{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ease of Use\n",
    "\n",
    "*Max Zwiessele* 20th of September 2015\n",
    "\n",
    "*Minor edits by Alan Saul* 19th of February 2016\n",
    "\n",
    "GPy is deveoped for the easy application of Gaussian process based analyses, for the user to not be confused by the complexity of some applications. This improves readability and prevents errors of scientific code of Gaussian process based applications. This platform is meant as a framework for your work evolving around GPs.\n",
    "\n",
    "A model in GPy is an object with an objective function. If necessary, this object can include gradients w.r.t. its parameters, in order for gradient based optimizations to take place. The useability of GPy comes with its great power and handling of its parameters. The parameters of a model are always nameable, accessible and interchangeable.\n",
    "\n",
    "We want to demonstrate the light handedness of GPys parameterized framework on a simple Gaussian process regression example in order to show how easy it is to generate an analysis flow in GPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Caching disabled: False\n"
     ]
    }
   ],
   "source": [
    "import numpy as np, GPy, pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purpose of this notebook we will use the regression task of the abalone dataset - the prediction of age of Abalone (edible snails) from physical measurements. \n",
    "\n",
    "We can download the dataset from http://www.cs.toronto.edu/%7Edelve/data/abalone/desc.html. For convenience we include alittle script which downloads the data and saves it locally as a pickle file. The data gets saved in this directory. When running the script it loads the data into a pandas data frame called `data`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sex</th>\n",
       "      <th>length</th>\n",
       "      <th>diameter</th>\n",
       "      <th>height</th>\n",
       "      <th>whole_weight</th>\n",
       "      <th>shucked_weight</th>\n",
       "      <th>viscera_weight</th>\n",
       "      <th>shell_weight</th>\n",
       "      <th>rings</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>M</td>\n",
       "      <td>0.455</td>\n",
       "      <td>0.365</td>\n",
       "      <td>0.095</td>\n",
       "      <td>0.5140</td>\n",
       "      <td>0.2245</td>\n",
       "      <td>0.1010</td>\n",
       "      <td>0.150</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>M</td>\n",
       "      <td>0.350</td>\n",
       "      <td>0.265</td>\n",
       "      <td>0.090</td>\n",
       "      <td>0.2255</td>\n",
       "      <td>0.0995</td>\n",
       "      <td>0.0485</td>\n",
       "      <td>0.070</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>F</td>\n",
       "      <td>0.530</td>\n",
       "      <td>0.420</td>\n",
       "      <td>0.135</td>\n",
       "      <td>0.6770</td>\n",
       "      <td>0.2565</td>\n",
       "      <td>0.1415</td>\n",
       "      <td>0.210</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>M</td>\n",
       "      <td>0.440</td>\n",
       "      <td>0.365</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.5160</td>\n",
       "      <td>0.2155</td>\n",
       "      <td>0.1140</td>\n",
       "      <td>0.155</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>I</td>\n",
       "      <td>0.330</td>\n",
       "      <td>0.255</td>\n",
       "      <td>0.080</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.0895</td>\n",
       "      <td>0.0395</td>\n",
       "      <td>0.055</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  sex  length  diameter  height  whole_weight  shucked_weight  viscera_weight  \\\n",
       "0   M   0.455     0.365   0.095        0.5140          0.2245          0.1010   \n",
       "1   M   0.350     0.265   0.090        0.2255          0.0995          0.0485   \n",
       "2   F   0.530     0.420   0.135        0.6770          0.2565          0.1415   \n",
       "3   M   0.440     0.365   0.125        0.5160          0.2155          0.1140   \n",
       "4   I   0.330     0.255   0.080        0.2050          0.0895          0.0395   \n",
       "\n",
       "   shell_weight  rings  \n",
       "0         0.150     15  \n",
       "1         0.070      7  \n",
       "2         0.210      9  \n",
       "3         0.155     10  \n",
       "4         0.055      7  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%run load_abalone\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Make training and test possible, by subsetting the data randomly. \n",
    "# We will use 1/8 of the data as training set:\n",
    "train_idx = np.random.choice(data.shape[0], data.shape[0]/8)\n",
    "test_idx = np.setdiff1d(np.arange(data.shape[0]), train_idx)[:400]\n",
    "# make sex a categorical factor, for usage in regression task\n",
    "_tmp = data.copy()\n",
    "sex_labels, sex_uniques = pd.factorize(data['sex'], size_hint=3)\n",
    "_tmp['sex'] = sex_labels\n",
    "data_train, data_test = _tmp.loc[train_idx].copy(), _tmp.loc[test_idx].copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have the data, we can start writing a GP, with which we will show how you can manipulate and show the model easily. We will have one kernel for each input dimension, named after the data input. For starters we will use only one input, and expand. This will also show how easy it is to create complex GPy models and still have full access to all parameters and their settings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Select one input for now: we will use the diameter:\n",
    "selected_input = 'length'\n",
    "simple_kern = GPy.kern.Matern32(1, # How many dimension does this kernel have?\n",
    "                                name=selected_input # The name of this kernel\n",
    "                               )\n",
    "# Try out different kernels and see how the output changes. \n",
    "# This process is called model selection, as the kernel\n",
    "# represents the prior believe over function\n",
    "# values of the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_train = data_train.loc[:, 'sex':'shell_weight']\n",
    "Y_train = data_train.loc[:, ['rings']]\n",
    "\n",
    "X_test = data_test.loc[:, 'sex':'shell_weight']\n",
    "Y_test = data_test.loc[:, ['rings']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note! Carefull with this next line on slow or low memory machines. We are running a GP on more then 2000 datapoints. If you are not sure, try modifying `GPRegression` into `SparseGPRegression`, which will load a memory and runtime efficient version of GPRegression. This will add additional parameters `inducing_input`, which are due to the sparse model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "simple_model = GPy.models.GPRegression(X_train.loc[:,[selected_input]].values, Y_train.values, kernel=simple_kern)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       ".pd{\n",
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       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: 2170.64968542<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 3<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
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       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  length.variance        </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  length.lengthscale     </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x7fc7525ba9d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first thing which we can see, is that the diameter kernel was added properly into the model and we can see its name in the output. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Optimize the simple model and plot the result\n",
    "simple_model.optimize(messages=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vgGYWlZWV/OMfr7F27Vre2riR7OXL+b//+w2apgWs3T8ixdsYY+jQ4I0xQo3i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\nlceHkt6RdHQbdTapzr5SrbdQ0nZJFzZZX1tqHkM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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc7525c73d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = simple_model.plot(plot_training_data=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the GP can fit the data ok, although the noise on the data is clearly poisson distributed. You can try to run the Poisson regression on this data now (see e.g. [Posson regression](../GPy/Poisson regression tutorial.ipynb)). We will go on using more inputs and showing the parameter handling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def log_likelihood(m, X_test, Y_test):\n",
    "    import scipy as sp\n",
    "    mu, var = m.predict(X_test, full_cov=True)\n",
    "    return sp.stats.multivariate_normal.logpdf(Y_test.flatten(), mu.flatten(), var).sum()\n",
    "\n",
    "def RMSE(m, X_test, Y_test):\n",
    "    mu, var = m.predict(X_test, full_cov=False)\n",
    "    return np.sqrt(((mu - Y_test)**2).mean())\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_df = pd.DataFrame(index=['Log-likelihood', 'Root-mean-squared-error'])\n",
    "result_df['simple'] = [log_likelihood(simple_model, X_test[[selected_input]].values, Y_test.values), RMSE(simple_model, X_test[[selected_input]].values, Y_test.values)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>simple</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Log-likelihood</th>\n",
       "      <td>-1097.859349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Root-mean-squared-error</th>\n",
       "      <td>3.683326</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              simple\n",
       "Log-likelihood          -1097.859349\n",
       "Root-mean-squared-error     3.683326"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now use the full data set, but will switch to a sparse GP for better performace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create one kernel for each input dimension, except the categorical (sex) dimension:\n",
    "kernels = []\n",
    "for dim, name in enumerate(X_train.columns):\n",
    "    if name != \"sex\":\n",
    "        kernels.append(GPy.kern.Matern32(1, #input dim\n",
    "                                         active_dims=[dim], # Dimension of X to work on\n",
    "                                         name=name\n",
    "                                        )\n",
    "                      )\n",
    "kern_numeric = reduce(lambda a,b: a+b, kernels)\n",
    "kern_numeric.name = 'kernel'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
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       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  kernel.                   </b></th><th><b>value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  length.variance           </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  length.lengthscale        </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  diameter.variance         </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  diameter.lengthscale      </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  height.variance           </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  height.lengthscale        </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  whole_weight.variance     </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  whole_weight.lengthscale  </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  shucked_weight.variance   </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  shucked_weight.lengthscale</td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  viscera_weight.variance   </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  viscera_weight.lengthscale</td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  shell_weight.variance     </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  shell_weight.lengthscale  </td><td class=tg-right>  1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.kern.src.add.Add at 0x7fc750823dd0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kern_numeric"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have a kernel over all input dimensions named in the right way. We can use this kernel in a `SparseGPRegression` model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "numerical_model = GPy.models.SparseGPRegression(X_train.values, Y_train.values, \n",
    "                                                kernel=kern_numeric, num_inducing=40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: sparse gp<br>\n",
       "<b>Objective</b>: 1742.19660811<br>\n",
       "<b>Number of Parameters</b>: 335<br>\n",
       "<b>Number of Optimization Parameters</b>: 335<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
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       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  sparse_gp.                       </b></th><th><b>  value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  inducing inputs                  </td><td class=tg-right>(40, 8)</td><td class=tg-center>           </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.length.variance           </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.length.lengthscale        </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.diameter.variance         </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.diameter.lengthscale      </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.height.variance           </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.height.lengthscale        </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.whole_weight.variance     </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.whole_weight.lengthscale  </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.shucked_weight.variance   </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.shucked_weight.lengthscale</td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.viscera_weight.variance   </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.viscera_weight.lengthscale</td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.shell_weight.variance     </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  kernel.shell_weight.lengthscale  </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance          </td><td class=tg-right>    1.0</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.sparse_gp_regression.SparseGPRegression at 0x7fc750809cd0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numerical_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "numerical_model.optimize(messages=1, max_iters=3e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc7507ca650>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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YN24cv/zyC3Xq1KF79+689tprvPrqq6WWlCzw3HPPMWTIEF566SVuvfVW+vbt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\n8tVXX5V73MLNN0uXLqVPnz6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EjE8RkWznvwkislpEljgLhcwvtE6qiEx1Fjv5SkTaOue7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\ngCigZOOpXfUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc7507ca710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "numerical_model.kern.plot_ARD()\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Evaluate the log likelihood for the whole numerical model:\n",
    "result_df['all numerics'] = [log_likelihood(numerical_model, X_test.values, Y_test.values),\n",
    "          RMSE(numerical_model, X_test.values, Y_test.values)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>simple</th>\n",
       "      <th>all numerics</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Log-likelihood</th>\n",
       "      <td>-1097.859349</td>\n",
       "      <td>-1034.375885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Root-mean-squared-error</th>\n",
       "      <td>3.683326</td>\n",
       "      <td>3.002696</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              simple  all numerics\n",
       "Log-likelihood          -1097.859349  -1034.375885\n",
       "Root-mean-squared-error     3.683326      3.002696"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When comparing to the model with only the one selected input we have a slight improvement in RMSE. Now we have an additional input, which seperates the data into three different tasks. We can resolve different tasks in GPs using the so-called coregionalization technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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D4JZb0sfXxPrU8uQCpryccyikJFHW1B+PiIv7tr+/2vY+SZcAIxFxybTndmIopAQd+DU7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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc7505e2810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = data[['sex','rings']].boxplot(by='sex')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to add coregionalization to a model we merely have to create the right kernel, which understands the coregionalization structure in the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "kern_coreg = GPy.kern.Coregionalize(1, # Dimensionality of coregionalize input\n",
    "                                    len(sex_uniques), # How many different tasks do we have?\n",
    "                                    rank=3, # How deep is the coregionaliztion,\n",
    "                                    # the higher the rank, the more flexible the\n",
    "                                    # coregionalization, rank >= 1\n",
    "                                    active_dims=[X_train.columns.get_loc('sex')] ,\n",
    "                                    # Which dimension of the input carries the task information?\n",
    "                                    name = 'sex',\n",
    "                                   ) * kern_numeric.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "full_model = GPy.models.SparseGPRegression(X_train.values, Y_train.values, kernel=kern_coreg, num_inducing=40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "full_model.optimize(messages=1, max_iters=3e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jbk/yrSTvGfU8SU5NsjvJG1s12VFK6pQpR+9dwO9V1Y4kTwf+NcnXquqOwUVJtgIfBq4D\n0trUjlJSp+yd4Fitqh6oqh392z8C7gB+ZsjSdwNXAg+upSY7SkmdMquTOUmeDZwC3Lzq/mcBbwB+\nGTiVNbzd0aCU1CnjTuY80D9a+mP3lcBF/c5y0KXA+6qqkoQ1jN4GpaROGddRHts/9rllyJokTwGu\nAv6iqv56yJJfAP5yJSM5Bvi1JLuq6upRz2tQSuqUaUbvfof4SWBnVV06bE1VPXdg/RXANeNCEgxK\nSR0z5fsozwDOA25Nsr1/38XAiQBVte1ANjUoJXXKNB1lVX2dCd7NU1VvX8s6g1JSp3gJoyQ1dPES\nRoNSUqfYUUpSgx2lJDXYUUpSg0EpSQ2O3pLUYEcpSQ275l3AEAalpE6xo5SkBl+jlKQGO0pJajAo\nJanB0VuSGuwoJanBoJSkBkdvSWqwo5SkBjtKSWqwo5SkBoNSkhocvSWpwY5SkhoMSklqcPSWpAY7\nSklq6GJHmaqazUbJbDaStGFUVWa534HkyKxrGGZmQSlJi2rLvAuQpK4zKCWpwaCUpAaDUpIaDEpJ\navh/rMQ/jv2YNGcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc75086bc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "W, k = full_model.kern.sex.parameters\n",
    "coregionalization_matrix = GPy.util.linalg.tdot(W)\n",
    "GPy.util.diag.add(coregionalization_matrix, k)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "c = ax.matshow(coregionalization_matrix, cmap=plt.cm.hot)\n",
    "ax.set_xticks([0, 1, 2])\n",
    "ax.set_xticklabels(sex_uniques[[0, 1, 2]], fontdict=dict(size=23))\n",
    "ax.set_yticks([0, 1, 2])\n",
    "ax.set_yticklabels(sex_uniques[[0, 1, 2]], fontdict=dict(thickness='bold'))\n",
    "ax.xaxis.tick_top()\n",
    "plt.colorbar(c, ax=ax)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3b9/O7t276dq1K/7+/tSpU6fcUSidOnUiMDCQyZMnM2LECGrXrs0P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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc74c0cf950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "full_model.kern.kernel.plot_ARD()\n",
    "_ = plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Evaluate the log likelihood for the whole numerical model with coregionalization:\n",
    "result_df['coreg'] = (\n",
    "    log_likelihood(full_model, X_test.values, Y_test.values),\n",
    "    RMSE(full_model, X_test.values, Y_test.values)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>simple</th>\n",
       "      <th>all numerics</th>\n",
       "      <th>coreg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Log-likelihood</th>\n",
       "      <td>-1097.859349</td>\n",
       "      <td>-1034.375885</td>\n",
       "      <td>-1051.892968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Root-mean-squared-error</th>\n",
       "      <td>3.683326</td>\n",
       "      <td>3.002696</td>\n",
       "      <td>3.034311</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              simple  all numerics        coreg\n",
       "Log-likelihood          -1097.859349  -1034.375885 -1051.892968\n",
       "Root-mean-squared-error     3.683326      3.002696     3.034311"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this particular case we can see, that making the model more flexible by adding more inputs and priors leads to a better result, this is not necessarily true, as the model may get too flexible and overdoes the fitting of the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen how easy it is to build a complex model around a dataset using GPy. As a last I want to show the comparison between all three models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result_df.loc['neg-log-likelihood'] = -result_df.loc['Log-likelihood']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tn5aOh9EIzl29tTR/RQw29jMmuFgbEccAxwxalpmZTZ7vZC1TC88gGsO5q7eW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\n5QrezKyhXMGbmTWUK3gzs4b6/8NRTwV9jqGbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc745f905d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = result_df.T[['neg-log-likelihood', 'Root-mean-squared-error']].plot(kind='bar', subplots=True, legend=False)"
   ]
  }
 ],
 "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
}