812 lines
42 KiB
Plaintext
812 lines
42 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### General guidance\n",
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"\n",
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"This serves as a template which will guide you through the implementation of this task. It is advised\n",
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"to first read the whole template and get a sense of the overall structure of the code before trying to fill in any of the TODO gaps.\n",
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"This is the jupyter notebook version of the template. For the python file version, please refer to the file `template_solution.py`.\n",
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"\n",
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"First, we import necessary libraries:"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-11T20:25:46.118936Z",
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"start_time": "2026-03-11T20:25:46.115270Z"
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}
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},
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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"from sklearn.model_selection import KFold\n",
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"\n",
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"# Add any additional imports here (however, the task is solvable without using \n",
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"# any additional imports)\n",
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"# import ..."
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],
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"outputs": [],
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"execution_count": 55
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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" #### Loading data"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-11T20:25:46.151114Z",
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"start_time": "2026-03-11T20:25:46.143378Z"
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}
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},
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"source": [
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"data = pd.read_csv(\"train.csv\")\n",
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"y = data[\"y\"].to_numpy()\n",
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"data = data.drop(columns=\"y\")\n",
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"# print a few data samples\n",
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"print(data.head())"
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],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 \\\n",
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"0 0.06724 0.0 3.24 0.0 0.460 6.333 17.2 5.2146 4.0 430.0 16.9 \n",
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"1 9.23230 0.0 18.10 0.0 0.631 6.216 100.0 1.1691 24.0 666.0 20.2 \n",
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"2 0.11425 0.0 13.89 1.0 0.550 6.373 92.4 3.3633 5.0 276.0 16.4 \n",
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"3 24.80170 0.0 18.10 0.0 0.693 5.349 96.0 1.7028 24.0 666.0 20.2 \n",
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"4 0.05646 0.0 12.83 0.0 0.437 6.232 53.7 5.0141 5.0 398.0 18.7 \n",
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"\n",
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" x12 x13 \n",
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"0 375.21 7.34 \n",
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"1 366.15 9.53 \n",
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"2 393.74 10.50 \n",
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"3 396.90 19.77 \n",
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"4 386.40 12.34 \n"
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]
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}
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],
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"execution_count": 56
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Calculating the average RMSE"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-11T20:25:46.175778Z",
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"start_time": "2026-03-11T20:25:46.173181Z"
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}
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},
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"source": [
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"def calculate_RMSE(w, X, y):\n",
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" \"\"\"This function takes test data points (X and y), and computes the empirical RMSE of \n",
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" predicting y from X using a linear model with weights w. \n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" w: array of floats: dim = (13,), optimal parameters of ridge regression \n",
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" X: matrix of floats, dim = (15,13), inputs with 13 features\n",
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" y: array of floats, dim = (15,), input labels\n",
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"\n",
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" Returns\n",
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" ----------\n",
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" rmse: float: dim = 1, RMSE value\n",
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" \"\"\"\n",
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" rmse = 0\n",
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" n = X.shape[0]\n",
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" rmse = np.sqrt(1/n * np.sum( (y - X @ w)**2 ))\n",
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" assert np.isscalar(rmse)\n",
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" return rmse"
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],
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"outputs": [],
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"execution_count": 57
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Fitting the regressor"
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]
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": [
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"The fitting can be carried out by solving the normal equations:\n",
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"$$\n",
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"(\\lambda \\cdot \\mathbf{I} + \\mathbf{X}) \\mathbf{w} = \\mathbf{X}^{T}\\cdot \\mathbf{y}\n",
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"$$\n"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-11T20:25:46.200893Z",
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"start_time": "2026-03-11T20:25:46.197877Z"
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}
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},
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"source": [
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"def fit(X, y, lam):\n",
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" \"\"\"\n",
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" This function receives training data points, then fits the ridge regression on this data\n",
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" with regularization hyperparameter lambda. The weights w of the fitted ridge regression\n",
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" are returned. \n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" X: matrix of floats, dim = (135,13), inputs with 13 features\n",
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" y: array of floats, dim = (135,), input labels\n",
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" lam: float. lambda parameter, used in regularization term\n",
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"\n",
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" Returns\n",
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" ----------\n",
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" w: array of floats: dim = (13,), optimal parameters of ridge regression\n",
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" \"\"\"\n",
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" weights = np.zeros((13,))\n",
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" A = lam * np.identity(13) + np.transpose(X) @ X\n",
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" b = X.T @ y\n",
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" weights = np.linalg.solve(A, b)\n",
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"\n",
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" assert weights.shape == (13,)\n",
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" return weights"
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],
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"outputs": [],
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"execution_count": 58
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Performing computation"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-11T20:27:41.325447Z",
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"start_time": "2026-03-11T20:27:41.305479Z"
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}
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},
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"source": [
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"\"\"\"\n",
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"Main cross-validation loop, implementing 10-fold CV. In every iteration \n",
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"(for every train-test split), the RMSE for every lambda is calculated, \n",
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"and then averaged over iterations.\n",
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"\n",
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"Parameters\n",
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"---------- \n",
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"X: matrix of floats, dim = (150, 13), inputs with 13 features\n",
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"y: array of floats, dim = (150, ), input labels\n",
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"lambdas: list of floats, len = 5, values of lambda for which ridge regression is fitted and RMSE estimated\n",
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"n_folds: int, number of folds (pieces in which we split the dataset), parameter K in KFold CV\n",
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"\n",
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"Compute\n",
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"----------\n",
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"avg_RMSE: array of floats: dim = (5,), average RMSE value for every lambda\n",
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"\"\"\"\n",
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"X = data.to_numpy()\n",
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"# The function calculating the average RMSE\n",
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"lambdas = [0.1, 1, 10, 100, 200]\n",
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"n_folds = 10\n",
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"\n",
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"RMSE_mat = np.zeros((n_folds, len(lambdas)))\n",
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"\n",
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"\n",
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"# and fill all entries in the matrix 'RMSE_mat'\n",
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"for k in range(n_folds):\n",
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" fold = 150 // n_folds\n",
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" X_train = np.concatenate((X[:k*fold,:], X[(k+1)*fold:,:]),axis=0) # leave out the validation set\n",
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" X_validation = X[k*fold:(k+1)*fold,:]\n",
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" y_train = np.concatenate((y[:k*fold], y[(k+1)*fold:]))\n",
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" y_validation = y[k*fold:(k+1)*fold]\n",
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" for i in range(len(lambdas)):\n",
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" w = fit(X_train, y_train, lambdas[i])\n",
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" RMSE_mat[k,i] = calculate_RMSE(w, X_validation, y_validation)\n",
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"avg_RMSE = np.mean(RMSE_mat, axis=0) # avg_RMSE: array of floats: dim = (5,), average RMSE value for every lambda\n",
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"assert avg_RMSE.shape == (5,)"
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],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
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|
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" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
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" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
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|
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" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
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" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
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" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
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" [4.88759828 0. 0. 0. 0. ]\n",
|
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" [0. 0. 0. 0. 0. ]]\n",
|
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"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
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" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
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" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
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" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
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" [4.88759828 4.88177704 0. 0. 0. ]\n",
|
|
" [0. 0. 0. 0. 0. ]]\n",
|
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"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
|
" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
|
" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
|
" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
|
" [4.88759828 4.88177704 4.70584949 0. 0. ]\n",
|
|
" [0. 0. 0. 0. 0. ]]\n",
|
|
"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
|
" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
|
" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
|
" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
|
" [4.88759828 4.88177704 4.70584949 4.30299719 0. ]\n",
|
|
" [0. 0. 0. 0. 0. ]]\n",
|
|
"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
|
" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
|
" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
|
" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
|
" [4.88759828 4.88177704 4.70584949 4.30299719 4.45025962]\n",
|
|
" [0. 0. 0. 0. 0. ]]\n",
|
|
"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
|
" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
|
" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
|
" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
|
" [4.88759828 4.88177704 4.70584949 4.30299719 4.45025962]\n",
|
|
" [3.5549224 0. 0. 0. 0. ]]\n",
|
|
"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
|
" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
|
" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
|
" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
|
" [4.88759828 4.88177704 4.70584949 4.30299719 4.45025962]\n",
|
|
" [3.5549224 3.47254925 0. 0. 0. ]]\n",
|
|
"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
|
" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
|
" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
|
" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
|
" [4.88759828 4.88177704 4.70584949 4.30299719 4.45025962]\n",
|
|
" [3.5549224 3.47254925 3.38243796 0. 0. ]]\n",
|
|
"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
|
" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
|
" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
|
" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
|
" [4.88759828 4.88177704 4.70584949 4.30299719 4.45025962]\n",
|
|
" [3.5549224 3.47254925 3.38243796 3.79878164 0. ]]\n",
|
|
"[[7.4412339 7.47793331 7.58146902 8.19645872 8.50748161]\n",
|
|
" [5.12826602 4.88393133 4.45282503 3.55256057 3.60399295]\n",
|
|
" [7.70764701 7.70279186 7.72774439 7.77994411 7.88968326]\n",
|
|
" [4.54006065 4.50059526 4.33989198 4.94678494 5.24054741]\n",
|
|
" [4.07531646 4.0726219 4.19425423 4.89426434 5.24272243]\n",
|
|
" [5.10975443 5.15192098 5.39446252 7.11982551 7.87880031]\n",
|
|
" [6.55136404 6.56151161 6.55275056 7.13545034 7.47865912]\n",
|
|
" [6.04021985 6.09837022 6.36717035 7.59224397 7.99355906]\n",
|
|
" [4.88759828 4.88177704 4.70584949 4.30299719 4.45025962]\n",
|
|
" [3.5549224 3.47254925 3.38243796 3.79878164 4.14775924]]\n"
|
|
]
|
|
}
|
|
],
|
|
"execution_count": 64
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2026-03-11T20:25:46.251095Z",
|
|
"start_time": "2026-03-11T20:25:46.248154Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"A = np.array([[1,2],[3,4]])\n",
|
|
"#print(A[:,:1])\n",
|
|
"#print(np.transpose(A), A, np.transpose(A) @ A)\n",
|
|
"print(np.concatenate((A,A),axis=1))"
|
|
],
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"[[1 2 1 2]\n",
|
|
" [3 4 3 4]]\n"
|
|
]
|
|
}
|
|
],
|
|
"execution_count": 60
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2026-03-11T20:25:46.295067Z",
|
|
"start_time": "2026-03-11T20:25:46.292066Z"
|
|
}
|
|
},
|
|
"source": [
|
|
"# Save results in the required format\n",
|
|
"np.savetxt(\"./results.csv\", avg_RMSE, fmt=\"%.12f\")"
|
|
],
|
|
"outputs": [],
|
|
"execution_count": 61
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2026-03-11T20:25:46.321558Z",
|
|
"start_time": "2026-03-11T20:25:46.319798Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": "# Validate",
|
|
"outputs": [],
|
|
"execution_count": 62
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": ".venv",
|
|
"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"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|