examples/notebooks/Getting started with monkeys.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Getting started with monkeys\n",
    "\n",
    "This guide will show you how to start using `monkeys` and introduce you to the `monkeys` type system. Let's imagine a scenario: we have a number of data points representing horsepower versus miles per gallon in cars made between 1970 and 1982, and want to discover an equation that best fits this relationship. First, let's visualize our data, as taken from the [Auto MPG data set](https://archive.ics.uci.edu/ml/datasets/Auto+MPG)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd2aba2bc10>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dR+PVV18d8Pc777wT+/btw5kzZzBz5ky88cYbWLZsGRYsWAAAWL16NRoaGnDk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\niKiH1K3P7tZqLWeK24Oi1WoBAA0NDeLjnudRUVH9vu/8+fM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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd2aba2b590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import pandas\n",
    "import matplotlib\n",
    "matplotlib.style.use('ggplot')\n",
    "\n",
    "df = pandas.read_csv(\n",
    "    'http://archive.ics.uci.edu/ml/machine-learning-databases/auto-mpg/auto-mpg.data',\n",
    "    delimiter='\\s+',\n",
    "    header=None,\n",
    "    names='mpg cylinders disp horsepower weight acceleration year origin name'.split(),\n",
    "    na_values=['?'],\n",
    ")\n",
    "df.plot.scatter(x='horsepower', y='mpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Specifying solution structure\n",
    "\n",
    "As noted in the [`README.md`](https://github.com/hchasestevens/monkeys/blob/master/README.md), one of the requirements of using genetic programming is specifying what you want solutions to your problem to look like. In `monkeys`, this is accomplished through a rudimentary type system that allows you to restrict how functions can be composed together. By applying the `params` and `rtype` decorators to a function, you declare the types the function expects to receive as arguments and the type the function returns. \n",
    "\n",
    "Supposing we wanted to allow our equation to contain multiplication, division, addition, squaring, and negation, these could be declared as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from monkeys.typing import params, rtype, ignore\n",
    "import sys\n",
    "\n",
    "@params(float, float)  # expects two floats\n",
    "@rtype(float)  # returns a float\n",
    "def multiply(a, b):\n",
    "    return a * b\n",
    "\n",
    "@params(float, float)\n",
    "@rtype(float)\n",
    "@ignore(sys.maxsize, ZeroDivisionError)  # in the event of division by zero, return sys.maxsize\n",
    "def divide(a, b):\n",
    "    return a / b\n",
    "\n",
    "@params(float, float)\n",
    "@rtype(float)\n",
    "def add(a, b):\n",
    "    return a + b\n",
    "\n",
    "@params(float)  # expects only a single float\n",
    "@rtype(float)\n",
    "@ignore(sys.maxsize, OverflowError, ValueError, ZeroDivisionError)\n",
    "def square(a):\n",
    "    return a ** 2\n",
    "\n",
    "@params(float)\n",
    "@rtype(float)\n",
    "def negate(a):\n",
    "    return -a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `params` decorator can also be used without specifying any types. In this case, the function can be run without supplying any parameters, and is known as a \"terminal\" node. When creating your system, you must supply at least one terminal node -- otherwise, `monkeys` won't have any \"end point\" at which it can stop constructing the program. In cases where we want to supply a single value of a certain type, without the need to define a function, we can use the `constant` function. Since we don't have any way of generating `float`s right now, let's declare a few."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from monkeys.typing import constant\n",
    "\n",
    "one = constant(float, 1.0)\n",
    "two = constant(float, 2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need a means of providing input to our program. This can be done using the `make_input` function, which requires us to specify the input's type, as well as the input's initial value and name optionally. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from monkeys.trees import make_input\n",
    "\n",
    "horsepower = make_input(float, name='horsepower')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may also want to specify for clerical reasons an \"Equation\" type, which can be made from any program returning a float:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@params(float)\n",
    "@rtype('Equation')  # monkeys will, if provided a string, make a new type for us\n",
    "def equation(a):\n",
    "    return a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to, we can now visualize the system we've set up using `type_graph`. Note that this requires `graphviz` to be installed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      "text/plain": [
       "<graphviz.dot.Digraph at 0x7fd2a6e4b2d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from monkeys.tools.display import type_graph\n",
    "\n",
    "type_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This diagram shows the relationship between our types, and what we can construct from what. The ε at the top of the diagram in a dotted circle represents \"nothing\" -- this is to say, we can create `float`s out of thin air, by using our constants or our horsepower input. `float`s can be made into `float`s directly (via `negate`), or can be combined with other `float`s (resulting in a synthetic `(float, float)` type, represented as a dashed rectagle) to make `floats`, via `multiply`, `divide`, etc. If there is an obvious type we might want to generate, as is the case with `Equation`, `monkeys` will double-circle this to indicate as much."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scoring solutions\n",
    "\n",
    "Now that we've specified how solutions can be made, we have to come up with a means of evaluating how well a potential solution solves the problem we have. In this case, let's take a random sample of our data and calculate the mean squared error of the function. We'll ask `monkeys` to minimize this error by applying the `minimize` decorator. We also need to make sure to require that our `horsepower` input be used in the equation, via the `require` decorator, and specify that solutions should match the `Equation` return type by using `params`. Note that objective functions such as `score` must accept one (and only one) parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from monkeys.search import minimize, require\n",
    "\n",
    "SAMPLE_SIZE = 200\n",
    "MAX_ERROR = sys.maxsize\n",
    "\n",
    "@require(horsepower)\n",
    "@params('Equation')\n",
    "@minimize\n",
    "def score(equation):\n",
    "    squared_error = 0.0\n",
    "    \n",
    "    sample = df[df.horsepower.notnull()].sample(n=SAMPLE_SIZE)\n",
    "    for car in sample.T.to_dict().values():\n",
    "        result = equation(horsepower=car['horsepower'])\n",
    "        expected = car['mpg']\n",
    "        try:\n",
    "            squared_error += abs(result - expected) ** 2\n",
    "        except OverflowError:\n",
    "            return MAX_ERROR\n",
    "        \n",
    "    mean_squared_error = squared_error / float(SAMPLE_SIZE)\n",
    "    return min(mean_squared_error, MAX_ERROR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running the search\n",
    "\n",
    "We're now ready to begin the genetic programming search process. By default, `optimize` uses a population of 250 solutions and evolves them over 25 iterations -- but these settings can be adjusted. For now, let's stick with the defaults."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating initial population of 250.\n",
      "Optimizing...\n",
      "Iteration 1:\tBest: -110.10\tAverage: -11210184411392862.00\n",
      "Iteration 2:\tBest: -102.82\tAverage: -102.82\n",
      "Iteration 3:\tBest: -121.44\tAverage: -16186762938351.88\n",
      "Iteration 4:\tBest: -116.19\tAverage: -379.00\n",
      "Iteration 5:\tBest: -106.35\tAverage: -16436566342076830.00\n",
      "Iteration 6:\tBest: -124.94\tAverage: -124.94\n",
      "Iteration 7:\tBest: -118.20\tAverage: -40138303329582424.00\n",
      "Iteration 8:\tBest: -121.49\tAverage: -57688896256341.84\n",
      "Iteration 9:\tBest: -122.15\tAverage: -18089255744683184.00\n",
      "Iteration 10:\tBest: -115.49\tAverage: -115.49\n",
      "Iteration 11:\tBest: -108.19\tAverage: -2962855507208080.50\n",
      "Iteration 12:\tBest: -119.86\tAverage: -3124.77\n",
      "Iteration 13:\tBest: -112.66\tAverage: -92759496804264672.00\n",
      "Iteration 14:\tBest: -110.41\tAverage: -115.67\n",
      "Iteration 15:\tBest: -99.58\tAverage: -3813395410567650.00\n",
      "Iteration 16:\tBest: -102.31\tAverage: -131165652.08\n",
      "Iteration 17:\tBest: -114.03\tAverage: -38357827111306168.00\n",
      "Iteration 18:\tBest: -106.58\tAverage: -270.35\n",
      "Iteration 19:\tBest: -63.54\tAverage: -17185871063826430.00\n",
      "Iteration 20:\tBest: -70.72\tAverage: -2459.45\n",
      "Iteration 21:\tBest: -67.96\tAverage: -28756372723160.10\n",
      "Iteration 22:\tBest: -78.94\tAverage: -78.94\n",
      "Iteration 23:\tBest: -19.99\tAverage: -8689734769036688.00\n",
      "Iteration 24:\tBest: -22.50\tAverage: -324.86\n",
      "Iteration 25:\tBest: -24.66\tAverage: -19440523176918800.00\n"
     ]
    }
   ],
   "source": [
    "from monkeys.search import optimize\n",
    "\n",
    "best_equation = optimize(score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the equation we arrived at either as a string, or as a graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "equation(divide(divide(negate(add(square(horsepower()), add(negate(square(_const_2.0())), add(multiply(_const_1.0(), divide(_const_2.0(), _const_2.0())), negate(_const_2.0()))))), add(_const_1.0(), _const_2.0())), negate(horsepower())))\n"
     ]
    }
   ],
   "source": [
    "print(str(best_equation))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "<!-- 21 -->\n",
       "<g id=\"node22\" class=\"node\"><title>21</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"433.445\" cy=\"-90\" rx=\"60.3893\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"433.445\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">_const_2.0</text>\n",
       "</g>\n",
       "<!-- 20&#45;&#45;21 -->\n",
       "<g id=\"edge21\" class=\"edge\"><title>20&#45;&#45;21</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M405.401,-144.055C411.133,-133.211 418.548,-119.183 424.313,-108.275\"/>\n",
       "</g>\n",
       "<!-- 23 -->\n",
       "<g id=\"node24\" class=\"node\"><title>23</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"438.445\" cy=\"-234\" rx=\"65.7887\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"438.445\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\">horsepower</text>\n",
       "</g>\n",
       "<!-- 22&#45;&#45;23 -->\n",
       "<g id=\"edge23\" class=\"edge\"><title>22&#45;&#45;23</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M424.044,-288.055C426.987,-277.211 430.795,-263.183 433.756,-252.275\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Graph at 0x7fd2a88f1250>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from monkeys.tools.display import node_graph\n",
    "\n",
    "node_graph(best_equation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph above corresponds to the equation:\n",
    "\n",
    "$y = \\frac{-x}{\\frac{2 + 1}{{-2} + ((2 / 2)* 1) - (2^2) + x^2)}}$\n",
    "\n",
    "which, when simplified, yields:\n",
    "\n",
    "$y = -\\frac{1}{3} x (5 - x^2)$\n",
    "\n",
    "where $x$ is horsepower and $y$ is miles per gallon.\n",
    "\n",
    "Finally, let's see how our equation compares against the original data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fd2a7a017d0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Dcqxe4Yd5mW6PFUzLwG4P/IsvXDsWy07I7lwb3iUbVQlOhOjnZAVF9Et+kyLj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\nQBHCH3/t1cNRwtqTXZr9ffmazWaKioq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3XjXUbSWkoc3Kd782gruvGUasUce+0zUcKHMk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\n3kb5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd2a750db90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter(x='horsepower', y='mpg')\n",
    "\n",
    "predictions = [\n",
    "    (horsepower, round(best_equation(horsepower=horsepower), 2))\n",
    "    for horsepower in \n",
    "    range(50, 230)\n",
    "]\n",
    "matplotlib.pyplot.scatter(*zip(*predictions), color='black', s=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naturally, were we not happy with this result, we could have run the optimization process any number of times, or even tried supplying additional constructs for `monkeys` to play with - however, in this case, the framework appears to have found an equation which gives relatively good fit to the data.\n",
    "\n",
    "## Further reading\n",
    "\n",
    "In this getting started guide, we went through how to use `monkeys` to compose Python functions in order to create a program -- in our case, an equation. It is also possible to use `monkeys` to generate executable Python code directly. This is covered in the notebook [Monkeys in abstract syntax trees](https://github.com/hchasestevens/monkeys/blob/master/examples/notebooks/Monkeys%20in%20abstract%20syntax%20trees.ipynb). \n",
    "\n",
    "`monkeys` can also be used to discover and diagnose bugs in an existing codebase. This is demonstrated in [Debugging with monkeys](https://github.com/hchasestevens/monkeys/blob/master/examples/notebooks/Debugging%20with%20monkeys.ipynb).\n",
    "\n",
    "For further reading on the broader topic of genetic programming, the freely-available book [A Field Guide to Genetic Programming](http://cswww.essex.ac.uk/staff/rpoli/gp-field-guide/toc.html) is both an excellent starting resource and reference for more advanced topics. "
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}