Chapter 18. Entropy Features.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set(palette='Set2')\n",
    "import plotly.graph_objects as go\n",
    "\n",
    "from typing import Any, Tuple, Optional\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import nbimporter\n",
    "from Functions import get_dollar_bars, get_returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Auxilary Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pmf1(msg: Any, w: int) -> dict:\n",
    "    '''\n",
    "    Computes the probability mass function for a one-dim random variable (len(msg) - w occurences).\n",
    "    \n",
    "        Parameters:\n",
    "            msg (Any): sequence with observations (usually a string)\n",
    "            w (int): word length used for pmf estimation\n",
    "            \n",
    "        Returns:\n",
    "            pmf (dict): dictionary with words as keys and their estimated probabilities as values.\n",
    "    '''\n",
    "    lib = {}\n",
    "    if not isinstance(msg, str):\n",
    "        msg = ''.join(map(str, msg))\n",
    "    for i in range(w, len(msg)):\n",
    "        msg_ = msg[i - w: i]\n",
    "        if msg_ not in lib:\n",
    "            lib[msg_] = [i - w]\n",
    "        else:\n",
    "            lib[msg_] = lib[msg_] + [i - w]\n",
    "    length = float(len(msg) - w)\n",
    "    pmf = {i: len(lib[i]) / length for i in lib}\n",
    "    return pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plug_in(msg: Any, w: int) -> Tuple[float, dict]:\n",
    "    '''\n",
    "    Computes the maximum likelihood estimate for the entropy rate.\n",
    "\n",
    "        Parameters:\n",
    "            msg (Any): sequence with observations (usually a string)\n",
    "            w (int): word length used for pmf estimation\n",
    "\n",
    "        Returns:\n",
    "            out (float): entropy estimate\n",
    "            pmf (dict): dictionary with words as keys and their estimated probabilities as values.\n",
    "    '''\n",
    "    pmf = pmf1(msg, w)\n",
    "    out = -sum([pmf[i] * np.log2(pmf[i]) for i in pmf]) / w\n",
    "    return out, pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lempel_ziv_lib(msg: str) -> list:\n",
    "    '''\n",
    "    Implements the LZ algorithm to construct library.\n",
    "    \n",
    "        Parameters:\n",
    "            msg (str): sequence with observations\n",
    "            \n",
    "        Returns:\n",
    "            lib (list): list containing unique words\n",
    "    '''\n",
    "    i, lib = 1, [msg[0]]\n",
    "    while i < len(msg):\n",
    "        for j in range(i, len(msg)):\n",
    "            msg_ = msg[i: j + 1]\n",
    "            if msg_ not in lib:\n",
    "                lib.append(msg_)\n",
    "                break\n",
    "        i = j + 1\n",
    "    return lib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def match_length(msg: str, i: int, n: int) -> Tuple[int, str]:\n",
    "    '''\n",
    "    Computes the length of the longest match.\n",
    "    \n",
    "        Parameters:\n",
    "            msg (str): sequence with observations\n",
    "            i (int): position before which we look for a match\n",
    "            n (int): size of the window for searching for a match\n",
    "            \n",
    "        Returns:\n",
    "            len(subS) + 1 (int): length of the match + 1\n",
    "            subS (str): matched substring\n",
    "    '''\n",
    "    subS = ''\n",
    "    for l in range(n):\n",
    "        msg1 = msg[i: i + 1 + l]\n",
    "        for j in range(i - n, i):\n",
    "            msg0 = msg[j: j + 1 + l]\n",
    "            if msg1 == msg0:\n",
    "                subS = msg1\n",
    "                break\n",
    "    return len(subS) + 1, subS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "def konto(msg: Any, window: Optional[int] = None) -> dict:\n",
    "    '''\n",
    "    Kontoyiannis' LZ entropy estimate, 2013 version (centered window). Inverse of the avg length of the shortest\n",
    "    non redundant substring. If non redundant substrings are short, the text is highly entropic.\n",
    "    window=None for expanding window , in which case len(msg)%2=0.\n",
    "    If the end of the message is more relevant, try conto(msg[::-1]).\n",
    "    \n",
    "        Parameters:\n",
    "            msg (Any): sequence with observations (usually a string)\n",
    "            window (Optional[int]): winodw size for constant window\n",
    "            \n",
    "        Returns:\n",
    "            out (dict): dictionary with results\n",
    "    '''\n",
    "    out = {'num': 0, 'sum': 0, 'subS': []}\n",
    "    if not isinstance(msg, str):\n",
    "        msg = ''.join(map(str, msg))\n",
    "    if window is None:\n",
    "        points = range(1, len(msg) // 2 + 1)\n",
    "    else:\n",
    "        window = min(window, len(msg) // 2)\n",
    "        points = range(window, len(msg) - window + 1)\n",
    "    for i in points:\n",
    "        if window is None:\n",
    "            l, msg_ = match_length(msg, i, i)\n",
    "            out['sum'] += np.log2(i + 1) / l    # to avoid Doeblin condition\n",
    "        else:\n",
    "            l, msg_ = match_length(msg, i, window)\n",
    "            out['sum'] += np.log2(window + 1) / l    # to avoid Doeblin condition\n",
    "        out['subS'].append(msg_)\n",
    "        out['num'] += 1\n",
    "    out['h'] = out['sum'] / out['num']\n",
    "    out['r'] = 1 - out['h'] / np.log2(len(msg))    # redundancy, 0 <= r <= 1\n",
    "    return out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Firstly, I download the data, transform it into dollar bars and calculate returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2010-01-03 17:04:29    0.000179\n",
       "2010-01-03 17:15:11    0.000538\n",
       "2010-01-03 17:52:34    0.000090\n",
       "2010-01-03 18:47:00    0.000269\n",
       "2010-01-03 19:43:18   -0.000538\n",
       "dtype: float64"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('sp10-19.csv')\n",
    "dollar_bars = get_dollar_bars(data['price'].values, data['volume'].values, data['datetime'].values, 50000)\n",
    "dollar_bars_df = pd.DataFrame(data=dollar_bars[:, 1:], index=dollar_bars[:, 0],\n",
    "                           columns=['open', 'high', 'low', 'close', 'volume'])\n",
    "dollar_bars_df = dollar_bars_df[~dollar_bars_df.index.duplicated(keep='first')]\n",
    "ret = get_returns(dollar_bars)\n",
    "ret.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Quantization & Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.1 Binary quantization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "ret_binary = (ret >= 0).astype(int)\n",
    "message = ''.join(map(str, ret_binary.values))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plug-In Entropy estimation: 0.1631972503574526\n",
      "Konto's Entropy estimation: 0.8686435204826694\n"
     ]
    }
   ],
   "source": [
    "print(f'Plug-In Entropy estimation: {plug_in(msg=message, w=100)[0]}')\n",
    "konto_est = konto(msg=message, window=100)['h']\n",
    "print(f'Konto\\'s Entropy estimation: {konto_est}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.2 Quantile encoding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "ret_quantile = pd.qcut(ret, q=10, labels=range(10))\n",
    "message = ''.join(map(str, ret_quantile.values))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plug-In Entropy estimation: 0.1631972503574526\n",
      "Konto's Entropy estimation: 2.479176924111044\n"
     ]
    }
   ],
   "source": [
    "print(f'Plug-In Entropy estimation: {plug_in(msg=message, w=100)[0]}')\n",
    "konto_est = konto(msg=message, window=100)['h']\n",
    "print(f'Konto\\'s Entropy estimation: {konto_est}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.3 Sigma encoding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_buckets(series: pd.Series, sigma: float) -> list:\n",
    "    '''\n",
    "    Generates a list of segments corresponding to each bucket.\n",
    "    \n",
    "        Parameters:\n",
    "            series (pd.Series): series with data\n",
    "            sigma (float): size of each segment\n",
    "            \n",
    "        Returns:\n",
    "            segments (list): list with segments\n",
    "    '''\n",
    "    segments = []\n",
    "    cnt = 1\n",
    "    while series.min() + (cnt - 1) * sigma < series.max():\n",
    "        segments.append([series.min() + (cnt - 1) * sigma, series.min() + cnt * sigma])\n",
    "        cnt += 1\n",
    "    return segments\n",
    "\n",
    "\n",
    "def encode_single_obs(obs: float, segments: list) -> str:\n",
    "    '''\n",
    "    Given a number, returns its code according to the generated segments using sigma encoding.\n",
    "    NOTE: for encoding, I use sumbols starting from 48th ASCII code ('0').\n",
    "    \n",
    "        Parameters:\n",
    "            obs (float): observation value\n",
    "            segments (list): list with buckets boundaries\n",
    "            \n",
    "        Returns:\n",
    "            code (str): encoded observation\n",
    "    '''\n",
    "    for i in range(len(segments)):\n",
    "        if segments[i][0] <= obs < segments[i][1]:\n",
    "            code = chr(48 + i)\n",
    "            return code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "segments = generate_buckets(series=ret, sigma=ret.std())\n",
    "ret_sigma = ret.apply(lambda obs: encode_single_obs(obs=obs, segments=segments))\n",
    "message = ''.join(map(str, ret_sigma.values))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plug-In Entropy estimation: 0.1631972503574526\n",
      "Konto's Entropy estimation: 1.3696225581174863\n"
     ]
    }
   ],
   "source": [
    "print(f'Plug-In Entropy estimation: {plug_in(msg=message, w=100)[0]}')\n",
    "konto_est = konto(msg=message, window=100)['h']\n",
    "print(f'Konto\\'s Entropy estimation: {konto_est}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Normal Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The true entropy of the standord normal distribution equals\n",
    "$$\\dfrac{1}{2}\\log{(2\\pi e)}\\approx1.42$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's make some samples and estimate the entropy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = np.random.normal(size=1000)\n",
    "samples_quantile = pd.qcut(samples, q=8, labels=range(8))\n",
    "message = ''.join(map(str, samples_quantile))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Plug-In method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plug-In Entropy estimation: 0.9951284714966828\n"
     ]
    }
   ],
   "source": [
    "print(f'Plug-In Entropy estimation: {plug_in(msg=message, w=10)[0]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Kontoyiannis method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Konto's Entropy estimation (window size 10): 2.0976991828199743\n",
      "Konto's Entropy estimation (window size 100): 2.348799781077258\n"
     ]
    }
   ],
   "source": [
    "konto_est_10 = konto(msg=message, window=10)['h']\n",
    "print(f'Konto\\'s Entropy estimation (window size 10): {konto_est_10}')\n",
    "konto_est_100 = konto(msg=message, window=100)['h']\n",
    "print(f'Konto\\'s Entropy estimation (window size 100): {konto_est_100}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Entropy of a Stochastic Process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we define a process\n",
    "$$y_t=\\rho y_{t-1}+x_t,$$ where $\\rho=0.5$, $y_0=0$, and $x_t$ are the observations generated from the standard normal distribution in the previous exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = np.array([0])\n",
    "for i in range(1, len(samples) + 1):\n",
    "    y = np.append(y, 0.5 * y[-1] + samples[i - 1])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 7))\n",
    "ax.plot(y)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we quantize the derived series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_quantile = pd.qcut(y, q=8, labels=range(8))\n",
    "message = ''.join(map(str, y_quantile))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Plug-In method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plug-In Entropy estimation: 0.9952741247186501\n"
     ]
    }
   ],
   "source": [
    "print(f'Plug-In Entropy estimation: {plug_in(msg=message, w=10)[0]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Kontoyiannis method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Konto's Entropy estimation (window size 10): 2.042812656036942\n",
      "Konto's Entropy estimation (window size 100): 2.2644521115442293\n"
     ]
    }
   ],
   "source": [
    "konto_est_10 = konto(msg=message, window=10)['h']\n",
    "print(f'Konto\\'s Entropy estimation (window size 10): {konto_est_10}')\n",
    "konto_est_100 = konto(msg=message, window=100)['h']\n",
    "print(f'Konto\\'s Entropy estimation (window size 100): {konto_est_100}')"
   ]
  }
 ],
 "metadata": {
  "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}