{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise 4.2 - Solution\n", "## Linear regression\n", "In this task we will design and train a linear model using [Keras](https://keras.io/).\n", "\n", "### Tasks\n", "1. Complete the implemetation of the LinearLayer\n", "2. Define a meaningful objective\n", "3. Implement gradient descent and train the linear model for 80 epochs." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import tensorflow as tf\n", "from tensorflow import keras\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "layers = keras.layers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation of data\n", "Let's first simulate some noisy data" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x.shape: (100, 1)\n", "y.shape: (100,)\n" ] } ], "source": [ "np.random.seed(1904)\n", "x = np.float32(np.linspace(-1, 1, 100)[:,np.newaxis])\n", "y = np.float32(2 * x[:,0] + 0.3 * np.random.randn(100))\n", "print(\"x.shape:\", x.shape)\n", "print(\"y.shape:\", y.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implement linear model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we have to design a linear layer that maps from the input $x$ to the output $y$ using a single adaptive weight $w$:\n", " \n", "$$y = w \\cdot x$$\n", "\n", "### Task 1\n", "Complete the implementation of the LinearLayer by adding the linear transformation in the call function." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "class LinearLayer(layers.Layer):\n", "\n", " def __init__(self, units=1, input_dim=1): # when intializing the layer the weights have to be initialized\n", " super(LinearLayer, self).__init__()\n", " w_init = tf.random_normal_initializer()\n", " self.w = tf.Variable(initial_value=w_init(shape=(input_dim, units), dtype=\"float32\"),\n", " trainable=True)\n", "\n", " def call(self, inputs): # when calling the layer the linear transformation has to be performed\n", " return tf.matmul(inputs, self.w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Build a model using the implemented layer." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "model = keras.models.Sequential()\n", "model.add(LinearLayer(units=1, input_dim=1))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: \"sequential\"\n", "_________________________________________________________________\n", "Layer (type) Output Shape Param # \n", "=================================================================\n", "linear_layer (LinearLayer) (None, 1) 1 \n", "=================================================================\n", "Total params: 1\n", "Trainable params: 1\n", "Non-trainable params: 0\n", "_________________________________________________________________\n", "None\n" ] } ], "source": [ "model.build((None, 1))\n", "print(model.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Performance before the training\n", "Plot data and model before the training" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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