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March 29, 2023 14:19
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "# A2 Q2\n", | |
| "\n", | |
| "Standardized exploratory data analysis process" | |
| ], | |
| "metadata": { | |
| "collapsed": false, | |
| "pycharm": { | |
| "name": "#%% md\n" | |
| } | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "outputs": [], | |
| "source": [ | |
| "# -*- coding: utf-8 -*-\n", | |
| "from sklearn.preprocessing import PolynomialFeatures\n", | |
| "\n", | |
| "\"\"\"\n", | |
| "Author: Hirsun MAXWELL「韩佳明」\n", | |
| "Homepage: https://guomaimang.github.io\n", | |
| "License: MIT\n", | |
| "\"\"\"\n", | |
| "\n", | |
| "import numpy as np\n", | |
| "import seaborn as sns\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "from sklearn.linear_model import LogisticRegression\n", | |
| "from sklearn.metrics import f1_score" | |
| ], | |
| "metadata": { | |
| "collapsed": false, | |
| "pycharm": { | |
| "name": "#%%\n" | |
| } | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "(500, 3)\n", | |
| "float64\n", | |
| "[[ 0.613314 1.138547 1. ]\n", | |
| " [ 0.262046 0.245954 1. ]\n", | |
| " [ 0.809557 1.481712 0. ]\n", | |
| " [-0.718433 1.017201 0. ]\n", | |
| " [ 1.029742 -0.930264 1. ]\n", | |
| " [ 0.774779 0.4216 1. ]\n", | |
| " [-0.199856 0.834872 1. ]\n", | |
| " [ 1.375865 1.069579 0. ]\n", | |
| " [ 1.989108 -1.011556 0. ]\n", | |
| " [-0.824581 1.162131 0. ]]\n", | |
| "False\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# Load the dataset\n", | |
| "data = np.loadtxt(\"problem2data.txt\")\n", | |
| "\n", | |
| "# Preview data\n", | |
| "print(data.shape)\n", | |
| "print(data.dtype)\n", | |
| "print(data[:10])\n", | |
| "\n", | |
| "# Check for missing values\n", | |
| "print(np.any(np.isnan(data)))" | |
| ], | |
| "metadata": { | |
| "collapsed": false, | |
| "pycharm": { | |
| "name": "#%%\n" | |
| } | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Fold 1 f1 score: 0.0\n", | |
| "Fold 2 f1 score: 0.5585585585585586\n", | |
| "Fold 3 f1 score: 0.4375\n", | |
| "Fold 4 f1 score: 0.6315789473684211\n", | |
| "Fold 5 f1 score: 0.44\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "# Skip to split the data into training and testing, according to the requirement of assignment (I think it is necessary to divide the data into training and testing sets according to 80% and 20% before cross-validation.)\n", | |
| "X = data[:,0:2]\n", | |
| "y = data[:,2]\n", | |
| "\n", | |
| "# Split data into training set and validation set for each fold\n", | |
| "each_num_spl = data.shape[0] // 5\n", | |
| "X_folds = np.split(X[:each_num_spl*5], 5)\n", | |
| "y_folds = np.split(y[:each_num_spl*5], 5)\n", | |
| "\n", | |
| "# Create a logistic regression model\n", | |
| "model = LogisticRegression()\n", | |
| "\n", | |
| "# scores = cross_val_score(model, X, y, cv=5, score = \"f1\" ) -> Implement cross-validation manually and check the f1 score after each fold\n", | |
| "\n", | |
| "scores = [[] for i in range(12)]\n", | |
| "\n", | |
| "for i in range(5):\n", | |
| " # Each round drop one fold\n", | |
| " X_train = np.concatenate(X_folds[:i] + X_folds[i+1:])\n", | |
| " X_valid = X_folds[i]\n", | |
| " y_train = np.concatenate(y_folds[:i] + y_folds[i+1:])\n", | |
| " y_valid = y_folds[i]\n", | |
| "\n", | |
| " model.fit(X_train, y_train)\n", | |
| " y_pred = model.predict(X_valid)\n", | |
| " f1 = f1_score(y_valid, y_pred)\n", | |
| " scores[0].append(f1)\n", | |
| " print(f'Fold {i + 1} f1 score: {f1}')" | |
| ], | |
| "metadata": { | |
| "collapsed": false, | |
| "pycharm": { | |
| "name": "#%%\n" | |
| } | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Order = 2 Fold 1 f1 score: 0.8500000000000001\n", | |
| "Order = 2 Fold 2 f1 score: 0.8247422680412372\n", | |
| "Order = 2 Fold 3 f1 score: 0.8247422680412372\n", | |
| "Order = 2 Fold 4 f1 score: 0.7500000000000001\n", | |
| "Order = 2 Fold 5 f1 score: 0.7115384615384615\n", | |
| "\n", | |
| "\n", | |
| "Order = 3 Fold 1 f1 score: 0.8571428571428572\n", | |
| "Order = 3 Fold 2 f1 score: 0.8247422680412372\n", | |
| "Order = 3 Fold 3 f1 score: 0.8210526315789473\n", | |
| "Order = 3 Fold 4 f1 score: 0.7422680412371134\n", | |
| "Order = 3 Fold 5 f1 score: 0.6990291262135921\n", | |
| "\n", | |
| "\n", | |
| "Order = 4 Fold 1 f1 score: 0.8333333333333334\n", | |
| "Order = 4 Fold 2 f1 score: 0.8247422680412372\n", | |
| "Order = 4 Fold 3 f1 score: 0.8247422680412372\n", | |
| "Order = 4 Fold 4 f1 score: 0.7446808510638298\n", | |
| "Order = 4 Fold 5 f1 score: 0.7102803738317756\n", | |
| "\n", | |
| "\n", | |
| "Order = 5 Fold 1 f1 score: 0.8292682926829268\n", | |
| "Order = 5 Fold 2 f1 score: 0.8282828282828283\n", | |
| "Order = 5 Fold 3 f1 score: 0.8080808080808082\n", | |
| "Order = 5 Fold 4 f1 score: 0.7422680412371134\n", | |
| "Order = 5 Fold 5 f1 score: 0.709090909090909\n", | |
| "\n", | |
| "\n", | |
| "Order = 6 Fold 1 f1 score: 0.8455284552845529\n", | |
| "Order = 6 Fold 2 f1 score: 0.8\n", | |
| "Order = 6 Fold 3 f1 score: 0.7722772277227722\n", | |
| "Order = 6 Fold 4 f1 score: 0.7474747474747475\n", | |
| "Order = 6 Fold 5 f1 score: 0.7142857142857142\n", | |
| "\n", | |
| "\n", | |
| "Order = 7 Fold 1 f1 score: 0.8387096774193549\n", | |
| "Order = 7 Fold 2 f1 score: 0.8\n", | |
| "Order = 7 Fold 3 f1 score: 0.7920792079207921\n", | |
| "Order = 7 Fold 4 f1 score: 0.7422680412371134\n", | |
| "Order = 7 Fold 5 f1 score: 0.6956521739130435\n", | |
| "\n", | |
| "\n", | |
| "Order = 8 Fold 1 f1 score: 0.8253968253968255\n", | |
| "Order = 8 Fold 2 f1 score: 0.787878787878788\n", | |
| "Order = 8 Fold 3 f1 score: 0.7619047619047619\n", | |
| "Order = 8 Fold 4 f1 score: 0.7200000000000001\n", | |
| "Order = 8 Fold 5 f1 score: 0.7027027027027027\n", | |
| "\n", | |
| "\n", | |
| "Order = 9 Fold 1 f1 score: 0.8253968253968255\n", | |
| "Order = 9 Fold 2 f1 score: 0.787878787878788\n", | |
| "Order = 9 Fold 3 f1 score: 0.7692307692307693\n", | |
| "Order = 9 Fold 4 f1 score: 0.7346938775510203\n", | |
| "Order = 9 Fold 5 f1 score: 0.6902654867256637\n", | |
| "\n", | |
| "\n", | |
| "Order = 10 Fold 1 f1 score: 0.8095238095238094\n", | |
| "Order = 10 Fold 2 f1 score: 0.8080808080808081\n", | |
| "Order = 10 Fold 3 f1 score: 0.7572815533980582\n", | |
| "Order = 10 Fold 4 f1 score: 0.6990291262135923\n", | |
| "Order = 10 Fold 5 f1 score: 0.6964285714285714\n", | |
| "\n", | |
| "\n", | |
| "Order = 11 Fold 1 f1 score: 0.8031496062992126\n", | |
| "Order = 11 Fold 2 f1 score: 0.8039215686274509\n", | |
| "Order = 11 Fold 3 f1 score: 0.7572815533980582\n", | |
| "Order = 11 Fold 4 f1 score: 0.6862745098039216\n", | |
| "Order = 11 Fold 5 f1 score: 0.7130434782608696\n", | |
| "\n", | |
| "\n", | |
| "Order = 12 Fold 1 f1 score: 0.7874015748031497\n", | |
| "Order = 12 Fold 2 f1 score: 0.8039215686274509\n", | |
| "Order = 12 Fold 3 f1 score: 0.7722772277227722\n", | |
| "Order = 12 Fold 4 f1 score: 0.6857142857142857\n", | |
| "Order = 12 Fold 5 f1 score: 0.7027027027027027\n", | |
| "\n", | |
| "\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "for d in range(2,12+1):\n", | |
| " # Create polynomial features of the input variables\n", | |
| " poly = PolynomialFeatures(degree=d)\n", | |
| " X_poly = poly.fit_transform(X)\n", | |
| "\n", | |
| " X_folds = np.split(X_poly[:each_num_spl*5], 5)\n", | |
| " y_folds = np.split(y[:each_num_spl*5], 5)\n", | |
| "\n", | |
| " model = LogisticRegression(max_iter=10000)\n", | |
| "\n", | |
| " for i in range(5):\n", | |
| " # Each round drop one fold\n", | |
| " X_train = np.concatenate(X_folds[:i] + X_folds[i+1:])\n", | |
| " X_valid = X_folds[i]\n", | |
| " y_train = np.concatenate(y_folds[:i] + y_folds[i+1:])\n", | |
| " y_valid = y_folds[i]\n", | |
| "\n", | |
| " model.fit(X_train, y_train)\n", | |
| " y_pred = model.predict(X_valid)\n", | |
| " f1 = f1_score(y_valid, y_pred)\n", | |
| " scores[d-1].append(f1)\n", | |
| " print(f'Order = {d} Fold {i + 1} f1 score: {f1}')\n", | |
| " print(\"\\n\")" | |
| ], | |
| "metadata": { | |
| "collapsed": false, | |
| "pycharm": { | |
| "name": "#%%\n" | |
| } | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": "<Figure size 432x288 with 1 Axes>", | |
| "image/png": 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\n" | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "text/plain": "<Figure size 432x288 with 0 Axes>" | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Seaborn plot\n", | |
| "axis_y = np.array(scores).sum(axis=1)/5\n", | |
| "axis_x = np.arange(1,12+1)\n", | |
| "\n", | |
| "f, ax= plt.subplots()\n", | |
| "\n", | |
| "sns.scatterplot(x = axis_x, y=axis_y)\n", | |
| "sns.lineplot(x = axis_x, y=axis_y)\n", | |
| "\n", | |
| "ax.tick_params(axis='x',labelsize=12)\n", | |
| "\n", | |
| "plt.xlabel('Order')\n", | |
| "plt.ylabel('F1 Score')\n", | |
| "plt.title('F1 Score Indicators')\n", | |
| "\n", | |
| "plt.show()\n", | |
| "plt.clf()" | |
| ], | |
| "metadata": { | |
| "collapsed": false, | |
| "pycharm": { | |
| "name": "#%%\n" | |
| } | |
| } | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "## Discuss\n", | |
| "\n", | |
| "- When the order changes from 1 to 2, the f1 score increases significantly. It means in this case, increasing the polynomial order to 2 may improve the fit of the model to the data and result in better performance.\n", | |
| "- However, after order 2, f1 score start to gradually decline. Since it increases the complexity of the model. It lead to overfitting, where the model fits the training data too closely and does not generalize well to new data." | |
| ], | |
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| Problem 2 (5 points) | |
| Load dataset in problem2data.txt by using “numpy.loadtxt()” in Python, which contains two synthetic classes separated by a non-linear function y = f (x), with additive noise. The last column contains “0” or “1”, indicating the corresponding classes. You are asked to investigate the extent to which polynomial functions can be used to build a logistic regression classifier. | |
| (a) Build a logistic regression classifier by using a polynomial function of order 1 (e.g., θ0 + θ1x1 + θ2x2). Apply 5-fold-cross-validation to generate training and test sets. Use the training set to train the model. Compute its five F1 scores on test set (one F1 score for each fold). Compute its five F1 scores on training set. You will need “f1 score” from “sklearn.metrics”. | |
| (b) Repeat part (a) for polynomials of order 2 to 12. You will need “PolynomialFeatures” from “sklearn.preprocessing”. | |
| (c) Repeatparts(a-b)50times,andestimatetheaverageF1scoreforeachpolynomialorder(average across its 5 × 50 runs, both for training and test sets). Generate a plot that shows the F1 scores versus the polynomial order. | |
| (d) Discuss how the F1 scores of the model changes as a function of the polynomial order. | |
| (e) Use Jupyter Notebook to perform implementation. You are required to submit your “.ipynb” file. You could use “LogisticRegression” from “sklearn.linear model”. Do not add any regulariza- tions. |
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| 1.317895 1.429511 0 |
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