Add Network Modeling Assignment 1 notes
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David Doebel
253
IML Projects/Task 1b /task1b_ql4jfi6af0/template_solution.ipynb
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IML Projects/Task 1b /task1b_ql4jfi6af0/template_solution.ipynb
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{
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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": "2026-03-15T18:22:13.169924Z",
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"start_time": "2026-03-15T18:22:13.165934Z"
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}
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},
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"source": [
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"import numpy as np\n",
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"import pandas as pd\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": 30
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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": "2026-03-15T18:22:13.190312Z",
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"start_time": "2026-03-15T18:22:13.181357Z"
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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=[\"Id\", \"y\"])\n",
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"# print a few data samples\n",
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"print(data.head())\n",
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"X = data.to_numpy()"
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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\n",
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"0 0.02 0.05 -0.09 -0.43 -0.08\n",
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"1 -0.13 0.11 -0.08 -0.29 -0.03\n",
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"2 0.08 0.06 -0.07 -0.41 -0.03\n",
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"3 0.02 -0.12 0.01 -0.43 -0.02\n",
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"4 -0.14 -0.12 -0.08 -0.02 -0.08\n"
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]
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}
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],
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"execution_count": 31
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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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"#### Transform features"
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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": "2026-03-15T18:22:13.201976Z",
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"start_time": "2026-03-15T18:22:13.198370Z"
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}
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},
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"source": [
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"\"\"\"\n",
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"Transform the 5 input features of matrix X (x_i denoting the i-th component of a given row in X) \n",
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"into 21 new features phi(X) in the following manner:\n",
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"5 linear features: phi_1(X) = x_1, phi_2(X) = x_2, phi_3(X) = x_3, phi_4(X) = x_4, phi_5(X) = x_5\n",
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"5 quadratic features: phi_6(X) = x_1^2, phi_7(X) = x_2^2, phi_8(X) = x_3^2, phi_9(X) = x_4^2, phi_10(X) = x_5^2\n",
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"5 exponential features: phi_11(X) = exp(x_1), phi_12(X) = exp(x_2), phi_13(X) = exp(x_3), phi_14(X) = exp(x_4), phi_15(X) = exp(x_5)\n",
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"5 cosine features: phi_16(X) = cos(x_1), phi_17(X) = cos(x_2), phi_18(X) = cos(x_3), phi_19(X) = cos(x_4), phi_20(X) = cos(x_5)\n",
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"1 constant feature: phi_21(X)=1\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 = (700,5), inputs with 5 features\n",
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"\n",
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"Compute\n",
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"----------\n",
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"X_transformed: matrix of floats: dim = (700,21), transformed input with 21 features\n",
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"\"\"\"\n",
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"X_transformed = np.zeros((700, 21))\n",
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"quadratic_features = np.power(X,2)\n",
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"exponential_features = np.exp(X)\n",
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"cosine_features = np.cos(X)\n",
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"constant_feature = np.ones((X.shape[0],1))\n",
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"X_transformed = np.concatenate((X, quadratic_features, exponential_features, cosine_features, constant_feature), axis=1)\n",
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"assert X_transformed.shape == (700, 21)"
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],
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"outputs": [],
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"execution_count": 32
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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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"#### Fit 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": "2026-03-15T18:22:13.625674Z",
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"start_time": "2026-03-15T18:22:13.217438Z"
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}
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},
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"source": [
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"\"\"\"\n",
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"Use the transformed data points X_transformed and fit the logistic regression on this \n",
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"transformed data. Finally, compute the weights of the fitted logistic regression. \n",
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"\n",
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"Parameters\n",
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"----------\n",
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"X_transformed: array of floats: dim = (700,21), transformed input with 21 features\n",
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"y: array of integers \\in {0,1}, dim = (700,), input labels\n",
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"\n",
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"Compute\n",
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"----------\n",
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"w: array of floats: dim = (21,), optimal parameters of logistic regression\n",
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"\"\"\"\n",
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"weights = np.zeros((21,))\n",
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"learning_rate = 2 * X.shape[0] / np.linalg.svd(X_transformed, compute_uv=False)[0]**2\n",
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"tolerance = 0.001\n",
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"sigma = lambda x : 1/(1+np.exp(-x))\n",
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"gradient = lambda w, X, y: X.T @ (sigma(X @ w) - y) / X.shape[0]\n",
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"update = 1000000\n",
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"while np.linalg.norm(update) > tolerance:\n",
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" # Select a random batch (SGD)\n",
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" selection = np.random.choice(X_transformed.shape[0], 100, replace=False)\n",
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" X_random = X_transformed[selection,:]\n",
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" update = learning_rate * gradient(weights, X_random, y[selection])\n",
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" weights -= update\n",
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"\n",
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"assert weights.shape == (21,)"
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],
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"outputs": [],
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"execution_count": 33
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-15T18:22:13.630314Z",
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"start_time": "2026-03-15T18:22:13.629075Z"
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}
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},
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"cell_type": "code",
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"source": "",
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"outputs": [],
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"execution_count": null
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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": "2026-03-15T18:22:13.636358Z",
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"start_time": "2026-03-15T18:22:13.633885Z"
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}
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},
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"source": [
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"# Save results in the required format\n",
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"np.savetxt(\"./results.csv\", weights, fmt=\"%.12f\")"
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],
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"outputs": [],
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"execution_count": 34
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-15T18:22:13.643898Z",
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"start_time": "2026-03-15T18:22:13.641041Z"
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}
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},
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"cell_type": "code",
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"source": [
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"matrix = np.array([[1,2],[3,4],[5,6],[7,8],[9,10]])\n",
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"np.linalg.svd(X_transformed,compute_uv=False)\n",
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"matrix[np.random.choice(matrix.shape[0], 1, replace=False), :]"
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],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[1, 2]])"
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]
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},
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"execution_count": 35,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"execution_count": 35
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2026-03-15T18:22:13.707327Z",
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"start_time": "2026-03-15T18:22:13.706165Z"
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}
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},
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"cell_type": "code",
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"source": "",
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"outputs": [],
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"execution_count": null
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": ".venv",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.12"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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