaultdict\n",
    "import glob\n",
    "import csv\n",
    "from tqdm import tqdm\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "580f7091",
   "metadata": {},
   "source": [
    "## Basic usage\n",
    "\n",
    "Say you have a sample which is a list of observations (for example, `heads` and `tails` from flipping a coin). `entropy.prob()` extracts various useful statistics from your sample, which are to be fed to an entropy estimator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3b6191d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0.5, 0.5], 4, Counter({'heads': 2, 'tails': 2}))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coins = ['heads', 'heads', 'tails', 'tails']\n",
    "entropy.prob(coins)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "648c0803",
   "metadata": {},
   "source": [
    "As you can see, `entropy.prob` returns the discrete probability distribution, the number of observations in the sample, and a counter over the sample.\n",
    "\n",
    "We can run all the estimators in `entropy.funcs` on our sample to see what's available. By default, `entropy` returns estimates in nats. For reference, 1 nat = $\\frac{1}{\\ln{2}} \\approx 1.44$ bits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "55a24f0b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mle 0.6931471805599453\n",
      "miller_madow 0.8181471805599453\n",
      "jackknife 0.8630462173553428\n",
      "horvitz_thompson 0.7393569925972749\n",
      "chao_shen 0.7393569925972749\n",
      "wolpert_wolf 0.6166666666666667\n",
      "nsb 1.4118281434807918\n"
     ]
    }
   ],
   "source": [
    "for estimator in entropy.funcs:\n",
    "    print(estimator.__name__, estimator(*entropy.prob(coins)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b10a535a",
   "metadata": {},
   "source": [
    "Briefly, here is how each of these estimators work:\n",
    "\n",
    "1. **Maximum Likelihood Estimation (MLE)**: This is the usual naive way to calculate the entropy of a sample--just measure the observed probabilities over outcomes and plug those in as if they were the true values (i.e. we have a model of the distribution that maximises the likelihood of our observations).\n",
    "2. **Miller-Madow**: Applies a first-order Taylor correction to MLE.\n",
    "3. **Jackknife**: Using subsamples of our sample, it attempts to project the entropy estimate for the whole sample.\n",
    "4. **Horvitz-Thompson**: Takes into account the likelihood of an outcome occurring at all in our sample--less-frequent outcomes contribute more to the entropy in order to compensate for MLE's negative bias.\n",
    "4. **Chao-Shen**: Modifies Horvitz-Thompson to use a coverage-reduced estimate of the probability of the outcomes. Empirically better than it.\n",
    "5. **Wolpert-Wolf**: First Bayesian entropy estimator with a Dirichlet prior.\n",
    "5. **Nemenman-Shafee-Bialek (NSB)**: Improves upon Wolpert-Wolf.\n",
    "\n",
    "For the equations for each and their derivations, see [our paper](https://aclanthology.org/2022.acl-short.20/)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d1d6004",
   "metadata": {},
   "source": [
    "## Experiment 1: A Fair Coin\n",
    "\n",
    "A fair coin, assigning probablility 0.5 to each heads and tails, would have an entropy of 1 bit $\\approx$ 0.6944 nats. How do various estimators converge to the true entropy as we obtain more samples from a fair coin? Here we will simulate 100 coin flips and plot the entropy estimate after each one.\n",
    "\n",
    "Here is our sample generator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5ae1632d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def coin_flip():\n",
    "    if random.random() >= 0.5: return 'heads'\n",
    "    else: return 'tails'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c302fef2",
   "metadata": {},
   "source": [
    "Now we generate the estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "77b6d3f8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First 5 observations: ['heads', 'tails', 'heads', 'tails', 'heads']\n",
      "First 5 MLE entropy estimates: [-0.0, 0.6931471805599453, 0.6365141682948128, 0.6931471805599453, 0.6730116670092565]\n"
     ]
    }
   ],
   "source": [
    "X = list(range(100))\n",
    "estimates = {estimator.__name__: [] for estimator in entropy.funcs}\n",
    "\n",
    "sample = []\n",
    "for i in X:\n",
    "    sample.append(coin_flip())\n",
    "    stats = entropy.prob(sample) # get necessary statistics\n",
    "    for estimator in entropy.funcs:\n",
    "        estimates[estimator.__name__].append(estimator(*stats)) # append estimate\n",
    "\n",
    "print('First 5 observations:', sample[:5])\n",
    "print('First 5 MLE entropy estimates:', estimates['mle'][:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38cad8d0",
   "metadata": {},
   "source": [
    "Finally, we can plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7c6b0111",
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "true = math.log(2)\n",
    "for name, vals in estimates.items():\n",
    "    plt.plot(X, vals, label=name)\n",
    "\n",
    "plt.axhline(true, label='True')\n",
    "plt.legend()\n",
    "plt.xlabel('# observations')\n",
    "plt.ylabel('Entropy (nats)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38938d41",
   "metadata": {},
   "source": [
    "### Evaluating entropy estimators\n",
    "\n",
    "While we can sort of eyeball the convergence of each estimators, it would be better to use some statistical metrics to compare their performance. From statistical estimation theory, we know to use the mean squared error (MSE) as a good judge of the bias-variance tradeoff. Let's plot that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "72ebd148",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MSEs = {estimator.__name__: [] for estimator in entropy.funcs}\n",
    "for name in estimates:\n",
    "    for estimate in estimates[name]:\n",
    "        MSE = (estimate - true)**2\n",
    "        MSEs[name].append(MSE)\n",
    "\n",
    "for name, vals in MSEs.items():\n",
    "    plt.plot(X, vals, label=name)\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('# observations')\n",
    "plt.ylabel('MSE (nats$^2$)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43e3c958",
   "metadata": {},
   "source": [
    "## Experiment 2: Symmetric Dirichlet distributions\n",
    "\n",
    "A question that often comes up, given the wide variety of entropy estimators proposed in the information-theoretic literature, is \"which estimator is best?\". One way to more generally test the performance of estimators is to empirically test their performance over many distributions.\n",
    "\n",
    "In this section, we'll sample a bunch of distributions from the [Dirichlet distribution](https://en.wikipedia.org/wiki/Dirichlet_distribution) (with equal weight for each outcome, hence symmetric) and, over the whole set of distributions we have, plot the MSE and mean bias of the estimators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b53ae408",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from collections import defaultdict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6451c59a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_dirichlet(distribution):\n",
    "    obs = random.random()\n",
    "    total = 0\n",
    "    for outcome, prob in enumerate(distribution):\n",
    "        total += prob\n",
    "        if total >= obs:\n",
    "            return outcome"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33a2b0fb",
   "metadata": {},
   "source": [
    "Now we generate 100 distributions, each of which will have 5 possible discrete outcomes with probabilities sampled from the Dirichlet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bcb6273a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.09336365, 0.43863102, 0.05569544, 0.23931554, 0.17299436])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = 5\n",
    "distribs = np.random.dirichlet([1] * K, 100)\n",
    "distribs[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c06fe04",
   "metadata": {},
   "source": [
    "And now collecting the actual estimates. We'll run the estimators on sample sizes from 1 to 20."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "c481bd32",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n",
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n"
     ]
    }
   ],
   "source": [
    "biases = {estimator.__name__: defaultdict(list) for estimator in entropy.funcs}\n",
    "\n",
    "for key, distrib in enumerate(distribs):\n",
    "    true_entropy = -sum([x * math.log(x) for x in distrib])\n",
    "    sample = []\n",
    "    \n",
    "    for i in range(20):\n",
    "        add = sample_dirichlet(distrib)\n",
    "        sample.append(add)\n",
    "        \n",
    "        for estimator in entropy.funcs:\n",
    "            estimate = estimator(*entropy.prob(sample))\n",
    "            biases[estimator.__name__][i].append(estimate - true_entropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55562c18",
   "metadata": {},
   "source": [
    "Great, we have our observations! Now let's plot the bias and MSE of the maximum-likelihood estimator. Mathematically, MLE is known to be negatively biased in expectation but does converge to true entropy with greater numbers of samples, so we should expect bias to approach 0 from below and MSE to decrease with sample size. (And indeed, we do see that.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "0e5fddfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2)\n",
    "axs[0].boxplot([biases['mle'][x] for x in biases['mle']])\n",
    "axs[0].set(ylabel='Bias (nats)')\n",
    "plt.xlabel('Sample size')\n",
    "axs[1].boxplot([[z**2 for z in biases['mle'][x]] for x in biases['mle']])\n",
    "axs[1].set(ylabel='MSE (nats$^2$)', yscale='log')\n",
    "fig.suptitle('Performance of the MLE estimator')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2496a230",
   "metadata": {},
   "source": [
    "How do the other estimators fare in comparison? Pretty much everything estimates a higher entropy than MLE, except for the Wolpert-Wolf estimator. Interestingly, the NSB estimator gives a pretty big overestimate before beginning converging down to the true value. All estimators converge to the true entropy gradually--the are provably asymptotically consistent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "94195f71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2)\n",
    "for estimator in biases:\n",
    "    avgs = [sum(biases[estimator][sample_size]) / len(distribs) for sample_size in biases[estimator]]\n",
    "    axs[0].plot(avgs, label=estimator)\n",
    "axs[0].set(ylabel='Bias (nats)')\n",
    "axs[0].axhline(0, label='True')\n",
    "plt.xlabel('Sample size')\n",
    "for estimator in biases:\n",
    "    avgs = [sum([x**2 for x in biases[estimator][sample_size]]) / len(distribs) for sample_size in biases[estimator]]\n",
    "    axs[1].plot(avgs, label=estimator)\n",
    "axs[1].set(ylabel='MSE (nats$^2$)', yscale='log')\n",
    "fig.suptitle('Symmetric Dirichlet entropy, all estimators')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45e5db3f",
   "metadata": {},
   "source": [
    "## Experiment 3: Unigram distribution\n",
    "\n",
    "Now, we'll try an actual linguistic problem where the choice of estimator matters: measuring the entropy of the **unigram distribution**, i.e. the non-contextual distribution over unigram tokens for a particular language.\n",
    "\n",
    "The language we will estimate the entropy of the unigram distribution of is Mongolian. We will use frequency counts from the Mongolian Wikipedia as the \"gold\" entropy, and take subsamples from that distribution to run our entropy estimators on. We have processed a file (`mongolian.txt`) which already has the counts of tokens from the Mongolian Wikipedia.\n",
    "\n",
    "This is a replication of part of [section 4.1 of our paper](https://aclanthology.org/2022.acl-short.20/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1c482db6",
   "metadata": {},
   "outputs": [],
   "source": [
    "counts = Counter()\n",
    "N = 0\n",
    "with open('acl_2022/data/LDC96L14/mongolian.txt', 'r') as fin:\n",
    "    for row in fin:\n",
    "        row = row.rstrip()\n",
    "        word, freq = row.split()\n",
    "        counts[word] += int(freq)\n",
    "        N += int(freq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b46291f5",
   "metadata": {},
   "source": [
    "And here's a look at what our data is: raw frequency counts of tokens, from the original corpus of 4.7 million tokens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1e9436bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('нь', 125174), ('оны', 36778), ('юм', 34835), ('онд', 33600), ('байна', 27782), ('болон', 26016), ('байсан', 24806), ('энэ', 22333), ('сарын', 22282), ('бөгөөд', 21971)]\n",
      "4708173 total tokens\n"
     ]
    }
   ],
   "source": [
    "print(counts.most_common(10))\n",
    "print(f'{N} total tokens')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c851889",
   "metadata": {},
   "source": [
    "We just need to make the actual probability distribution now for passing to the estimators, which `entropy.prob_counts()` handles. (It's just the frequencies divided by the sum of frequencies, for each class in our distribution.)\n",
    "\n",
    "We'll also get the \"gold\" entropy, i.e. the MLE entropy over the whole corpus. This is not the actual unigram entropy for Mongolian, but since our corpus is fairly large it is a good estimate and a baseline to compare our much smaller subsample estimates against."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "b318f136",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.02658653367240329, 0.007811522643709141, 0.007398836024079829, 0.007136526206662329, 0.00590080271052062, 0.005525710291444261, 0.0052687103893591, 0.00474345356468422, 0.004732621337406251, 0.004666565990671966]\n",
      "True entropy: 9.15953158361596 nats\n"
     ]
    }
   ],
   "source": [
    "S = entropy.prob_counts(counts, N)\n",
    "print(S[:10])\n",
    "\n",
    "true_entropy = entropy.mle(S, N, counts)\n",
    "print(f'True entropy: {true_entropy} nats')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0455949d",
   "metadata": {},
   "source": [
    "I will use a more efficient sampler than before for this problem because our distribution has a very large sample space. The code is below, but is not really necessary to understand."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "bead078c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[7, 980, 29191, 688, 16049, 1075, 52, 70, 46704, 463]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from bisect import bisect_left\n",
    "\n",
    "# precompute partial sums to speed up sampling\n",
    "distribution = [int(x * N) for x in S]\n",
    "for i in range(1, len(distribution)):\n",
    "    distribution[i] += distribution[i - 1]\n",
    "distribution = [x / N for x in distribution]\n",
    "\n",
    "# use binary search to find sampled item from random number\n",
    "def sample_corpus(distrib, sample_size):\n",
    "    return [bisect_left(distrib, obs) for obs in np.random.rand(sample_size)]\n",
    "\n",
    "sample_corpus(distribution, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f36ab1e8",
   "metadata": {},
   "source": [
    "Now, we actually get our entropy estimates. We will run our estimators on subsamples of the Mongolian corpus of the size: $10^1, 10^2, 10^3, 10^4, 10^5, 10^6$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "728d051d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Insufficient data (no coincidences found in counts). Return plugin estimate.\n"
     ]
    }
   ],
   "source": [
    "biases = {estimator.__name__: [] for estimator in entropy.funcs}\n",
    "\n",
    "X = [10, 10**2, 10**3, 10**4, 10**5, 10**6]\n",
    "for sample_size in X:\n",
    "    sample = sample_corpus(distribution, sample_size)\n",
    "    stats = entropy.prob(sample)\n",
    "    \n",
    "    for estimator in entropy.funcs:\n",
    "        estimate = estimator(*stats)\n",
    "        biases[estimator.__name__].append(estimate - true_entropy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "9d2ba5db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mle                 : -6.86 -4.58 -2.68 -1.23 -0.44 -0.11 \n",
      "miller_madow        : -6.41 -4.10 -2.28 -0.96 -0.31 -0.06 \n",
      "jackknife           : -5.91 -3.61 -1.93 -0.75 -0.22 -0.03 \n",
      "horvitz_thompson    : -5.62 -2.01  0.20  1.11  0.85  0.42 \n",
      "chao_shen           : -4.34 -1.35 -1.62 -0.86 -0.29  0.00 \n",
      "wolpert_wolf        : -7.06 -4.80 -2.77 -1.08 -0.10  0.20 \n",
      "nsb                 : -6.86 -0.49 -1.19 -0.44 -0.09  0.02 \n"
     ]
    }
   ],
   "source": [
    "for estimator in biases:\n",
    "    print(f'{estimator:<20}:', end=' ')\n",
    "    for bias in biases[estimator]:\n",
    "        print(f'{bias:>5.2f}', end=' ')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbdbb27f",
   "metadata": {},
   "source": [
    "As you can see above, we get bias converging to 0 for all the estimators by the time our sample size is $10^6$ (except for Horvitz-Thompson, which gets to a pretty big positive bias but is on the way down). Now let's plot the bias and MSE of all of the estimators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "e892119e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2)\n",
    "for estimator in biases:\n",
    "    axs[0].plot(X, biases[estimator], label=estimator)\n",
    "axs[0].set(ylabel='Bias (nats)', xscale='log')\n",
    "axs[0].axhline(0, label='True')\n",
    "plt.xlabel('Sample size')\n",
    "for estimator in biases:\n",
    "    axs[1].plot(X, [x**2 for x in biases[estimator]], label=estimator)\n",
    "axs[1].set(ylabel='MSE (nats$^2$)', yscale='log', xscale='log')\n",
    "fig.suptitle('Unigram entropy, all estimators')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d3330cb",
   "metadata": {},
   "source": [
    "## Experiment 4: Replication of [McCarthy et al. (2020)](https://aclanthology.org/2020.emnlp-main.456/)\n",
    "\n",
    "Finally, we will replicate McCarthy et al. (2020)'s study comparing the grammatical gender systems of several European languages, using mutual information (to compare sets of genders for words with the same meanings across languages).\n",
    "\n",
    "First, we define functions to calculate these information theoretic quantities:\n",
    "\n",
    "1. **Conditional entropy** $$\\hat{H}(Y \\mid X) = \\sum_{x \\in \\mathcal{X}}{\\hat{p}(x) \\hat{H}(Y \\mid X = x)}$$\n",
    "2. **Mutual information** $$\\hat{I}(X; Y) = \\hat{H}(X) - \\hat{H}(X \\mid Y)$$\n",
    "3. **Variation of information** $$\\hat{VI}(X; Y) = \\hat{H}(X \\mid Y) + \\hat{H}(Y \\mid X)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0e6daeab",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cond_H(p, q, funcs, counts_q, N_q):\n",
    "    res = [0 for func in funcs]\n",
    "    for val in counts_q:\n",
    "        sample = []\n",
    "        for i in range(len(q)):\n",
    "            if q[i] == val:\n",
    "                sample.append(p[i])\n",
    "        for i, func in enumerate(funcs):\n",
    "            S, N, counts = entropy.prob(sample)\n",
    "            est = func(S, N, counts)\n",
    "            res[i] += (counts_q[val] / N_q) * est\n",
    "    return res\n",
    "\n",
    "def mi(p, q, funcs):\n",
    "    S_p, N_p, counts_p = entropy.prob(p)\n",
    "    S_q, N_q, counts_q = entropy.prob(q)\n",
    "    res = [func(S_p, N_p, counts_p) for func in funcs]\n",
    "    sub = cond_H(p, q, funcs, counts_q, N_q)\n",
    "    for i in range(len(funcs)):\n",
    "        res[i] -= sub[i]\n",
    "    if res[0] < 0:\n",
    "        print(sub)\n",
    "        input()\n",
    "    return res\n",
    "\n",
    "def vi(p, q, funcs):\n",
    "    S_p, N_p, counts_p = entropy.prob(p)\n",
    "    S_q, N_q, counts_q = entropy.prob(q)\n",
    "    res = cond_H(p, q, funcs, counts_q, N_q)\n",
    "    add = cond_H(q, p, funcs, counts_p, N_p)\n",
    "    for i in range(len(funcs)):\n",
    "        res[i] += add[i]\n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6a58fa7",
   "metadata": {},
   "source": [
    "To test the statistical significance of the comparison between the gender partitions of two language, we will run permutation tests:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "d9f27073",
   "metadata": {},
   "outputs": [],
   "source": [
    "def permutation_test(p, q, true_mi, true_vi, funcs, perms=1000):\n",
    "    p = [x for x in p]\n",
    "    q = [x for x in q]\n",
    "    gq_mi, lq_vi = [1 for func in funcs], [1 for func in funcs]\n",
    "    for i in range(perms - 1):\n",
    "        p = np.random.permutation(p)\n",
    "        q = np.random.permutation(q)\n",
    "        mi_t = mi(p, q, funcs)\n",
    "        vi_t = vi(p, q, funcs)\n",
    "        for num, func in enumerate(funcs):\n",
    "            if mi_t[num] >= true_mi[num]: gq_mi[num] += 1\n",
    "            if vi_t[num] <= true_vi[num]: lq_vi[num] += 1\n",
    "    return [x / perms for x in gq_mi], [x / perms for x in lq_vi]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "228f90fc",
   "metadata": {},
   "source": [
    "Now some data processing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "de31e941",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "acl_2022/data/mccarthy/gender-dictionaries/he.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/es.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/sl.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/da.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/lv.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/pt.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/sv.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/sk.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/lt.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/fr.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/pl.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/hi.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/ro.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/ca.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/ru.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/bg.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/uk.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/el.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/hr.lemma.processed\n",
      "acl_2022/data/mccarthy/gender-dictionaries/it.lemma.processed\n"
     ]
    }
   ],
   "source": [
    "LS = len('acl_2022/data/mccarthy/gender-dictionaries/')\n",
    "\n",
    "genders = defaultdict(dict)\n",
    "for file in glob.glob('acl_2022/data/mccarthy/gender-dictionaries/*'):\n",
    "    print(file)\n",
    "    with open(file, 'r') as fin:\n",
    "        for row in fin:\n",
    "            word, gender = row.strip().split('\\t')\n",
    "            genders[file[LS:LS+2]][word] = gender"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "3bf2fb70",
   "metadata": {},
   "outputs": [],
   "source": [
    "swadesh = ['hr', 'sk', 'ru', 'bg', 'uk', 'fr', 'ca', 'it', 'es', 'pt']\n",
    "res = defaultdict(list)\n",
    "missing = []\n",
    "\n",
    "with open('acl_2022/data/mccarthy/inanimate_swadesh.csv', 'r') as fin:\n",
    "    reader = csv.DictReader(fin)\n",
    "    for i, row in enumerate(reader):\n",
    "        # print(row)\n",
    "        for lang in row:\n",
    "            if lang not in swadesh:\n",
    "                continue\n",
    "            word = row[lang].split(',')[0].strip()\n",
    "            if word not in genders[lang]:\n",
    "                t = unidecode.unidecode(word)\n",
    "                if t not in genders[lang]:\n",
    "                    missing.append([lang, word])\n",
    "                    print([lang, word])\n",
    "                else:\n",
    "                    res[lang].append(genders[lang][t])\n",
    "            else:\n",
    "                res[lang].append(genders[lang][word])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "7ec86106",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(['MASC', 'FEM', 'MASC', 'FEM', 'MASC'],\n",
       " ['MASC', 'MASC', 'MASC', 'FEM', 'FEM'])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res['it'][:5], res['es'][:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6951a655",
   "metadata": {},
   "source": [
    "And now we can actually calculate the mutual informations using all our estimators, and then run permutation tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "29c6e111",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        mle     mm   jack     ht     cs     ww    nsb\n",
      "hr sk  0.54   0.52   0.50   0.48   0.46   0.46   0.46 \n",
      "hr ru  0.43   0.41   0.40   0.39   0.38   0.37   0.35 \n",
      "hr bg  0.34   0.31   0.30   0.28   0.27   0.28   0.25 \n",
      "hr uk  0.16   0.14   0.13   0.15   0.14   0.15   0.08 \n",
      "hr fr  0.02   0.01   0.01   0.02   0.02   0.03  -0.01 \n",
      "hr ca  0.01  -0.01  -0.01   0.01   0.01   0.02  -0.03 \n",
      "hr it  0.03   0.02   0.02   0.03   0.03   0.04  -0.00 \n",
      "hr es  0.01  -0.01  -0.01   0.01   0.01   0.02  -0.03 \n",
      "hr pt  0.01  -0.01  -0.01   0.01   0.01   0.02  -0.03 \n",
      "sk ru  0.42   0.40   0.39   0.38   0.36   0.36   0.34 \n",
      "sk bg  0.30   0.27   0.26   0.26   0.25   0.25   0.21 \n",
      "sk uk  0.21   0.19   0.18   0.19   0.18   0.19   0.13 \n",
      "sk fr  0.02   0.01   0.01   0.02   0.02   0.03  -0.01 \n",
      "sk ca  0.01  -0.00  -0.00   0.01   0.01   0.02  -0.02 \n",
      "sk it  0.02   0.00   0.00   0.02   0.02   0.03  -0.02 \n",
      "sk es  0.01  -0.01  -0.01   0.01   0.01   0.02  -0.03 \n",
      "sk pt  0.02   0.00  -0.00   0.02   0.02   0.02  -0.02 \n",
      "ru bg  0.32   0.30   0.30   0.31   0.31   0.31   0.26 \n",
      "ru uk  0.26   0.24   0.22   0.22   0.20   0.22   0.18 \n",
      "ru fr  0.01  -0.00  -0.01   0.01   0.01   0.02  -0.03 \n",
      "ru ca  0.02   0.00  -0.00   0.01   0.01   0.02  -0.02 \n",
      "ru it  0.02   0.00   0.00   0.02   0.02   0.02  -0.02 \n",
      "ru es  0.03   0.01   0.01   0.02   0.02   0.03  -0.01 \n",
      "ru pt  0.01  -0.00  -0.00   0.01   0.01   0.02  -0.02 \n",
      "bg uk  0.14   0.11   0.10   0.12   0.11   0.13   0.06 \n",
      "bg fr  0.03   0.01   0.01   0.03   0.03   0.04  -0.01 \n",
      "bg ca  0.01  -0.01  -0.01   0.01   0.01   0.02  -0.03 \n",
      "bg it  0.04   0.03   0.03   0.04   0.04   0.05   0.01 \n",
      "bg es  0.04   0.03   0.03   0.04   0.04   0.05   0.01 \n",
      "bg pt  0.04   0.02   0.02   0.04   0.04   0.04   0.00 \n",
      "uk fr  0.00  -0.01  -0.02  -0.01  -0.01  -0.01  -0.04 \n",
      "uk ca  0.02   0.00  -0.01  -0.01  -0.02   0.00  -0.02 \n",
      "uk it  0.02   0.01   0.00  -0.01  -0.01   0.01  -0.01 \n",
      "uk es  0.01  -0.00  -0.00  -0.00  -0.00   0.00  -0.02 \n",
      "uk pt  0.01  -0.00  -0.01  -0.00  -0.00   0.00  -0.03 \n",
      "fr ca  0.13   0.12   0.12   0.13   0.13   0.12   0.10 \n",
      "fr it  0.09   0.08   0.08   0.09   0.09   0.08   0.06 \n",
      "fr es  0.10   0.09   0.09   0.10   0.10   0.09   0.07 \n",
      "fr pt  0.18   0.17   0.17   0.18   0.18   0.16   0.15 \n",
      "ca it  0.20   0.20   0.20   0.20   0.20   0.19   0.18 \n",
      "ca es  0.23   0.22   0.22   0.23   0.23   0.21   0.20 \n",
      "ca pt  0.21   0.20   0.20   0.21   0.21   0.19   0.18 \n",
      "it es  0.20   0.20   0.20   0.20   0.20   0.19   0.18 \n",
      "it pt  0.28   0.27   0.27   0.27   0.27   0.25   0.25 \n",
      "es pt  0.35   0.34   0.34   0.34   0.34   0.31   0.32 \n"
     ]
    }
   ],
   "source": [
    "langs = swadesh\n",
    "final = {}\n",
    "print(f'     {\"mle\":>6} {\"mm\":>6} {\"jack\":>6} {\"ht\":>6} {\"cs\":>6} {\"ww\":>6} {\"nsb\":>6}')\n",
    "for num1, lang1 in enumerate(langs):\n",
    "    for num2, lang2 in enumerate(langs[num1 + 1:]):\n",
    "        num2 = num1 + 1 + num2\n",
    "        mi_c = mi(res[lang1], res[lang2], entropy.funcs)\n",
    "        vi_c = vi(res[lang1], res[lang2], entropy.funcs)\n",
    "        mi_stats, vi_stats = permutation_test(res[lang1], res[lang2], mi_c, vi_c, entropy.funcs, perms=1000)\n",
    "        print(f'{lang1} {lang2}', end='')\n",
    "        for i in mi_c:\n",
    "            print(f'{i:>6.2f}', end=' ')\n",
    "        print()\n",
    "        final[(num1, num2)] = [mi_c, mi_stats]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "213dc666",
   "metadata": {},
   "source": [
    "We can plot the mutual informations between language pairs. A clear pattern emerges, dividing the languages into two unassociated sets (languages across these two sets have almost 0 mutual information between their gender partitions). These are in fact the Romance and Slavic languages, so we have replicated a key finding of McCarthy et al. (2020) with our other estimators. But note that e.g. NSB has much lower mutual informations than MLE, since MLE's negative bias causes an overestimate of MI."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "0f774471",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[nan,\n",
       " 0.5419641313474668,\n",
       " 0.43001075131576494,\n",
       " 0.343881373304876,\n",
       " 0.1627497969774483,\n",
       " 0.021151408472735778,\n",
       " 0.007105386508325928,\n",
       " 0.03138585136375305,\n",
       " 0.007505247151008643,\n",
       " 0.0095133489778787]"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrices = [[[np.nan for i in range(len(langs))] for i in range(len(langs))] for i in range(len(entropy.funcs))]\n",
    "for x, y in final:\n",
    "    for i in range(len(entropy.funcs)):\n",
    "        matrices[i][x][y] = final[(x, y)][0][i]\n",
    "        matrices[i][y][x] = final[(x, y)][0][i]\n",
    "matrices[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "9488ada8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1700x500 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [17, 5]\n",
    "fig, axs = plt.subplots(1, 7, sharex='all', sharey='all')\n",
    "for i in range(len(entropy.funcs)):\n",
    "    axs[i].set_xticks(ticks=list(range(len(langs))), labels=langs)\n",
    "    axs[i].set_yticks(ticks=list(range(len(langs))), labels=langs)\n",
    "    axs[i].imshow(matrices[i], vmin=0, vmax=0.54)\n",
    "    axs[i].set(title=entropy.funcs[i].__name__)\n",
    "    axs[i].invert_yaxis()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33743569",
   "metadata": {},
   "source": [
    "Now, we can look at which gender partitions are statistically significantly different, i.e. if the permutation test $p$-value is less than $0.05$. We nicely get the Romance and Slavic families as two separate groups again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "d5ae54f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[nan, True, True, True, True, False, False, False, False, False]"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrices = [[[np.nan for i in range(len(langs))] for i in range(len(langs))] for i in range(len(entropy.funcs))]\n",
    "for x, y in final:\n",
    "    for i in range(len(entropy.funcs)):\n",
    "        matrices[i][x][y] = final[(x, y)][1][i] < 0.05\n",
    "        matrices[i][y][x] = final[(x, y)][1][i] < 0.05\n",
    "matrices[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "9840fb11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1700x500 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [17, 5]\n",
    "fig, axs = plt.subplots(1, 7, sharex='all', sharey='all')\n",
    "for i in range(len(entropy.funcs)):\n",
    "    axs[i].set_xticks(ticks=list(range(len(langs))), labels=langs)\n",
    "    axs[i].set_yticks(ticks=list(range(len(langs))), labels=langs)\n",
    "    axs[i].imshow(matrices[i], vmin=0, vmax=1)\n",
    "    axs[i].set(title=entropy.funcs[i].__name__)\n",
    "    axs[i].invert_yaxis()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}