diff --git a/002/exercise/lasso_regression.ipynb b/002/exercise/lasso_regression.ipynb
new file mode 100644
index 00000000..b55b330a
--- /dev/null
+++ b/002/exercise/lasso_regression.ipynb
@@ -0,0 +1,471 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Hi - Welcome to the Lasso Regression excercise\n",
+ "\n",
+ "## This notebook is based on the Linear Regression notebook\n",
+ "\n",
+ "## The main task of the assignment is in the second half of the notebook\n",
+ "\n",
+ "### Run cells below which import all required libraries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import sklearn, sklearn.model_selection\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below retreives the data and splits it into train_x, train_y, valid_x, valid_y, test_x, test_y"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# pick how big the validation/test portion of the data is, currently set to 20% validation, 20% test, and 60% train\n",
+ "valid_size = 0.2\n",
+ "test_size = 0.2\n",
+ "\n",
+ "# load the data from the .csv file\n",
+ "github_url = 'https://raw.githubusercontent.com/gimseng/99-ML-Learning-Projects/'\n",
+ "data_source = 'master/002/data/housing_prices.csv'\n",
+ "data = pd.read_csv(github_url+data_source)\n",
+ "\n",
+ "def train_valid_test_split(data, valid_size, test_size):\n",
+ " # split into train and test\n",
+ " train, test = sklearn.model_selection.train_test_split(data, test_size=test_size)\n",
+ " # further split train into train and validation. (valid_size needs to be recalculated to properly split train)\n",
+ " valid_size = valid_size/(1-test_size)\n",
+ " train, valid = sklearn.model_selection.train_test_split(train, test_size=valid_size)\n",
+ " return train, valid, test\n",
+ "\n",
+ "train, valid, test = train_valid_test_split(data, valid_size, test_size)\n",
+ "train_x, train_y = train.iloc[:, :-1], train.iloc[:, -1:]\n",
+ "valid_x, valid_y = valid.iloc[:, :-1], valid.iloc[:, -1:]\n",
+ "test_x, test_y = test.iloc[:, :-1], test.iloc[:, -1:]\n",
+ "\n",
+ "print(f'train size: {len(train_x)}, valid size: {len(valid_x)}, test size: {len(test_x)}')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below helps us view a few of our data points and also view how the selling price varies for different features"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "data.head(10)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "fig, axes = plt.subplots(nrows=1, ncols=2)\n",
+ "fig=(20,7)\n",
+ "data.groupby('YearBuilt').mean()['SalePrice'].plot(ylabel='Sale Price',xlabel='Year Built',ax=axes[0],figsize=fig)\n",
+ "data.groupby('GarageCars').mean()['SalePrice'].plot(kind='bar',ylabel='Sale Price',xlabel='Garage car room',ax=axes[1],figsize=fig)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below scales the numeric features using a min_max_scaler (scales them between 0 and 1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "numeric_columns = train_x.select_dtypes(include='number').columns\n",
+ "# scaler = sklearn.preprocessing.MinMaxScaler()\n",
+ "# scaler = sklearn.preprocessing.KBinsDiscretizer(n_bins=10, encode='ordinal')\n",
+ "scaler = sklearn.preprocessing.StandardScaler()\n",
+ "# train on concatenation of train and validation\n",
+ "scaler.fit(pd.concat((train_x[numeric_columns], valid_x[numeric_columns])))\n",
+ "# apply on all data\n",
+ "train_x[numeric_columns] = scaler.transform(train_x[numeric_columns])\n",
+ "valid_x[numeric_columns] = scaler.transform(valid_x[numeric_columns])\n",
+ "test_x[numeric_columns] = scaler.transform(test_x[numeric_columns])\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below one-hot encodes the data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def get_dummies_column_keys(dataFrames):\n",
+ " '''returns a column list of get dummies for concatenated dataframes'''\n",
+ " return pd.get_dummies(pd.concat(dataFrames)).columns.tolist()\n",
+ "\n",
+ "def get_dummies_using_keys(dataFrame, column_keys):\n",
+ " '''returns get dummies result with columns matching column_keys'''\n",
+ " result = pd.get_dummies(dataFrame)\n",
+ " result = result.reindex(columns=column_keys).fillna(0.00)\n",
+ " return result\n",
+ "\n",
+ "# get the keys for the concatenation of all datasets \n",
+ "column_keys = get_dummies_column_keys((train_x, valid_x, test_x))\n",
+ "train_x = get_dummies_using_keys(train_x, column_keys)\n",
+ "valid_x = get_dummies_using_keys(valid_x, column_keys)\n",
+ "test_x = get_dummies_using_keys(test_x, column_keys)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below appends a '1' to all rows by adding a 'Bias' feature with the value of 1 for all rows
This is to simulate a bias without adding any bias functionality to the Linear Regression algorithm "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "train_x['Bias'] = 1\n",
+ "valid_x['Bias'] = 1\n",
+ "test_x['Bias'] = 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### This last cell gets the numpy arrays that we will work on from the panda dataframes"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# store the dataframes in df_* variables\n",
+ "df_train_x, df_train_y = train_x, train_y\n",
+ "df_valid_x, df_valid_y = valid_x, valid_y\n",
+ "df_test_x, df_test_y = test_x, test_y\n",
+ "\n",
+ "# store the numpy arrays in the regular variables\n",
+ "train_x, train_y = train_x.values, train_y.values\n",
+ "valid_x, valid_y = valid_x.values, valid_y.values\n",
+ "test_x, test_y = test_x.values, test_y.values"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Proceed with any data analysis in the next cell\n",
+ "\n",
+ "## (Optional but encouraged)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# This is the main task of the exercise\n",
+ "\n",
+ "## You need to implement the following functions which
implement Linear Regression and all it's required functions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The first major function is the 'predict' function
Remember the Linear Regression equation is\n",
+ "$$\\hat{Y} = w_0 + w_1 x_1 + w_2 x_2 + ... + w_m x_m$$\n",
+ "\n",
+ "### hint: try to implement a 'vectorized' version by using a matrix multiplication
which will massively increase performance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "\n",
+ "def predict(w, x):\n",
+ " '''\n",
+ " Return the linear regression prediction from the weights and input features\n",
+ " Args:\n",
+ " w: The weight vector, shape: (features, 1)\n",
+ " x: The input data, shape: (num_samples, features)\n",
+ " Returns:\n",
+ " The prediction of the model, shape: (num_samples, 1)\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ " raise NotImplementedError\n",
+ "\n",
+ "def init_weights(x):\n",
+ " '''\n",
+ " Initialize the weights vector, the data is passed in to know how many weights you need\n",
+ " Args:\n",
+ " x: The input data, shape: (num_samples, features)\n",
+ " Returns:\n",
+ " The initial weight vector of random values, shape: (features, 1)\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ " raise NotImplementedError"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Next you have to implement the Mean Squared Error Loss calculation following the following formula \n",
+ "$$LOSS(W)=\\frac{1}{2n} \\sum_{i=1}^{n} (\\hat{y}_i-y_i)^2$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def loss(y_hat, y):\n",
+ " '''\n",
+ " Calculate the Mean Squared Error based on the y_hat (the predicted value) and y (the true values)\n",
+ " Args:\n",
+ " y_hat: the predicted values of the input, shape: (num_samples, 1)\n",
+ " y: the true values of the input, shape: (num_samples, 1)\n",
+ " Returns:\n",
+ " Mean Squared Error, shape: Scaler\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ " raise NotImplementedError"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Next you have to implement the gradient calculation for the weights accoarding to the formula\n",
+ "\n",
+ "$$\\frac{\\partial LOSS(W)}{\\partial W_j} \n",
+ "= \\sum_{i=1}^{n} (2*(\\hat{y}_i-y_i)*x_{i,j} + \\eta * \\frac{\\lvert{\\partial W_j}\\lvert}{\\partial W_j})$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def get_gradient(w, x, y_hat, y, l1_coeff):\n",
+ " '''\n",
+ " Get the gradient of the weights using the parameters passed \n",
+ " (Note: not all parameters passed have to be used)\n",
+ " Args:\n",
+ " w: The weight vector, shape: (features, 1)\n",
+ " x: The input data, shape: (num_samples, features)\n",
+ " y_hat: the predicted values of the input, shape: (num_samples, 1)\n",
+ " y: the true values of the input, shape: (num_samples, 1)\n",
+ " l1_coeff: L1 regularization coefficient\n",
+ " Returns:\n",
+ " The gradients of the weight vector, shape: (features, 1)\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ " raise NotImplementedError"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Next you have to implement the gradient descent update for the weights accoarding to the formula\n",
+ "\n",
+ "$$w_j:=w_j - \\alpha * \\frac{\\partial LOSS(W)}{\\partial W_j} $$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def get_updated_weights(w, w_gradients, learning_rate):\n",
+ " '''\n",
+ " Calculate the new value of the weights after applying the gradient descent weight update rule \n",
+ " Args:\n",
+ " w: The weight vector, shape: (features, 1)\n",
+ " w_gradients: The gradients of the weight vector, shape: (features, 1)\n",
+ " learning_rate: The learning rate of the algorithm, shape: Scaler\n",
+ " Returns:\n",
+ " The updated value of the weights, shape: (features, 1)\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ " raise NotImplementedError"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Finally implement the training loop, this should simply be
a loop that calls the functions you implemented above"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def train(epochs, x, y, learning_rate=1e-3, initial_weights=None, l1_coeff=0, initial_b=0):\n",
+ " '''\n",
+ " The main train loop for the algorithm. This performs the gradient update step 'epochs' times.\n",
+ " Args:\n",
+ " x: The input data, shape: (num_samples, features)\n",
+ " y: the true values of the input, shape: (num_samples, 1)\n",
+ " learning_rate: The learning rate of the algorithm, shape: Scaler\n",
+ " initial_weights: The initial weight to start training, this should be passed to continue training\n",
+ " Returns:\n",
+ " The final weight values after applying 'epochs' number of updates on 'initial_weights', shape: (features, 1)\n",
+ " '''\n",
+ " if initial_weights is None:\n",
+ " weight = init_weights(x)\n",
+ " else:\n",
+ " weight = initial_weights\n",
+ " \n",
+ " for epoch in range(epochs):\n",
+ " ### YOUR CODE HERE\n",
+ " raise NotImplementedError"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below will run your code\n",
+ "\n",
+ "### After 200,000 epochs our results were the following: \n",
+ "### Train loss:1.9036887e+08
Valid loss: 4.7176443e+08
Test loss: 1.08308357e+09"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%%time\n",
+ "w = None\n",
+ "weights=[]\n",
+ "l1_coeff = .0001\n",
+ "for i in range(20):\n",
+ " w = train(10000, train_x, train_y, learning_rate=5e-3, l1_coeff=l1_coeff, initial_weights=w)\n",
+ " weights.append(w)\n",
+ " print('epoch:', (i+1)*10000, end=' ')\n",
+ " print('Train loss:', loss(predict(w, train_x), train_y), end=' ')\n",
+ " print('Valid loss:', loss(predict(w, valid_x), valid_y))\n",
+ "print('Final Model -- Test loss:', loss(predict(w, test_x), test_y))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below shows us how the prediction improves while training over the span of 200,000 epochs ( By steps of 10000 epochs)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import IPython\n",
+ "for w in weights: \n",
+ " IPython.display.clear_output(wait=True)\n",
+ " pd.DataFrame({'Actual': train_y.flatten(), 'Predicted': predict(w,train_x).flatten()}).head(15).plot(kind='bar',figsize=(10,8))\n",
+ " plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "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": "3.7.4"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/002/exercise/readme.md b/002/exercise/readme.md
index 817cfe85..03e770db 100644
--- a/002/exercise/readme.md
+++ b/002/exercise/readme.md
@@ -4,6 +4,7 @@
- Learn your first ML model which is Linear Regression
- Learn how to evaluate models through a 'Loss function'
- Learn how to optimize a model through Gradient Descent
+- Learn how to implement L1 norm for regularization in Linear Regression (Lasso Regression)
# Data
@@ -21,6 +22,12 @@ Data source/credit: [Kaggle](https://www.kaggle.com/c/house-prices-advanced-regr
[](https://nbviewer.jupyter.org/github/gimseng/99-ML-Learning-Projects/blob/master/002/exercise/linear_regression.ipynb)
+`lasso-regression.ipynb`
+
+[](https://colab.research.google.com/github/gimseng/99-ML-Learning-Projects/blob/master/002/exercise/lasso_regression.ipynb)
+
+[](https://nbviewer.jupyter.org/github/gimseng/99-ML-Learning-Projects/blob/master/002/exercise/lasso_regression.ipynb)
+
# Resources on linear regression
@@ -34,4 +41,4 @@ Data source/credit: [Kaggle](https://www.kaggle.com/c/house-prices-advanced-regr
- [[Blog] Everything You Need To Know About Linear Regression](https://towardsdatascience.com/everything-you-need-to-know-about-linear-regression-b791e8f4bd7a)
- [Mandatory for Beginners] After getting the theoretical background for Linear Regression learn how to implement it practically using Sklearn
- [[Video] Linear Regression Python Sklearn [FROM SCRATCH]](https://www.youtube.com/watch?v=b0L47BeklTE)
-
+- [[Lasso Regression] Learn how L1 and L2 work using gradient descent](https://towardsdatascience.com/intuitions-on-l1-and-l2-regularisation-235f2db4c261)
\ No newline at end of file
diff --git a/002/solution/lasso_regression.ipynb b/002/solution/lasso_regression.ipynb
new file mode 100644
index 00000000..aa7ad9be
--- /dev/null
+++ b/002/solution/lasso_regression.ipynb
@@ -0,0 +1,905 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Hi - Welcome to the Lasso Regression excercise\n",
+ "\n",
+ "## This notebook is based on the Linear Regression notebook\n",
+ "\n",
+ "## The main task of the assignment is in the second half of the notebook\n",
+ "\n",
+ "### Run cells below which import all required libraries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 182,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import sklearn, sklearn.model_selection\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below retreives the data and splits it into train_x, train_y, valid_x, valid_y, test_x, test_y"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 183,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "train size: 876, valid size: 292, test size: 292\n"
+ ]
+ }
+ ],
+ "source": [
+ "# pick how big the validation/test portion of the data is, currently set to 20% validation, 20% test, and 60% train\n",
+ "valid_size = 0.2\n",
+ "test_size = 0.2\n",
+ "\n",
+ "# load the data from the .csv file\n",
+ "github_url = 'https://raw.githubusercontent.com/gimseng/99-ML-Learning-Projects/'\n",
+ "data_source = 'master/002/data/housing_prices.csv'\n",
+ "data = pd.read_csv(github_url+data_source)\n",
+ "\n",
+ "def train_valid_test_split(data, valid_size, test_size):\n",
+ " # split into train and test\n",
+ " train, test = sklearn.model_selection.train_test_split(data, test_size=test_size)\n",
+ " # further split train into train and validation. (valid_size needs to be recalculated to properly split train)\n",
+ " valid_size = valid_size/(1-test_size)\n",
+ " train, valid = sklearn.model_selection.train_test_split(train, test_size=valid_size)\n",
+ " return train, valid, test\n",
+ "\n",
+ "train, valid, test = train_valid_test_split(data, valid_size, test_size)\n",
+ "train_x, train_y = train.iloc[:, :-1], train.iloc[:, -1:]\n",
+ "valid_x, valid_y = valid.iloc[:, :-1], valid.iloc[:, -1:]\n",
+ "test_x, test_y = test.iloc[:, :-1], test.iloc[:, -1:]\n",
+ "\n",
+ "print(f'train size: {len(train_x)}, valid size: {len(valid_x)}, test size: {len(test_x)}')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below helps us view a few of our data points and also view how the selling price varies for different features"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 184,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Id | \n",
+ " MSSubClass | \n",
+ " MSZoning | \n",
+ " LotFrontage | \n",
+ " LotArea | \n",
+ " Street | \n",
+ " Alley | \n",
+ " LotShape | \n",
+ " LandContour | \n",
+ " Utilities | \n",
+ " ... | \n",
+ " PoolArea | \n",
+ " PoolQC | \n",
+ " Fence | \n",
+ " MiscFeature | \n",
+ " MiscVal | \n",
+ " MoSold | \n",
+ " YrSold | \n",
+ " SaleType | \n",
+ " SaleCondition | \n",
+ " SalePrice | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 1 | \n",
+ " 60 | \n",
+ " RL | \n",
+ " 65.0 | \n",
+ " 8450 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " Reg | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " 0 | \n",
+ " 2 | \n",
+ " 2008 | \n",
+ " WD | \n",
+ " Normal | \n",
+ " 208500 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 2 | \n",
+ " 20 | \n",
+ " RL | \n",
+ " 80.0 | \n",
+ " 9600 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " Reg | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " 0 | \n",
+ " 5 | \n",
+ " 2007 | \n",
+ " WD | \n",
+ " Normal | \n",
+ " 181500 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 3 | \n",
+ " 60 | \n",
+ " RL | \n",
+ " 68.0 | \n",
+ " 11250 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " IR1 | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " 0 | \n",
+ " 9 | \n",
+ " 2008 | \n",
+ " WD | \n",
+ " Normal | \n",
+ " 223500 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 4 | \n",
+ " 70 | \n",
+ " RL | \n",
+ " 60.0 | \n",
+ " 9550 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " IR1 | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " 0 | \n",
+ " 2 | \n",
+ " 2006 | \n",
+ " WD | \n",
+ " Abnorml | \n",
+ " 140000 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 5 | \n",
+ " 60 | \n",
+ " RL | \n",
+ " 84.0 | \n",
+ " 14260 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " IR1 | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " 0 | \n",
+ " 12 | \n",
+ " 2008 | \n",
+ " WD | \n",
+ " Normal | \n",
+ " 250000 | \n",
+ "
\n",
+ " \n",
+ " | 5 | \n",
+ " 6 | \n",
+ " 50 | \n",
+ " RL | \n",
+ " 85.0 | \n",
+ " 14115 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " IR1 | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " MnPrv | \n",
+ " Shed | \n",
+ " 700 | \n",
+ " 10 | \n",
+ " 2009 | \n",
+ " WD | \n",
+ " Normal | \n",
+ " 143000 | \n",
+ "
\n",
+ " \n",
+ " | 6 | \n",
+ " 7 | \n",
+ " 20 | \n",
+ " RL | \n",
+ " 75.0 | \n",
+ " 10084 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " Reg | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " 0 | \n",
+ " 8 | \n",
+ " 2007 | \n",
+ " WD | \n",
+ " Normal | \n",
+ " 307000 | \n",
+ "
\n",
+ " \n",
+ " | 7 | \n",
+ " 8 | \n",
+ " 60 | \n",
+ " RL | \n",
+ " NaN | \n",
+ " 10382 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " IR1 | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " Shed | \n",
+ " 350 | \n",
+ " 11 | \n",
+ " 2009 | \n",
+ " WD | \n",
+ " Normal | \n",
+ " 200000 | \n",
+ "
\n",
+ " \n",
+ " | 8 | \n",
+ " 9 | \n",
+ " 50 | \n",
+ " RM | \n",
+ " 51.0 | \n",
+ " 6120 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " Reg | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " 0 | \n",
+ " 4 | \n",
+ " 2008 | \n",
+ " WD | \n",
+ " Abnorml | \n",
+ " 129900 | \n",
+ "
\n",
+ " \n",
+ " | 9 | \n",
+ " 10 | \n",
+ " 190 | \n",
+ " RL | \n",
+ " 50.0 | \n",
+ " 7420 | \n",
+ " Pave | \n",
+ " NaN | \n",
+ " Reg | \n",
+ " Lvl | \n",
+ " AllPub | \n",
+ " ... | \n",
+ " 0 | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " NaN | \n",
+ " 0 | \n",
+ " 1 | \n",
+ " 2008 | \n",
+ " WD | \n",
+ " Normal | \n",
+ " 118000 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
10 rows × 81 columns
\n",
+ "
This is to simulate a bias without adding any bias functionality to the Linear Regression algorithm "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 188,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "train_x['Bias'] = 1\n",
+ "valid_x['Bias'] = 1\n",
+ "test_x['Bias'] = 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### This last cell gets the numpy arrays that we will work on from the panda dataframes"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 189,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# store the dataframes in df_* variables\n",
+ "df_train_x, df_train_y = train_x, train_y\n",
+ "df_valid_x, df_valid_y = valid_x, valid_y\n",
+ "df_test_x, df_test_y = test_x, test_y\n",
+ "\n",
+ "# store the numpy arrays in the regular variables\n",
+ "train_x, train_y = train_x.values, train_y.values\n",
+ "valid_x, valid_y = valid_x.values, valid_y.values\n",
+ "test_x, test_y = test_x.values, test_y.values"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Proceed with any data analysis in the next cell\n",
+ "\n",
+ "## (Optional but encouraged)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# This is the main task of the exercise\n",
+ "\n",
+ "## You need to implement the following functions which
implement Linear Regression and all it's required functions"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The first major function is the 'predict' function
Remember the Linear Regression equation is\n",
+ "$$\\hat{Y} = w_0 + w_1 x_1 + w_2 x_2 + ... + w_m x_m$$\n",
+ "\n",
+ "### hint: try to implement a 'vectorized' version by using a matrix multiplication
which will massively increase performance"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 190,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "\n",
+ "def predict(w, x):\n",
+ " '''\n",
+ " Return the linear regression prediction from the weights and input features\n",
+ " Args:\n",
+ " w: The weight vector, shape: (features, 1)\n",
+ " x: The input data, shape: (num_samples, features)\n",
+ " Returns:\n",
+ " The prediction of the model, shape: (num_samples, 1)\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ "# raise NotImplementedError\n",
+ " return x.dot(w)\n",
+ "\n",
+ "def init_weights(x):\n",
+ " '''\n",
+ " Initialize the weights vector, the data is passed in to know how many weights you need\n",
+ " Args:\n",
+ " x: The input data, shape: (num_samples, features)\n",
+ " Returns:\n",
+ " The initial weight vector of random values, shape: (features, 1)\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ "# raise NotImplementedError\n",
+ "# rv = np.zeros((x.shape[1], 1)) \n",
+ " return np.random.randn(x.shape[1], 1)/np.sqrt(x.shape[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Next you have to implement the Mean Squared Error Loss calculation following the following formula \n",
+ "$$LOSS(W)=\\frac{1}{2n} \\sum_{i=1}^{n} (\\hat{y}_i-y_i)^2$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 191,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def loss(y_hat, y):\n",
+ " '''\n",
+ " Calculate the Mean Squared Error based on the y_hat (the predicted value) and y (the true values)\n",
+ " Args:\n",
+ " y_hat: the predicted values of the input, shape: (num_samples, 1)\n",
+ " y: the true values of the input, shape: (num_samples, 1)\n",
+ " Returns:\n",
+ " Mean Squared Error, shape: Scaler\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ "# raise NotImplementedError\n",
+ " n = y.shape[0]\n",
+ " delta = y_hat - y\n",
+ " return ((delta.T @ delta) / (2*n))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Next you have to implement the gradient calculation for the weights accoarding to the formula\n",
+ "\n",
+ "$$\\frac{\\partial LOSS(W)}{\\partial W_j} \n",
+ "= \\sum_{i=1}^{n} (2*(\\hat{y}_i-y_i)*x_{i,j} + \\eta * \\frac{\\lvert{\\partial W_j}\\lvert}{\\partial W_j})$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 192,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def get_gradient(w, x, y_hat, y, l1_coeff):\n",
+ " '''\n",
+ " Get the gradient of the weights using the parameters passed \n",
+ " (Note: not all parameters passed have to be used)\n",
+ " Args:\n",
+ " w: The weight vector, shape: (features, 1)\n",
+ " x: The input data, shape: (num_samples, features)\n",
+ " y_hat: the predicted values of the input, shape: (num_samples, 1)\n",
+ " y: the true values of the input, shape: (num_samples, 1)\n",
+ " l1_coeff: L1 regularization coefficient\n",
+ " Returns:\n",
+ " The gradients of the weight vector, shape: (features, 1)\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ "# raise NotImplementedError\n",
+ "# https://towardsdatascience.com/intuitions-on-l1-and-l2-regularisation-235f2db4c261\n",
+ " n = y.shape[0]\n",
+ " delta = y_hat - y\n",
+ " dW = ( (2 * x.T.dot(delta) ) + np.sign(w) * l1_coeff ) / n\n",
+ " return dW"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Next you have to implement the gradient descent update for the weights accoarding to the formula\n",
+ "\n",
+ "$$w_j:=w_j - \\alpha * \\frac{\\partial LOSS(W)}{\\partial W_j} $$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 193,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def get_updated_weights(w, w_gradients, learning_rate):\n",
+ " '''\n",
+ " Calculate the new value of the weights after applying the gradient descent weight update rule \n",
+ " Args:\n",
+ " w: The weight vector, shape: (features, 1)\n",
+ " w_gradients: The gradients of the weight vector, shape: (features, 1)\n",
+ " learning_rate: The learning rate of the algorithm, shape: Scaler\n",
+ " Returns:\n",
+ " The updated value of the weights, shape: (features, 1)\n",
+ " '''\n",
+ " ### YOUR CODE HERE\n",
+ "# raise NotImplementedError\n",
+ " return w - learning_rate * w_gradients"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Finally implement the training loop, this should simply be
a loop that calls the functions you implemented above"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 194,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def train(epochs, x, y, learning_rate=1e-3, initial_weights=None, l1_coeff=0, initial_b=0):\n",
+ " '''\n",
+ " The main train loop for the algorithm. This performs the gradient update step 'epochs' times.\n",
+ " Args:\n",
+ " x: The input data, shape: (num_samples, features)\n",
+ " y: the true values of the input, shape: (num_samples, 1)\n",
+ " learning_rate: The learning rate of the algorithm, shape: Scaler\n",
+ " initial_weights: The initial weight to start training, this should be passed to continue training\n",
+ " Returns:\n",
+ " The final weight values after applying 'epochs' number of updates on 'initial_weights', shape: (features, 1)\n",
+ " '''\n",
+ " if initial_weights is None:\n",
+ " weight = init_weights(x)\n",
+ " else:\n",
+ " weight = initial_weights\n",
+ " \n",
+ " for epoch in range(epochs):\n",
+ " ### YOUR CODE HERE\n",
+ "# raise NotImplementedError\n",
+ " y_hat = predict(weight, train_x).reshape(-1, 1)\n",
+ " \n",
+ " delta = y_hat - y\n",
+ "\n",
+ " dW = get_gradient(weight, x, y_hat, y, l1_coeff)\n",
+ "# dW = ( -(2 * x.T.dot(-delta) ) + np.sign(weight) * l1_coeff ) / x.shape[0]\n",
+ " weight = get_updated_weights(weight, dW, learning_rate)\n",
+ "# weight = weight - learning_rate * dW\n",
+ " \n",
+ " delta = delta.reshape(-1)\n",
+ " meanSquareError = delta.dot(delta)/x.shape[1] # Capture MSE - and?\n",
+ "\n",
+ " return weight\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below will run your code\n",
+ "\n",
+ "### After 200,000 epochs our results were the following: \n",
+ "### Train loss:1.9036887e+08
Valid loss: 4.7176443e+08
Test loss: 1.08308357e+09"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 195,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "epoch: 10000 Train loss: [[2.4804421e+08]] Valid loss: [[3.34900642e+08]]\n",
+ "epoch: 20000 Train loss: [[2.27315727e+08]] Valid loss: [[3.5796312e+08]]\n",
+ "epoch: 30000 Train loss: [[2.16517742e+08]] Valid loss: [[3.72254317e+08]]\n",
+ "epoch: 40000 Train loss: [[2.09689841e+08]] Valid loss: [[3.83888202e+08]]\n",
+ "epoch: 50000 Train loss: [[2.05042711e+08]] Valid loss: [[3.94172634e+08]]\n",
+ "epoch: 60000 Train loss: [[2.01730763e+08]] Valid loss: [[4.03437126e+08]]\n",
+ "epoch: 70000 Train loss: [[1.99288268e+08]] Valid loss: [[4.11812646e+08]]\n",
+ "epoch: 80000 Train loss: [[1.97437495e+08]] Valid loss: [[4.19391221e+08]]\n",
+ "epoch: 90000 Train loss: [[1.96003669e+08]] Valid loss: [[4.26255866e+08]]\n",
+ "epoch: 100000 Train loss: [[1.94872149e+08]] Valid loss: [[4.32483734e+08]]\n",
+ "epoch: 110000 Train loss: [[1.93965135e+08]] Valid loss: [[4.3814508e+08]]\n",
+ "epoch: 120000 Train loss: [[1.93228301e+08]] Valid loss: [[4.43302553e+08]]\n",
+ "epoch: 130000 Train loss: [[1.92622764e+08]] Valid loss: [[4.48011256e+08]]\n",
+ "epoch: 140000 Train loss: [[1.92120095e+08]] Valid loss: [[4.5231931e+08]]\n",
+ "epoch: 150000 Train loss: [[1.91699114e+08]] Valid loss: [[4.56268633e+08]]\n",
+ "epoch: 160000 Train loss: [[1.91343773e+08]] Valid loss: [[4.59895749e+08]]\n",
+ "epoch: 170000 Train loss: [[1.9104173e+08]] Valid loss: [[4.63232563e+08]]\n",
+ "epoch: 180000 Train loss: [[1.90783367e+08]] Valid loss: [[4.6630703e+08]]\n",
+ "epoch: 190000 Train loss: [[1.90561097e+08]] Valid loss: [[4.69143745e+08]]\n",
+ "epoch: 200000 Train loss: [[1.9036887e+08]] Valid loss: [[4.7176443e+08]]\n",
+ "Final Model -- Test loss: [[1.08308357e+09]]\n",
+ "CPU times: user 8min 55s, sys: 48.1 s, total: 9min 44s\n",
+ "Wall time: 1min 6s\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%time\n",
+ "w = None\n",
+ "weights=[]\n",
+ "l1_coeff = .0001\n",
+ "for i in range(20):\n",
+ " w = train(10000, train_x, train_y, learning_rate=5e-3, l1_coeff=l1_coeff, initial_weights=w)\n",
+ " weights.append(w)\n",
+ " print('epoch:', (i+1)*10000, end=' ')\n",
+ " print('Train loss:', loss(predict(w, train_x), train_y), end=' ')\n",
+ " print('Valid loss:', loss(predict(w, valid_x), valid_y))\n",
+ "print('Final Model -- Test loss:', loss(predict(w, test_x), test_y))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### The cell below shows us how the prediction improves while training over the span of 200,000 epochs ( By steps of 10000 epochs)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 196,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import IPython\n",
+ "for w in weights: \n",
+ " IPython.display.clear_output(wait=True)\n",
+ " pd.DataFrame({'Actual': train_y.flatten(), 'Predicted': predict(w,train_x).flatten()}).head(15).plot(kind='bar',figsize=(10,8))\n",
+ " plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "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": "3.7.4"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/002/solution/readme.md b/002/solution/readme.md
index 2feed1ff..9277759c 100644
--- a/002/solution/readme.md
+++ b/002/solution/readme.md
@@ -6,3 +6,8 @@
[](https://colab.research.google.com/github/gimseng/99-ML-Learning-Projects/blob/master/002/solution/linear_regression.ipynb)
[](https://nbviewer.jupyter.org/github/gimseng/99-ML-Learning-Projects/blob/master/002/solution/linear_regression.ipynb)
+`lasso_regression.ipynb`
+
+[](https://colab.research.google.com/github/gimseng/99-ML-Learning-Projects/blob/master/002/solution/lasso_regression.ipynb)
+[](https://nbviewer.jupyter.org/github/gimseng/99-ML-Learning-Projects/blob/master/002/solution/lasso_regression.ipynb)
+
![](\"https://www.tensorflow.org/images/colab_logo_32px.png\"){kind=logo}
Run in Google Colab\n",
+ "