3 Non-linear fits.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1bba0128",
   "metadata": {},
   "source": [
    "# Non-linear fits as extensions of line fits\n",
    "\n",
    "Line fits are really useful and they can be easily modified to perform non-linear fits too.\n",
    "\n",
    "One way of modifying them is to simply \"create\" new variables. For example, if one would like to fit a parabola $y = f(x) = a x^2 + b x + c$, one could define a new variable $u = x^2$ and fit the \"plane\" $y = f(x, u) = a u + b x + c$. This fit may be performed with the methods described previously. There are even tools in standard libraries to aid fitting using such procedures.\n",
    "\n",
    "An alternative is to perform a non-linear transformation on $x$, in such a way that the important non-linear effects are captured.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "896d5976-fe56-4a2b-8093-c01fc53b0068",
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Tuple\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import matplotlib.pylab as pylab\n",
    "params = {'legend.fontsize': 'x-large',\n",
    "          'figure.figsize': (15, 5),\n",
    "         'axes.labelsize': 'x-large',\n",
    "         'axes.titlesize':'x-large',\n",
    "         'xtick.labelsize':'x-large',\n",
    "         'ytick.labelsize':'x-large'}\n",
    "pylab.rcParams.update(params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "843e1f00-4846-4e15-9861-6e9e866a6d62",
   "metadata": {},
   "source": [
    "## Fitting polynomials\n",
    "\n",
    "scikit-learn offers the possibility of easily creating new variables corresponding to the polynomial expansions of $x$.\n",
    "This can be done using: https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html#sklearn.preprocessing.PolynomialFeatures\n",
    "\n",
    "Let's look at an example of how this could be done:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb1286f0",
   "metadata": {},
   "source": [
    "The simulated example data will be $f(x) = 0.01 x^2 + 0.5 x + 0.3 + \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(\\mu=0, \\sigma=0.5)$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "aef54435-78af-4b13-aee2-2bc576c773cd",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def generate_data(N: int) -> np.ndarray:\n",
    "    x = 2*np.random.randn(N, 1)\n",
    "    epsilon = 0.5*np.random.randn(N, 1)\n",
    "    z = 0.1*x**2 + 0.5*x + 0.3 + epsilon\n",
    "    return np.concatenate((x, z), axis=1).astype(np.float32)\n",
    "\n",
    "data = generate_data(N=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00e098e8-0082-4451-927a-073cf242787e",
   "metadata": {},
   "source": [
    "Let's plot it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "08d9daaf-25c5-4d06-b4a6-6cecaaa35651",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f6b951cf280>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data[:,0], data[:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9932b25-ffa6-4690-965e-6822643a8edd",
   "metadata": {},
   "source": [
    "Now, let's fit it with a line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "50578b88-f210-4a35-bada-71a26e45e689",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>BayesianRidge()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">BayesianRidge</label><div class=\"sk-toggleable__content\"><pre>BayesianRidge()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "BayesianRidge()"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import BayesianRidge\n",
    "\n",
    "model = BayesianRidge()\n",
    "model.fit(data[:, [0]], data[:, 1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9e317638-ed75-418f-af18-da8dd585265a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f6b67add7b0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_axis = np.linspace(-5, 5, 100)\n",
    "y_p, y_u = model.predict(x_axis[:, np.newaxis], return_std=True)\n",
    "\n",
    "plt.scatter(data[:, 0], data[:, 1], c='b', label=\"Data\")\n",
    "plt.plot(x_axis, y_p, c='r', lw=2, ls='--', label=\"Prediction\")\n",
    "plt.fill_between(x_axis, y_p-2*y_u, y_p+2*y_u, color='red', alpha=0.2, label=\"95% CL uncertainty\")\n",
    "plt.legend(frameon=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "446bb34d-7ccc-481a-8514-c1ee20fcc5e0",
   "metadata": {},
   "source": [
    "This has a large uncertainty and it really does not capture the quadratic effect! Let's try to fit it adding one extra variable $u=x^2$. We could just calculate this variable and add it to the dataset, but when working with many dimensions and with higher powers (not only second-order polynomials), it is easier to use the auxiliary object `PolynomialFeatures`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "53a6c63b-0144-424d-b191-3dd8b6a090d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>BayesianRidge()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">BayesianRidge</label><div class=\"sk-toggleable__content\"><pre>BayesianRidge()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "BayesianRidge()"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import BayesianRidge\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "feature_extractor = PolynomialFeatures(2)\n",
    "data_preprocessed = feature_extractor.fit_transform(data[:, [0]])\n",
    "\n",
    "model = BayesianRidge()\n",
    "model.fit(data_preprocessed, data[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c9fd10d6-1c1b-4707-ad9f-bfed56e3ab9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f6be9ce3b50>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "preprocessed_x_axis = feature_extractor.fit_transform(x_axis[:, np.newaxis])\n",
    "y_p, y_u = model.predict(preprocessed_x_axis, return_std=True)\n",
    "\n",
    "plt.scatter(data[:, 0], data[:, 1], c='b', label=\"Data\")\n",
    "plt.plot(x_axis, y_p, c='r', lw=2, ls='--', label=\"Prediction\")\n",
    "plt.fill_between(x_axis, y_p-2*y_u, y_p+2*y_u, color='red', alpha=0.2, label=\"95% CL uncertainty\")\n",
    "plt.legend(frameon=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff9c4999-5ef9-42da-a748-6b1384f5651f",
   "metadata": {},
   "source": [
    "This looks much better! We can also do this in a more streamlined way using the concept of `Pipeline` in scikit-learn, which does this transformation for us in a more transparent way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9cc91240-2ad2-4912-b4a3-96e0d12f119a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;feature_extractor&#x27;, PolynomialFeatures()),\n",
       "                (&#x27;fit&#x27;, BayesianRidge())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Pipeline</label><div class=\"sk-toggleable__content\"><pre>Pipeline(steps=[(&#x27;feature_extractor&#x27;, PolynomialFeatures()),\n",
       "                (&#x27;fit&#x27;, BayesianRidge())])</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PolynomialFeatures</label><div class=\"sk-toggleable__content\"><pre>PolynomialFeatures()</pre></div></div></div><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">BayesianRidge</label><div class=\"sk-toggleable__content\"><pre>BayesianRidge()</pre></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('feature_extractor', PolynomialFeatures()),\n",
       "                ('fit', BayesianRidge())])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import BayesianRidge\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "model = Pipeline([('feature_extractor', PolynomialFeatures(2)),\n",
    "                  ('fit', BayesianRidge())\n",
    "                 ])\n",
    "model.fit(data[:,[0]], data[:,1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a16075c0-d671-4d06-9cfe-ab191cddd24d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f6b678146a0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_p, y_u = model.predict(x_axis[:, np.newaxis], return_std=True)\n",
    "\n",
    "plt.scatter(data[:, 0], data[:, 1], c='b', label=\"Data\")\n",
    "plt.plot(x_axis, y_p, c='r', lw=2, ls='--', label=\"Prediction\")\n",
    "plt.fill_between(x_axis, y_p-2*y_u, y_p+2*y_u, color='red', alpha=0.2, label=\"95% CL uncertainty\")\n",
    "plt.legend(frameon=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0a02e5f-ce76-4149-b51a-e114dccccf3c",
   "metadata": {},
   "source": [
    "## Kernel methods\n",
    "\n",
    "Another simple extension of linear fits is to apply a non-linear transformation on the input $x$ values indirectly. The logic here is the following: when looking at the derivation of the equations for linear fit results, we see that the results don't really depend on the $x$ values of each point directly. They only depend on the dot-product between $x$ values between different points, that is, on $\\vec{x}_1 \\cdot \\vec{x}_2 = \\sum_i x_{1i} x_{2i}$. If we substituted the *definition of dot product* in our space with something else, we are effectively changing how we measure distances in the space of points. This change in the curvature of the space may detect non-linear relationships more easily.\n",
    "\n",
    "When using this method we are effectively performing the fit:\n",
    "\n",
    "$y = f(x) = \\sum_i w_i \\phi_i(x_i) + w_0$\n",
    "\n",
    "The only change here is that the only thing that enters the method are the pre-transformed versions of the input $x_i$ components.\n",
    "We never really have to calculate $\\phi_i$, since the only thing that enters our linear fit equations for $\\phi_i(x_i)$ is actually $\\phi_i(x)_i \\phi_j(x_j)$ for all combinations of $i$ and $j$. We define this quantity kernel $K(x, x^\\prime) = \\phi(x) \\cdot \\phi(x^\\prime)$ and it is conceptualized as a measure of relationship between the different $x$ values."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "396e37cf-5597-468c-9272-30cb80c71e61",
   "metadata": {},
   "source": [
    "Let's look at an example of this using the kernel function $K(x, x^\\prime) = (\\gamma x \\cdot x^\\prime + 1)^3$. This is called the *polynomial* kernel, but you can define your own kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f294b5e9-cd9a-4c99-b9aa-08c4b0f8bfab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-4 {color: black;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KernelRidge(kernel=&#x27;polynomial&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" checked><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KernelRidge</label><div class=\"sk-toggleable__content\"><pre>KernelRidge(kernel=&#x27;polynomial&#x27;)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "KernelRidge(kernel='polynomial')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.kernel_ridge import KernelRidge\n",
    "\n",
    "model = KernelRidge(kernel=\"polynomial\")\n",
    "model.fit(data[:,[0]], data[:,1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "33a9a495-db13-44d8-95d9-6d0ca1401164",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f6b676cebc0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_p = model.predict(x_axis[:, np.newaxis])\n",
    "\n",
    "plt.scatter(data[:, 0], data[:, 1], c='b', label=\"Data\")\n",
    "plt.plot(x_axis, y_p, c='r', lw=2, ls='--', label=\"Prediction\")\n",
    "plt.legend(frameon=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d78f2e4-c687-4fbc-b5ab-3ad2b1175c03",
   "metadata": {},
   "source": [
    "This particular model implementation does not define uncertainties in the result (more on that later), but notice that the non-linearity is correctly captured by such a method."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc211612-29fc-45f4-bdd4-897778dac430",
   "metadata": {},
   "source": [
    "A different way of looking at this is that the kernel encodes a transformation to a space of functions that could fit this data. That is, there are infinite functions that fit the data, but the choice of the kernel selects some of them.\n",
    "\n",
    "The disadvantage here is that the parabolic nature of the original function is not so obvious, but the entire structure of the non-linearity is shifted to the choice of the kernel function. Choosing a different kernel leads to a very different result.\n",
    "\n",
    "The underlying code used here is actually very similar to the linear fit done previously: the key difference is that the *design* matrix is changed to depend on $K$ instead of the $x$ values directly. What we are doing here is still, behind the scenes, a linear fit!\n",
    "\n",
    "This method is called often the *kernel trick*, since it allows very complex fits with a small change in the fit procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b3ab83e-4be8-41c4-ade8-4ef19c638fbd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.12"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}