{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.linalg import svd\n",
    "from sklearn.datasets import load_boston\n",
    "from sklearn.linear_model import RidgeCV as skRidgeCV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation 1\n",
    "- based on svd\n",
    "- only support fit_intercept=False\n",
    "- similar to scikit-learn gcv_mode='svd'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RidgeCV():\n",
    "    def __init__(self, alphas=[0.1, 1.0, 10]):\n",
    "        self.alphas = alphas\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        U, S, VT = svd(X, full_matrices=False)\n",
    "        cv_values = np.zeros((X.shape[0], len(self.alphas)))\n",
    "        best_score, best_coef, best_alpha = None, None, None\n",
    "        for i, alpha in enumerate(self.alphas):\n",
    "            w = (S ** 2 + alpha) ** -1 - alpha ** -1\n",
    "            G_inv = np.dot(U * w[np.newaxis, :], U.T) + np.eye(X.shape[0]) * alpha ** -1\n",
    "            c = np.dot(G_inv, y)\n",
    "            looe = c / np.diag(G_inv)\n",
    "            errors = looe ** 2\n",
    "            cv_values[:, i] = errors\n",
    "            score = -np.mean(errors)\n",
    "            if best_score is None or best_score < score:\n",
    "                best_score = score\n",
    "                best_coef = c\n",
    "                best_alpha = alpha\n",
    "        self.cv_values_ = cv_values\n",
    "        self.best_score = best_score\n",
    "        self.coef_ = np.dot(X.T, best_coef)\n",
    "        self.alpha_ = best_alpha\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        return np.dot(X, self.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = load_boston(return_X_y=True)\n",
    "X -= X.mean(axis=0)\n",
    "y -= y.mean()\n",
    "alpha = [0.1, 1, 10]\n",
    "reg1 = RidgeCV().fit(X, y)\n",
    "reg2 = skRidgeCV(fit_intercept=False, store_cv_values=True).fit(X, y)\n",
    "assert np.allclose(reg1.cv_values_, reg2.cv_values_)\n",
    "assert np.allclose(reg1.coef_, reg2.coef_)\n",
    "assert np.allclose(reg1.alpha_, reg2.alpha_)\n",
    "pred1 = reg1.predict(X)\n",
    "pred2 = reg2.predict(X)\n",
    "assert np.allclose(pred1, pred2)"
   ]
  }
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