changepoint_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time series with change point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from changepoint.mean_shift_model import MeanShiftModel \n",
    "ts = np.concatenate([np.random.normal(0, 0.1, 10), np.random.normal(1, 0.1, 10)]) \n",
    "model = MeanShiftModel() \n",
    "stats_ts, pvals, nums = model.detect_mean_shift(ts, B=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pylab as pl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10cb4e210>]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Z0p5hH22dlYIjjoA5c2KFbT7f/nsE//e/MV/+vffgP/+BNdZItJkiUsE07JOS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\n/EVEMkjhLyKSQf8P/sBvW3sS3DcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c975450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10cc5da90>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MgffegwcfDP30kh/qlpF6W7oULrwwDJt7/HHYccfYiaTQPPZYuAZz/vlwwQXqk88HFXep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\n9AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cb827d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(stats_ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.30159999999999998,\n",
       " 0.2016,\n",
       " 0.1023,\n",
       " 0.040099999999999997,\n",
       " 0.0082000000000000007,\n",
       " 0.002,\n",
       " 0.0011000000000000001,\n",
       " 0.0001,\n",
       " 0.0,\n",
       " 0.0,\n",
       " 0.0,\n",
       " 0.0001,\n",
       " 0.00050000000000000001,\n",
       " 0.00029999999999999997,\n",
       " 0.00080000000000000004,\n",
       " 0.002,\n",
       " 0.0115,\n",
       " 0.019699999999999999,\n",
       " 0.1875]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmin(pvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([9]),)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(np.array(stats_ts)>1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One strategy to choose a change point is to pick a point which has a low pvalue and also has a large enough effect size. Note that a changepoint depends on 2 things (a) Effect size and (b) Significance (pvalue). It is possible for very small effect sizes to also be significant. That is why we need to use both criterion to ultimately get a estimate. Here I used the threshold for effect size as 1.0 (this depends on your data) and the significance level of 0.05  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time series with no change point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from changepoint.mean_shift_model import MeanShiftModel \n",
    "ts = np.concatenate([np.random.normal(0, 0.1, 10), np.random.normal(0, 0.1, 10)]) \n",
    "model = MeanShiftModel() \n",
    "stats_ts, pvals, nums = model.detect_mean_shift(ts, B=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d4a4990>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+nMc0EZkvIneVC0V5RC0MSYaRPJKoTKq3/AKYMHjkuUy1mCiFIW89DABNlRaI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\nwzA6YcJgGIZhdMKEwTAMw+jE/wdVZcadijwOmgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cda4890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(ts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.45469999999999999,\n",
       " 0.186,\n",
       " 0.36070000000000002,\n",
       " 0.52629999999999999,\n",
       " 0.33289999999999997,\n",
       " 0.22700000000000001,\n",
       " 0.44550000000000001,\n",
       " 0.50880000000000003,\n",
       " 0.79430000000000001,\n",
       " 0.74850000000000005,\n",
       " 0.53620000000000001,\n",
       " 0.29959999999999998,\n",
       " 0.14630000000000001,\n",
       " 0.13150000000000001,\n",
       " 0.3256,\n",
       " 0.40300000000000002,\n",
       " 0.49309999999999998,\n",
       " 0.1583,\n",
       " 0.19889999999999999]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([], dtype=int64),)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(np.array(pvals)<0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([], dtype=int64),)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(np.array(stats_ts)>1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here note that no point is significant as pvals are all > 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please cite the below if you use this package: \n",
    "    \n",
    "@inproceedings{Kulkarni:langchange,\n",
    " author = {Kulkarni,Vivek and Al-Rfou, Rami and Perozzi,Bryan and Skiena, Steven},\n",
    " title = {Statistically Significant Detection of Linguistic Change},\n",
    " booktitle = {Proceedings of the 24th International World Wide Web Conference},\n",
    " series = {WWW '15},\n",
    " year = {2015},\n",
    " location = {Florence, Italy},\n",
    " numpages = {11},\n",
    "} "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other references: http://viveksck.github.io/langchangetrack/ and http://www.variation.com/cpa/tech/changepoint.html"
   ]
  },
  {
   "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": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}