{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.linalg import inv\n",
    "from sklearn.datasets import load_boston\n",
    "from sklearn.kernel_ridge import KernelRidge as skKernelRidge\n",
    "from sklearn.linear_model import Ridge as skRidge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation 1\n",
    "- linear kernel\n",
    "- similar to sklearn kernel='linear'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class KernelRidge():\n",
    "    def __init__(self, alpha=1.0):\n",
    "        self.alpha = alpha\n",
    "\n",
    "    \"\"\"\n",
    "    @staticmethod\n",
    "    def _linear_kernel(X, Y):\n",
    "        K = np.zeros((X.shape[0], Y.shape[0]))\n",
    "        for i in range(X.shape[0]):\n",
    "            for j in range(Y.shape[0]):\n",
    "                K[i, j] = np.dot(X[i], Y[j])\n",
    "        return K\n",
    "    \"\"\"\n",
    "\n",
    "    @staticmethod\n",
    "    def _linear_kernel(X, Y):\n",
    "        K = np.dot(X, Y.T)\n",
    "        return K\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        A = self._linear_kernel(X, X) + np.diag(np.full(X.shape[0], self.alpha))\n",
    "        self.dual_coef_ = np.dot(inv(A), y)\n",
    "        self.X_fit_ = X\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        K = self._linear_kernel(X, self.X_fit_)\n",
    "        return np.dot(K, self.dual_coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "for alpha in [0.1, 1, 10]:\n",
    "    X, y = load_boston(return_X_y = True)\n",
    "    clf1 = KernelRidge(alpha=alpha).fit(X, y)\n",
    "    clf2 = skKernelRidge(alpha=alpha).fit(X, y)\n",
    "    assert np.allclose(clf1.dual_coef_, clf2.dual_coef_, atol=1e-5)\n",
    "    assert np.allclose(clf1.X_fit_, clf2.X_fit_)\n",
    "    pred1 = clf1.predict(X)\n",
    "    pred2 = clf2.predict(X)\n",
    "    assert np.allclose(pred1, pred2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# KernelRidge kernel='linear' is equivalant to Ridge\n",
    "X, y = load_boston(return_X_y = True)\n",
    "X = X - X.mean(axis=0)\n",
    "y = y - y.mean()\n",
    "clf1 = skKernelRidge().fit(X, y)\n",
    "clf2 = skRidge().fit(X, y)\n",
    "assert np.allclose(np.dot(X.T, clf1.dual_coef_), clf2.coef_)\n",
    "pred1 = clf1.predict(X)\n",
    "pred2 = clf2.predict(X)\n",
    "assert np.allclose(pred1, pred2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation 2\n",
    "- rbf kernel\n",
    "- similar to sklearn kernel='rbf'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class KernelRidge():\n",
    "    def __init__(self, alpha=1.0, gamma=None):\n",
    "        self.alpha = alpha\n",
    "        self.gamma = gamma\n",
    "\n",
    "    @staticmethod\n",
    "    def _rbf_kernel(X, Y, gamma):\n",
    "        if gamma is None:\n",
    "            gamma = 1 / X.shape[1]\n",
    "        K = np.zeros((X.shape[0], Y.shape[0]))\n",
    "        for i in range(X.shape[0]):\n",
    "            for j in range(Y.shape[0]):\n",
    "                K[i, j] = np.exp(-gamma * np.sum(np.square(X[i] - Y[j])))\n",
    "        return K\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        A = self._rbf_kernel(X, X, self.gamma) + np.diag(np.full(X.shape[0], self.alpha))\n",
    "        self.dual_coef_ = np.dot(inv(A), y)\n",
    "        self.X_fit_ = X\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        K = self._rbf_kernel(X, self.X_fit_, self.gamma)\n",
    "        return np.dot(K, self.dual_coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "for gamma in [0.1, 1, 10, None]:\n",
    "    X, y = load_boston(return_X_y = True)\n",
    "    clf1 = KernelRidge(gamma=gamma).fit(X, y)\n",
    "    clf2 = skKernelRidge(kernel='rbf', gamma=gamma).fit(X, y)\n",
    "    assert np.allclose(clf1.dual_coef_, clf2.dual_coef_)\n",
    "    assert np.allclose(clf1.X_fit_, clf2.X_fit_)\n",
    "    pred1 = clf1.predict(X)\n",
    "    pred2 = clf2.predict(X)\n",
    "    assert np.allclose(pred1, pred2)"
   ]
  }
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