1370 lines
423 KiB
Plaintext
1370 lines
423 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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"# EXERCISE 2 - ML - Grundlagen und Algorithmen\n",
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"**Solved by**: Pascal Schindler ujvhi@student.kit.edu, Paul Lödige ucycy@student.kit.edu"
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]
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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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"## 1.) Multiclass Classification\n",
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"\n",
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"The Iris Dataset is a very classical machine learning and statistics benchmark for classification, developed in the 1930's. The goal is to classify 3 types of flowers (more specifically, 3 types of flowers form the Iris species) based on 4 features: petal length, petal width, sepal length and sepal width.\n",
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"\n",
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"As we have $K=3$ different types of flowers we are dealing with a multi-class classification problem and need to extend our sigmoid-based classifier from the previous exercise / recap session. \n",
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"\n",
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"We will reuse our \"minimize\" and \"affine feature\" functions. Those are exactly as before. The affine features are sufficient here."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"from typing import Callable, Tuple\n",
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"from sklearn.ensemble import RandomForestRegressor\n",
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"import warnings\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"%matplotlib inline\n",
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"\n",
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"\n",
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"warnings.filterwarnings('ignore')\n",
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"\n",
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"\n",
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"def minimize(f: Callable, df: Callable, x0: np.ndarray, lr: float, num_iters: int) -> \\\n",
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" Tuple[np.ndarray, float, np.ndarray, np.ndarray]:\n",
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" \"\"\"\n",
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" :param f: objective function\n",
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" :param df: gradient of objective function\n",
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" :param x0: start point, shape [dimension]\n",
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" :param lr: learning rate\n",
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" :param num_iters: maximum number of iterations\n",
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" :return argmin, min, values of x for all interations, value of f(x) for all iterations\n",
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" \"\"\"\n",
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" # initialize\n",
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" x = np.zeros([num_iters + 1] + list(x0.shape))\n",
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" f_x = np.zeros(num_iters + 1)\n",
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" x[0] = x0\n",
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" f_x[0] = f(x0)\n",
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" for i in range(num_iters):\n",
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" # update using gradient descent rule\n",
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" grad = df(x[i])\n",
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" x[i + 1] = x[i] - lr * grad\n",
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" f_x[i + 1] = f(x[i + 1])\n",
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" # logging info for visualization\n",
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" return x[i+1], f_x[i+1], x[:i+1], f_x[:i+1]\n",
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"\n",
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"\n",
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"def affine_features(x: np.ndarray) -> np.ndarray:\n",
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" \"\"\"\n",
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" implements affine feature function\n",
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" :param x: inputs\n",
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" :return inputs with additional bias dimension\n",
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" \"\"\"\n",
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" return np.concatenate([x, np.ones((x.shape[0], 1))], axis=-1)\n"
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]
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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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"### Load and Prepare Data\n",
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"In the original dataset the different types of flowers are labeled with $0, 1$ and $2$. The output of our classifier will be a vector with $K=3$ entries, $\\begin{pmatrix}p(c=0 | \\boldsymbol x) & p(c=1 | \\boldsymbol x) & p(c=2 | \\boldsymbol x) \\end{pmatrix}$, i.e. the probability for each class that a given sample is an instance of that class, given a datapoint $\\boldsymbol x$. As presented in the lecture, working with categorical (=multinomial) distributions is easiest when we represent the labels in a different form, a so called one-hot encoding. This is a vector of the length of number of classes, in this case 3, with zeros everywhere except for the entry corresponding to the class number, which is one. For the train and test data we know to which class it belongs, so the probability for that class is one and the probability for all other classes zero."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [],
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"source": [
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"data = np.load(\"./iris_data.npz\")\n",
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"train_samples = data[\"train_features\"]\n",
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"train_labels = data[\"train_labels\"]\n",
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"test_samples = data[\"test_features\"]\n",
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"test_labels = data[\"test_labels\"]\n",
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"\n",
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"train_features = affine_features(train_samples)\n",
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"test_features = affine_features(test_samples)\n",
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"\n",
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"\n",
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"def generate_one_hot_encoding(y: np.ndarray, num_classes: int) -> np.ndarray:\n",
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" \"\"\"\n",
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" :param y: vector containing classes as numbers, shape: [N]\n",
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" :param num_classes: number of classes\n",
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" :return a matrix containing the labels in an one-hot encoding, shape: [N x K]\n",
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" \"\"\"\n",
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" y_oh = np.zeros([y.shape[0], num_classes])\n",
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"\n",
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" # can be done more efficiently using numpy with\n",
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" # y_oh[np.arange(y.size), y] = 1.0\n",
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" # we use the for loop for clarity\n",
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"\n",
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" for i in range(y.shape[0]):\n",
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" y_oh[i, y[i]] = 1.0\n",
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"\n",
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" return y_oh\n",
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"\n",
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"\n",
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"oh_train_labels = generate_one_hot_encoding(train_labels, 3)\n",
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"oh_test_labels = generate_one_hot_encoding(test_labels, 3)\n"
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]
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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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"## Optimization using Gradient Descent\n",
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"\n",
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"The multi-class generalization of the sigmoid is the softmax function. It takes an vector of length $K$ and outputs another vector of length $K$ where the $k$-th entry is given by\n",
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"$$ \\textrm{softmax}(\\boldsymbol{x})_k = \\dfrac{\\exp(x_k)}{\\sum_{j=1}^K \\exp(x_j)}.$$\n",
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"This vector contains positive elements which sum to $1$ and thus can be interpreted as parameters of a categorical distribution."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [],
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"source": [
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"def softmax(x: np.ndarray) -> np.ndarray:\n",
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" \"\"\"softmax function\n",
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" :param x: inputs, shape: [N x K]\n",
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" :return softmax(x), shape [N x K]\n",
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" \"\"\"\n",
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" a = np.max(x, axis=-1, keepdims=True)\n",
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" log_normalizer = a + np.log(np.sum(np.exp(x - a), axis=-1, keepdims=True))\n",
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" return np.exp(x - log_normalizer)\n"
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]
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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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"**Practical Aspect:** In the above implementation of the softmax we stayed in the log-domain until the very last command.\n",
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"We also used the log-sum-exp-trick (https://en.wikipedia.org/wiki/LogSumExp#log-sum-exp_trick_for_log-domain_calculations).\n",
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"Staying in the log domain and applying the log-sum-exp-trick whenever possible is a simple way to make the implementation\n",
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"numerically more robust. It does not change anything with regards to the underlying theory.\n",
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"\n",
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"We also need to extend our loss function. Instead of the log-likelihood of a Bernoulli distribution, we now maximize the log-likelihood of a categorical distribution which, for a single sample $\\boldsymbol{x}_i$, is given by\n",
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"$$\\log p(c_i | \\boldsymbol x_i) = \\sum_{k=1}^K h_{i, k} \\log(p_{i,k})$$\n",
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"where $\\boldsymbol h_i$ denotes the one-hot encoded true label and $p_{i,k} \\equiv p(c_i = k | \\boldsymbol x_i)$ the class probabilities predicted by the classifier. In multiclass classification, we learn one weight vector $\\boldsymbol w_k$ per class s.t. those probabilities are given by $p(c_i = k | \\boldsymbol x_i) = \\mathrm{softmax}(\\boldsymbol w_k^T \\boldsymbol \\phi (\\boldsymbol x_i)) $.\n",
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"We can now implement the (negative) log-likelihood of a categorical distribution (we use the negative log-likelihood as we will minimize the loss later on)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [],
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"source": [
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"def categorical_nll(predictions: np.ndarray, labels: np.ndarray, epsilon: float = 1e-12) -> np.ndarray:\n",
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" \"\"\"\n",
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" cross entropy loss function\n",
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" :param predictions: class labels predicted by the classifier, shape: [N x K]\n",
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" :param labels: true class labels, shape: [N x K]\n",
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" :param epsilon: small offset to avoid numerical instabilities (i.e log(0))\n",
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" :return negative log-likelihood of the labels given the predictions, shape: [N]\n",
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" \"\"\"\n",
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"\n",
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" return - np.sum(labels * np.log(predictions + epsilon), -1)\n"
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]
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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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"This gives us the loss for a single sample. To get the loss for all samples we will need to sum over loss for a single sample\n",
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"\n",
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"\\begin{align} \n",
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"\\mathcal L_{\\mathrm{cat-NLL}} \n",
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"=& - \\sum_{i=1}^N \\log p(c_i | \\boldsymbol x_i) \\\\\n",
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"=& - \\sum_{i=1}^N \\sum_{k=1}^K h_{i, k} \\log(p_{i,k}) \\\\\n",
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"=& - \\sum_{i=1}^N \\sum_{k=1}^K h_{i, k} \\log(\\textrm{softmax}(\\boldsymbol{w}_k^T \\boldsymbol \\phi(\\boldsymbol{x}_i))_k)\\\\\n",
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"=& - \\sum_{i=1}^N \\left(\\sum_{k=1}^K h_{i,k}\\boldsymbol{w}^T_k \\boldsymbol \\phi(\\boldsymbol{x}_i) - \\log \\sum_{j=1}^K \\exp(\\boldsymbol{w}_j^T \\boldsymbol \\phi(\\boldsymbol{x}_i))\\right).\n",
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"\\end{align}\n",
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"\n",
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"In order to use gradient based optimization for this, we of course also need to derive the gradient.\n",
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"This gives us the loss for a single sample. To get the loss for all samples we will need to sum over loss for a single sample\n",
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"\n",
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"\n",
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"\n",
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"### 1.1) Derivation (4 Points)\n",
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"Derive the gradient $\\dfrac{\\partial \\mathcal L_{\\mathrm{cat-NLL}}}{\\partial \\boldsymbol{w}}$ of the loss function w.r.t. the full weight vector $\\boldsymbol w \\equiv \\begin{pmatrix} \\boldsymbol w_1^T & \\dots & \\boldsymbol w_K^T \\end{pmatrix}^T$, which is obtained by stacking the class-specific weight vectors $\\boldsymbol w_k$.\n",
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"\n",
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"**Hint 1:** Follow the steps in the derivation of the gradient of the loss for the binary classification in the lecture.\n",
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"\n",
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"**Hint 2:** Derive the gradient not for the whole vector $\\boldsymbol w$ but only for $\\boldsymbol w_k$ i.e., $\\dfrac{\\partial \\mathcal L_{\\mathrm{cat-NLL}}}{\\partial \\boldsymbol{w}_k}$. The gradients for the individual\n",
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"$\\boldsymbol w_k$ can then be stacked to obtain the full gradient."
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]
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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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"\\begin{align}\n",
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"\\dfrac{\\partial \\mathcal L_{\\mathrm{cat-NLL}}}{\\partial \\boldsymbol{w_k}}\n",
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"&= \\frac{\\partial}{\\partial w_k}\\left(\\sum_{k=1}^Kh_{c_i,k} w_k^T \\phi(x_i) - \\log \\left(\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}\\right)\\right)\\\\\n",
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"\\end{align}"
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]
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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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"the $k$ in $\\partial w_k$ is not the same as the $k$ in the sum $\\sum_{k=1}^K$. To avoid confusion we will rename the first $w_k$ to $w_l$:"
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]
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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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"\\begin{align}\n",
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"\\dfrac{\\partial \\mathcal L_{\\mathrm{cat-NLL}}}{\\partial \\boldsymbol{w_l}}\n",
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"&= \\frac{\\partial}{\\partial w_l}\\left(\\sum_{k=1}^Kh_{c_i,k} w_k^T \\phi(x_i) - \\log \\left(\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}\\right)\\right)\\\\\n",
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"\\end{align}"
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]
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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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"because $h_{c_i,k}=\\begin{cases}0 & \\forall k\\neq l \\\\ 1 & \\text{for }k=l\\end{cases}$ the sum $\\sum_{k=1}^K$ collapses:"
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]
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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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"\\begin{align}\n",
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"&= \\frac{\\partial}{\\partial w_l}\\left(w_l^T \\phi(x_i)\\right) - \\frac{\\partial}{\\partial w_l}\\left( \\log \\left(\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}\\right)\\right)\\\\\n",
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"\\end{align}"
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]
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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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"from $\\frac{\\partial x^T a}{\\partial x}=a^T$ and $\\frac{\\partial \\log(f(x))}{\\partial x}=\\frac{f'(x)}{f(x)}$ follows:\n"
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]
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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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"\\begin{align}\n",
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"&= \\phi(x_i)^T - \\frac{\\frac{\\partial}{\\partial w_l}\\left(\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}\\right)}{\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}}\\\\\n",
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"\\end{align}"
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]
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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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"$\\frac{\\partial}{\\partial w_l} e^{w_j^T\\phi(x_i)} = \\begin{cases}0\\cdot e^{w_j^T\\phi(x_i)}=0 & \\forall w_j\\neq w_l\\\\ \\phi(x_i)^T e^{w_l^T\\phi(x_i)} &\\text{for } w_j=w_l\\end{cases}$ leads to:"
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]
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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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"\\begin{align}\n",
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"&= \\phi(x_i)^T - \\frac{ \\phi(x_i)^T e^{w_l^T \\phi(x_i)}}{\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}}\\\\\n",
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"&= \\phi(x_i)^T \\left(1 - \\frac{e^{w_l^T \\phi(x_i)}}{\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}}\\right)\\\\\n",
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"\\end{align}\n",
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"\n",
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"If we do the same thing for every $w_l$ we get\n",
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"\n",
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"$$\n",
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"\\dfrac{\\partial \\mathcal L_{\\mathrm{cat-NLL}}}{\\partial \\boldsymbol{w}}\n",
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"= \\begin{pmatrix}\n",
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"\\phi(x_i)^T \\left(1 - \\frac{e^{w_1^T \\phi(x_i)}}{\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}}\\right)\\\\\n",
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"\\vdots \\\\\n",
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"\\phi(x_i)^T \\left(1 - \\frac{e^{w_K^T \\phi(x_i)}}{\\sum_{j=1}^K e^{w_j^T \\phi(x_i)}}\\right)\\\\\n",
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"\\end{pmatrix}\n",
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"$$"
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]
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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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"## 1.2) Implementation (3 Points)\n",
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"Now that we have the formulas for the loss and its gradient, we can implement them. Fill in the function skeletons below so that they implement the loss and its gradient. Again, in praxis, it is advisable to work with the mean nll instead of the sum, as this simplifies setting the learning rate.\n",
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"\n",
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"Hint: The optimizer works with vectors only. So the function get the weights as vectors in the flat_weights parameter. Make sure you use efficient vectorized computations (no for-loops!). Thus, we reshape the weights appropriately before using them for the computations. For the gradients make sure to return again a vector by flattening the result."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [],
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"source": [
|
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"# objective\n",
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"def objective_cat(flat_weights: np.ndarray, features: np.ndarray, labels: np.ndarray) -> float:\n",
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" \"\"\"\n",
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" :param flat_weights: weights of the classifier (as flattened vector), shape: [feature_dim * K]\n",
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" :param features: samples to evaluate objective on, shape: [N x feature_dim]\n",
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" :param labels: labels corresponding to samples, shape: [N x K]\n",
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" :return cross entropy loss of the classifier given the samples \n",
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" \"\"\"\n",
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" num_features = features.shape[-1]\n",
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" num_classes = labels.shape[-1]\n",
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" weights = np.reshape(flat_weights, [num_features, num_classes])\n",
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"\n",
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" prediction = softmax(features @ weights)\n",
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" return np.mean(categorical_nll(prediction, labels))\n",
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"\n",
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"\n",
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"def d_objective_cat(flat_weights: np.ndarray, features: np.ndarray, labels: np.ndarray) -> np.ndarray:\n",
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" \"\"\"\n",
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" :param flat_weights: weights of the classifier (as flattened vector), shape: [feature_dim * K]\n",
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" :param features: samples to evaluate objective on, shape: [N x feature_dim]\n",
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" :param labels: labels corresponding to samples, shape: [N x K]\n",
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" :return gradient of cross entropy loss of the classifier given the samples, shape: [feature_dim * K]\n",
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" \"\"\"\n",
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" feature_dim = features.shape[-1] #(5)\n",
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" num_classes = labels.shape[-1] #(3)\n",
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" weights = np.reshape(flat_weights, [feature_dim, num_classes])\n",
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"\n",
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" diff = softmax(features @ weights) - labels\n",
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" grad = features.T @ diff / diff.shape[0]\n",
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" return grad.flatten() #grad shape (15,)"
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]
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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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"Finally, we can tie everything together again. Both train and test accuracy should be at least 0.9:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"scrolled": true
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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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"Final Loss: 0.35996997155270793\n",
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"Train Accuracy: 0.9583333333333334 Test Accuracy: 1.0\n"
|
|
]
|
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},
|
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# optimization\n",
|
|
"\n",
|
|
"w0_flat = np.zeros(5 * 3) # 4 features + bias, 3 classes\n",
|
|
"w_opt_flat, loss_opt, x_history, f_x_history = \\\n",
|
|
" minimize(lambda w: objective_cat(w, train_features, oh_train_labels),\n",
|
|
" lambda w: d_objective_cat(w, train_features, oh_train_labels),\n",
|
|
" w0_flat, 1e-2, 1000)\n",
|
|
"\n",
|
|
"w_opt = np.reshape(w_opt_flat, [5, 3])\n",
|
|
"\n",
|
|
"# plotting and evaluation\n",
|
|
"print(\"Final Loss:\", loss_opt)\n",
|
|
"plt.figure()\n",
|
|
"plt.plot(f_x_history)\n",
|
|
"plt.xlabel(\"iteration\")\n",
|
|
"plt.ylabel(\"negative categorical log-likelihood\")\n",
|
|
"\n",
|
|
"train_pred = softmax(train_features @ w_opt)\n",
|
|
"train_acc = np.count_nonzero(\n",
|
|
" np.argmax(train_pred, axis=-1) == np.argmax(oh_train_labels, axis=-1))\n",
|
|
"train_acc /= train_labels.shape[0]\n",
|
|
"test_pred = softmax(test_features @ w_opt)\n",
|
|
"test_acc = np.count_nonzero(\n",
|
|
" np.argmax(test_pred, axis=-1) == np.argmax(oh_test_labels, axis=-1))\n",
|
|
"test_acc /= test_labels.shape[0]\n",
|
|
"print(\"Train Accuracy:\", train_acc, \"Test Accuracy:\", test_acc)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## 2.) k-NN (3 Points)\n",
|
|
"Here we implement a simple k-NN approach. As we want to use it for classification now and later for regression, we choose a modular approach. Firstly we implement a function that returns the $k$ nearest neighbour points' x-values and (target) y-values, given a querry point. Then we implement a function to do a majority vote for classification, given the (target) y-values of the k nearest points. Note that we use the \"real\" labels, not the one-hot encoding for the k-NN classifier.\n",
|
|
"\n",
|
|
"Work flow and hints (get_k_nearest):\n",
|
|
"- Compute the distance (e.g. Euclidean) between the query point to all data points.\n",
|
|
"- Sort the data points according to their distance to the query point. Sort indices can be more efficient.\n",
|
|
"- Get the K nearest points, return their x and y values."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def get_k_nearest(k: int, query_point: np.ndarray, x_data: np.ndarray, y_data: np.ndarray) \\\n",
|
|
" -> Tuple[np.ndarray, np.ndarray]:\n",
|
|
" \"\"\"\n",
|
|
" :param k: number of nearest neigbours to return \n",
|
|
" :param query_point: point to evaluate, shape [dimension]\n",
|
|
" :param x_data: x values of the data [N x input_dimension]\n",
|
|
" :param y_data: y values of the data [N x target_dimension]\n",
|
|
" :return k-nearest x values [k x input_dimension], k-nearest y values [k x target_dimension]\n",
|
|
" \"\"\"\n",
|
|
"\n",
|
|
" distances = []\n",
|
|
" for i in range(x_data.shape[0]):\n",
|
|
" distances.append(np.linalg.norm(x_data[i]-query_point))\n",
|
|
" \n",
|
|
" data = np.column_stack((x_data,y_data,distances))\n",
|
|
" data = data[data[:,-1].argsort()]\n",
|
|
" nearest_x = data[0:k,0:-2]\n",
|
|
" nearest_y = data[0:k,-2].astype(int)\n",
|
|
" return nearest_x, nearest_y\n",
|
|
"\n",
|
|
"def majority_vote(y: np.ndarray) -> int:\n",
|
|
" \"\"\"\n",
|
|
" :param y: k nearest targets [K]\n",
|
|
" :return the number x which occours most often in y. \n",
|
|
" \"\"\"\n",
|
|
" return np.bincount(y).argmax()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"We run the classifier and measure the accuracy. For $k=5$ it should be $1.0$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Accuracy: 1.0\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"k = 5\n",
|
|
"predictions = np.zeros(test_features.shape[0])\n",
|
|
"for i in range(test_features.shape[0]):\n",
|
|
" _, nearest_y = get_k_nearest(\n",
|
|
" k, test_features[i], train_features, train_labels)\n",
|
|
" predictions[i] = majority_vote(nearest_y)\n",
|
|
"\n",
|
|
"print(\"Accuracy: \", np.count_nonzero(\n",
|
|
" predictions == test_labels) / test_labels.shape[0])\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## 3.) Hold-out and Cross Validation\n",
|
|
"In this part of the exercise we will have a closer look on the hold-out and cross validation methods for model selection. We will apply these methods to do model selection for different regression algorithms below.\n",
|
|
"\n",
|
|
"Let's first have a look at the data. Note that the data is given as a tensor of shape [20 x 50 x 1], corresponding to 20 different data sets (drawn from the same ground truth function) with 50 data points each. The data is 1-dimensional. \n",
|
|
"\n",
|
|
"**Note:** \n",
|
|
"In practice we typically have only one dataset available. We evaluate hold-out and cross validation for 20 different datasets here only to get a feeling for the robustness of these methods."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 9,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<matplotlib.legend.Legend at 0x7fe573439ac0>"
|
|
]
|
|
},
|
|
"execution_count": 9,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import matplotlib.pyplot as plt\n",
|
|
"import numpy as np\n",
|
|
"%matplotlib inline\n",
|
|
"\n",
|
|
"\n",
|
|
"np.random.seed(33)\n",
|
|
"\n",
|
|
"# Load 20 training sets with 50 samples in each set\n",
|
|
"x_samples = np.load('x_samples.npy') # shape: [20, 50, 1]\n",
|
|
"y_samples = np.load('y_samples.npy') # shape: [20, 50, 1]\n",
|
|
"\n",
|
|
"# Load the ground truth data\n",
|
|
"x_plt = np.load('x_plt.npy')\n",
|
|
"y_plt = np.load('y_plt.npy')\n",
|
|
"\n",
|
|
"# Plot the data (for the training data we just use the first training set)\n",
|
|
"plt.plot(x_plt, y_plt, c=\"blue\", label=\"Ground truth polynomial\")\n",
|
|
"plt.scatter(x_samples[0, :, :], y_samples[0, :, :],\n",
|
|
" c=\"orange\", label=\"Samples of first training set\")\n",
|
|
"plt.legend()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Utility Functions for Plotting\n",
|
|
"Before we start, we define some helper functions which we will make use of later on. You do not need to implement anything yourself here."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def plot(mse_val: np.ndarray, mse_train: np.ndarray, x_axis, m_star_idx: int, x_plt: np.ndarray, y_plt: np.ndarray,\n",
|
|
" x_samples: np.ndarray, y_samples: np.ndarray, model_best, model_predict_func: callable):\n",
|
|
" plt.figure(figsize=(20, 5))\n",
|
|
" plt.subplot(121)\n",
|
|
" plot_error_curves(mse_val, mse_train, x_axis, m_star_idx)\n",
|
|
" plt.subplot(122)\n",
|
|
" plot_best_model(x_plt, y_plt, x_samples, y_samples,\n",
|
|
" model_best, model_predict_func)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 11,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def plot_error_curves(MSE_val: np.ndarray, MSE_train: np.ndarray, x_axis, m_star_idx: int):\n",
|
|
" plt.yscale('log')\n",
|
|
" plt.plot(x_axis, np.mean(MSE_val, axis=0), color='blue',\n",
|
|
" alpha=1, label=\"mean MSE validation\")\n",
|
|
" plt.plot(x_axis, np.mean(MSE_train, axis=0),\n",
|
|
" color='orange', alpha=1, label=\"mean MSE train\")\n",
|
|
" plt.plot(x_axis[m_star_idx], np.min(\n",
|
|
" np.mean(MSE_val, axis=0)), \"x\", label='best model')\n",
|
|
" plt.xticks(x_axis)\n",
|
|
" plt.xlabel(\"Model complexity\")\n",
|
|
" plt.ylabel(\"MSE\")\n",
|
|
" plt.legend()\n",
|
|
"\n",
|
|
"\n",
|
|
"def plot_best_model(x_plt: np.ndarray, y_plt: np.ndarray, x_samples: np.ndarray, y_samples: np.ndarray,\n",
|
|
" model_best, model_predict_func: callable):\n",
|
|
" plt.plot(x_plt, y_plt, color='g', label=\"Ground truth\")\n",
|
|
" plt.scatter(x_samples, y_samples, label=\"Noisy data\", color=\"orange\")\n",
|
|
" f_hat = model_predict_func(model_best, x_plt)\n",
|
|
" plt.plot(x_plt, f_hat, label=\"Best model\")\n",
|
|
" plt.xlabel('x')\n",
|
|
" plt.ylabel('y')\n",
|
|
" plt.legend()\n",
|
|
"\n",
|
|
"\n",
|
|
"def plot_bars(M, std_mse_val_ho, std_mse_val_cv):\n",
|
|
" models = np.arange(1, M+1)\n",
|
|
" fig = plt.figure()\n",
|
|
" ax1 = fig.add_subplot(111)\n",
|
|
" ax1.bar(models, std_mse_val_ho, yerr=np.zeros(std_mse_val_ho.shape), align='center', alpha=0.5, ecolor='black',\n",
|
|
" color='red', capsize=None)\n",
|
|
" ax1.bar(models, std_mse_val_cv, yerr=np.zeros(std_mse_val_cv.shape), align='center', alpha=0.5, ecolor='black',\n",
|
|
" color='blue', capsize=None)\n",
|
|
" ax1.set_xticks(models)\n",
|
|
" ax1.set_xlabel('Model complexity')\n",
|
|
" ax1.set_ylabel('Standard deviation')\n",
|
|
" ax1.set_yscale('log')\n",
|
|
" ax1.set_xticklabels(models)\n",
|
|
" ax1.set_title('Standard Deviations of MSEs')\n",
|
|
" ax1.yaxis.grid(True)\n",
|
|
" plt.legend(['HO', 'CV'])\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### 3.1) Hold-Out Method (4 Points)\n",
|
|
"We will implement the hold-out method for model selection in this section. First, we require a function to split a dataset into a training set and a validation set. Please fill in the missing code snippets. Make sure that you follow the instructions written in the comments."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def split_data(data_in: np.ndarray, data_out: np.ndarray, split_coeff: float) -> Tuple[dict, dict]:\n",
|
|
" \"\"\"\n",
|
|
" Splits the data into a training data set and a validation data set. \n",
|
|
" :param data_in: The input data which we want to split, shape: [n_data x indim_data] \n",
|
|
" :param data_out: The output data which we want to split, shape: [n_data x outdim_data]\n",
|
|
" Note: each pair of data points with index i in data_in and data_out is considered as a \n",
|
|
" training/validation sample: (x_i, y_i)\n",
|
|
" :param split_coeff: A value between [0, 1], which determines the index to split data into test and validation set\n",
|
|
" according to: split_idx = int(n_data*split_coeff)\n",
|
|
" :return: A tuple of 2 dictionaries: the first element in the tuple is the training data set dictionary\n",
|
|
" containing the input data marked with key 'x' and the output data marked with key 'y'.\n",
|
|
" The second element in the tuple is the validation data set dictionary containing the input data \n",
|
|
" marked with key 'x' and the output data marked with key 'y'.\n",
|
|
" \"\"\"\n",
|
|
" n_data = data_in.shape[0]\n",
|
|
" # We use a dictionary to store the training and validation data.\n",
|
|
" # Please use 'x' as a key for the input data and 'y' as a key for the output data in the dictionaries\n",
|
|
" # for the training data and validation data.\n",
|
|
"\n",
|
|
" split_idx = int(n_data*split_coeff)\n",
|
|
"\n",
|
|
" train_data = {}\n",
|
|
" val_data = {}\n",
|
|
"\n",
|
|
" train_split_x = data_in[0: split_idx, :]\n",
|
|
" train_split_y = data_out[0: split_idx, :]\n",
|
|
"\n",
|
|
" test_split_x = data_in[split_idx : , :]\n",
|
|
" test_split_y = data_in[split_idx: , :]\n",
|
|
"\n",
|
|
" train_data['x'] = train_split_x\n",
|
|
" train_data['y'] = train_split_y\n",
|
|
"\n",
|
|
" val_data['x'] = test_split_x\n",
|
|
" val_data['y'] = test_split_y\n",
|
|
"\n",
|
|
" return train_data, val_data\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"This function implements the hold-out method. We split the dataset into a training and a validation data set (using the split_data function you have implemented above). Then, we train a model for a range of complexity values on the training set and choose the model complexity with the best MSE on the validation set. \n",
|
|
"\n",
|
|
"The function expects a callable `fit_func` and a callable `predict_func`. We will pass different functions to this argument depending on the regression algorithm we consider. The `fit_func` function returns model parameters obtained by training a given model with a given complexity on a given training data set. The `predict_func` function computes predictions using a given model with a given complexity. For more information, have a look at the comments.\n",
|
|
"\n",
|
|
"As noted above, we do hold-out for 20 different datasets to get a feeling for the robustness of this method. To this end, we compute the standard deviation of the resulting MSEs over the 20 datasets.\n",
|
|
"\n",
|
|
"You do not need to implement anything here."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def eval_hold_out(M: int, split_coeff: float, fit_func: callable, predict_func: callable) -> float:\n",
|
|
" \"\"\"\n",
|
|
" :param M: Determines the range of model complexity parameters. \n",
|
|
" We perform the hold_out method for model complexities (1, ..., M).\n",
|
|
" :param split_coeff: A value between [0, 1] determines the index to split data (cf. split_data function).\n",
|
|
" :param fit_func: Callable which fits the model: \n",
|
|
" (x_train: np.ndarray, y_train: np.ndarray, complexity_parameter: int) -> model_parameters: np.ndarray\n",
|
|
" :param predict_func: Callable which computes predictions with the model: \n",
|
|
" (model_parameters: np.ndarray, x_val: np.ndarray) -> y_pred_val: np.ndarray\n",
|
|
" \"\"\"\n",
|
|
" n_datasets = 20\n",
|
|
" mse_train_ho = np.zeros((n_datasets, M))\n",
|
|
" mse_val_ho = np.zeros((n_datasets, M))\n",
|
|
"\n",
|
|
" for d in range(n_datasets):\n",
|
|
" # Extract current data set and split it into train and validation data\n",
|
|
" c_x_samples = x_samples[d, :, :]\n",
|
|
" c_y_samples = y_samples[d, :, :]\n",
|
|
" train_data, val_data = split_data(\n",
|
|
" c_x_samples, c_y_samples, split_coeff)\n",
|
|
"\n",
|
|
" for m in range(M):\n",
|
|
" # Train model with complexity m on training set\n",
|
|
" p = fit_func(train_data['x'], train_data['y'], m + 1)\n",
|
|
"\n",
|
|
" # Compute MSE on validation set\n",
|
|
" y_pred_val = predict_func(p, val_data['x'])\n",
|
|
" mse_val_ho[d, m] = np.mean((y_pred_val - val_data['y'])**2)\n",
|
|
"\n",
|
|
" # For comparison, compute the MSE of the trained model on current training set\n",
|
|
" y_pred_train = predict_func(p, train_data['x'])\n",
|
|
" mse_train_ho[d, m] = np.mean((y_pred_train - train_data['y'])**2)\n",
|
|
"\n",
|
|
" # Compute mean and std-deviation of MSE over all datasets\n",
|
|
" mean_mse_train_ho = np.mean(mse_train_ho, axis=0)\n",
|
|
" mean_mse_val_ho = np.mean(mse_val_ho, axis=0)\n",
|
|
" std_mse_train_ho = np.std(mse_train_ho, axis=0)\n",
|
|
" std_mse_val_ho = np.std(mse_val_ho, axis=0)\n",
|
|
"\n",
|
|
" # Pick model with best mean validation loss\n",
|
|
" m_star_ho = np.argmin(mean_mse_val_ho)\n",
|
|
" print(\"Best model complexity determined with hold-out method: {}\".format(m_star_ho + 1))\n",
|
|
"\n",
|
|
" # Plot predictions with best model (use only the first data set for better readability)\n",
|
|
" train_data, val_data = split_data(\n",
|
|
" x_samples[0, :, :], y_samples[0, :, :], split_coeff)\n",
|
|
" p_best_ho = fit_func(train_data['x'], train_data['y'], m_star_ho + 1)\n",
|
|
" plot(mse_val_ho, mse_train_ho, np.arange(1, M+1), m_star_ho, x_plt, y_plt,\n",
|
|
" x_samples[0, :, :], y_samples[0, :, :], p_best_ho, predict_func)\n",
|
|
"\n",
|
|
" return std_mse_val_ho\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### 3.2) k-Fold-Cross Validation Method (4 Points)\n",
|
|
"We will now implement the $k$-fold cross validation method for model selection in this section. In contrast to the hold-out method, we do not use a single split of a given dataset into a training and validation sets, but rather $k$ different splits. Refer to the lecture slide 21 for our convention on how to define the $i$-th split.\n",
|
|
"\n",
|
|
"Please fill in the missing code snippets. Make sure that you follow the instructions written in the comments. You can refer to the `eval_hold_out`-function above for inspiration (note that for clarity we split the logic into two separate functions `k_fold_cross_validation` and `eval_k_fold_cross_validation` here)."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def k_fold_cross_validation(data_in: np.ndarray, data_out: np.ndarray, m: int, k: int, fit_func: callable,\n",
|
|
" predict_func: callable) -> Tuple[np.ndarray, np.ndarray]:\n",
|
|
" \"\"\"\n",
|
|
" Perform k-fold cross validation for a model with complexity m on data (data_in, data_out). \n",
|
|
" Return the mean squared error incurred on the training and the validation data sets.\n",
|
|
" :param data_in: The input data, shape: [N x indim_data] \n",
|
|
" :param data_out: The output data, shape: [N x outdim_data]\n",
|
|
" :param m: Model complexity parameter. \n",
|
|
" :param k: Number of partitions of the data set (not to be confused with k in kNN).\n",
|
|
" :param fit_func: Callable which fits the model: \n",
|
|
" (x_train: np.ndarray, y_train: np.ndarray, complexity_parameter: int) -> model_parameters: np.ndarray\n",
|
|
" :param predict_func: Callable which computes predictions with the model: \n",
|
|
" (model_parameters: np.ndarray, x_val: np.ndarray) -> y_pred_val: np.ndarray\n",
|
|
" :return mse_train: np.ndarray containg the mean squarred errors incurred on the training set for each split k, shape: [k]\n",
|
|
" :return mse_val: np.ndarray containing the mean squarred errors incurred on the validation set for each split, shape: [k]\n",
|
|
" \"\"\"\n",
|
|
"\n",
|
|
" # Check consistency of inputs and prepare some constants\n",
|
|
" n_data = data_in.shape[0] # total number of datapoints\n",
|
|
" assert k <= n_data # number of partitions has to be smaller than number of data points\n",
|
|
" # we assume that we can split the data into k equally sized partitions here\n",
|
|
" assert n_data % k == 0\n",
|
|
" n_val_data = n_data // k # number of datapoints in each validation set\n",
|
|
"\n",
|
|
" # Prepare return values\n",
|
|
" mse_train = np.zeros(k)\n",
|
|
" mse_val = np.zeros(k)\n",
|
|
"\n",
|
|
" for i in range(k):\n",
|
|
" # 1: Prepare i-th partition into training and validation data sets (cf. lecture slide 21)\n",
|
|
" i_training_split = data_in[i * n_val_data: (i+1)*n_val_data, :]\n",
|
|
" i_validation_split = data_out[i * n_val_data: (i+1)*n_val_data, :]\n",
|
|
"\n",
|
|
" # 2: Fit model on training set\n",
|
|
"\n",
|
|
" p = fit_func(i_training_split, i_validation_split, m)\n",
|
|
"\n",
|
|
"\n",
|
|
" # 3: Compute predictions on training set and validation set\n",
|
|
"\n",
|
|
" y_pred_train = predict_func(p, i_training_split)\n",
|
|
" y_pred_val = predict_func(p, i_validation_split)\n",
|
|
"\n",
|
|
" # 4: Compute the mean squarred error for the training and validation sets\n",
|
|
" # TODO\n",
|
|
"\n",
|
|
" mse_val[i] = np.mean((y_pred_val - data_out[i * n_val_data: (i+1)*n_val_data, :])**2)\n",
|
|
" mse_train[i] = np.mean((y_pred_train - data_in[i * n_val_data: (i+1)*n_val_data, :])**2)\n",
|
|
"\n",
|
|
" return mse_train, mse_val\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"This function will uses the functions you have implemented to evaluate the robustness of the k-fold cross validation method. Similar to the `eval_held_out` function above, it will perform cross validation on the 20 different data sets we have loaded at the beginning and return the standard deviation of the mean squarred errors over the 20 data sets of each different model it is tested on."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def eval_k_fold_cross_validation(M: int, k: int, fit_func: callable, predict_func: callable) -> float:\n",
|
|
" \"\"\"\n",
|
|
" :param M: Determines the range of model complexity parameters. \n",
|
|
" We perform the cross-validation method for model complexities (1, ..., M).\n",
|
|
" :param k: Number of partitions of the data set (not to be confused with k in kNN).\n",
|
|
" :param fit_func: Callable which fits the model: \n",
|
|
" (x_train: np.ndarray, y_train: np.ndarray, complexity_parameter: int) -> model_parameters: np.ndarray\n",
|
|
" :param predict_func: Callable which computes predictions with the model: \n",
|
|
" (model_parameters: np.ndarray, x_val: np.ndarray) -> y_pred_val: np.ndarray \n",
|
|
" \"\"\"\n",
|
|
" n_datasets = 20\n",
|
|
" mse_train_cv = np.zeros((n_datasets, M))\n",
|
|
" mse_val_cv = np.zeros((n_datasets, M))\n",
|
|
"\n",
|
|
" for d in range(n_datasets):\n",
|
|
" # Extract current data set and split it into train and validation data\n",
|
|
" c_x_samples = x_samples[d, :, :]\n",
|
|
" c_y_samples = y_samples[d, :, :]\n",
|
|
"\n",
|
|
" for m in range(M):\n",
|
|
" mse_train_k_cv, mse_val_k_cv = k_fold_cross_validation(\n",
|
|
" c_x_samples, c_y_samples, m + 1, k, fit_func, predict_func)\n",
|
|
" # Average MSEs over splits\n",
|
|
" mse_train_cv[d, m] = np.mean(mse_train_k_cv)\n",
|
|
" mse_val_cv[d, m] = np.mean(mse_val_k_cv)\n",
|
|
"\n",
|
|
" # Compute mean and std-deviation of MSE over all datasets\n",
|
|
" mean_mse_train_cv = np.mean(mse_train_cv, axis=0)\n",
|
|
" mean_mse_val_cv = np.mean(mse_val_cv, axis=0)\n",
|
|
" std_mse_train_cv = np.std(mse_train_cv, axis=0)\n",
|
|
" std_mse_val_cv = np.std(mse_val_cv, axis=0)\n",
|
|
"\n",
|
|
" # Pick model with best mean validation loss\n",
|
|
" m_star_cv = np.argmin(mean_mse_val_cv)\n",
|
|
" print(\"Best model complexity determined with cross-validation method: {}\".format(m_star_cv + 1))\n",
|
|
"\n",
|
|
" # Plot predictions with best model (use only the first data set for better readability)\n",
|
|
" train_data, val_data = split_data(\n",
|
|
" x_samples[0, :, :], y_samples[0, :, :], split_coeff)\n",
|
|
" p_best_cv = fit_func(train_data['x'], train_data['y'], m_star_cv + 1)\n",
|
|
" plot(mse_val_cv, mse_train_cv, np.arange(1, M+1), m_star_cv, x_plt, y_plt,\n",
|
|
" x_samples[0, :, :], y_samples[0, :, :], p_best_cv, predict_func)\n",
|
|
"\n",
|
|
" return std_mse_val_cv\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### 3.3) kNN Regression\n",
|
|
"We will now apply hold-out and k-fold cross validation on the regression problem using kNN Regression. In the following we provide a fit and an evaluate function for kNN, which we will use as the callables `fit_func` and `eval_func` for hold-out and cross validation."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 16,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def fit_knn_regressor(train_in: np.ndarray, train_out: np.ndarray, k: int) -> dict:\n",
|
|
" \"\"\"\n",
|
|
" Fit a k-nearest neighbors model to the data. This function just returns a compact representation of the input data\n",
|
|
" data provided, i.e. it stores the training in- and output data together with the number of k neighbors in a dictionary.\n",
|
|
" :param train_in: The training input data, shape: [N x input dim]\n",
|
|
" :param train_out: The training output data, shape: [N x output dim]\n",
|
|
" :param k: The parameter determining how many nearest neighbors to consider\n",
|
|
" :return: A dictionary containing the training data and the parameter k for k-nearest-neighbors.\n",
|
|
" Key 'x': the training input data, shape: [N x input dim]\n",
|
|
" Key 'y': the training output data, shape: [N x output dimension]\n",
|
|
" Key 'k': the parameter determining how many nearest neighbors to consider\n",
|
|
" \"\"\"\n",
|
|
"\n",
|
|
" model = {'x': train_in, 'y': train_out, 'k': k}\n",
|
|
" return model\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 17,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def predict_knn_regressor(model, data_in: np.ndarray) -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" This function will perform predictions using a k-nearest-neighbor regression model given the input data. \n",
|
|
" Note that knn is a lazy model and requires to store all the training data (see dictionary 'model').\n",
|
|
" :param model: A dictionary containing the training data and the parameter k for k-nearest-neighbors.\n",
|
|
" Key 'x': the training input data, shape: [N x input dim]\n",
|
|
" Key 'y': the training output data, shape: [N x output dimension]\n",
|
|
" Key 'k': the parameter determining how many nearest neighbors to consider\n",
|
|
" :param data_in: The data we want to perform predictions on, shape: [N x input dimension]\n",
|
|
" :return prediction based on k nearest neighbors (mean of the k - neares neighbors) (shape[N x output dimension])\n",
|
|
" \"\"\"\n",
|
|
" # Prepare data\n",
|
|
" if len(data_in.shape) == 1:\n",
|
|
" data_in = np.reshape(data_in, (-1, 1))\n",
|
|
" train_data_in = model['x']\n",
|
|
" train_data_out = model['y']\n",
|
|
" k = model['k']\n",
|
|
" if len(train_data_in.shape) == 1:\n",
|
|
" train_data_in = np.reshape(train_data_in, (-1, 1))\n",
|
|
"\n",
|
|
" # Perform predictions\n",
|
|
" predictions = np.zeros((data_in.shape[0], train_data_out.shape[1]))\n",
|
|
" for i in range(data_in.shape[0]):\n",
|
|
" _, nearest_y = get_k_nearest(\n",
|
|
" k, data_in[i, :], train_data_in, train_data_out)\n",
|
|
" # we take the mean of the nearest samples to perform predictions\n",
|
|
" predictions[i, :] = np.mean(nearest_y, axis=0)\n",
|
|
"\n",
|
|
" return predictions\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### 3.3.1) Apply Hold-Out and Cross-Validation to kNN Regression "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"We now apply $k$-nearest neighbor regression on our data set and use the hold-out and cross-validation methods to determine the complexity parameter of this model, i.e., the number $k$ of nearest neighbors to consider.\n",
|
|
"As described above, we furthermore plot and compare the standard deviations of the mean squared errors for each model based on the 20 data sets to get a feeling of the robustness of hold-out and cross validation."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"M_knn = 20 # Maximum number k of nearest neighbors\n",
|
|
"split_coeff = 0.8 # Split coefficient for the hold-out method\n",
|
|
"k = 10 # Number of splits for the cross validation method\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Best model complexity determined with hold-out method: 20\n",
|
|
"Best model complexity determined with cross-validation method: 2\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
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"text/plain": [
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"<Figure size 1440x360 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
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"data": {
|
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 1440x360 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
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"data": {
|
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Evaluate hold-out method\n",
|
|
"std_mse_val_ho_knn = eval_hold_out(M=M_knn, split_coeff=split_coeff, fit_func=fit_knn_regressor,\n",
|
|
" predict_func=predict_knn_regressor)\n",
|
|
"\n",
|
|
"# Evaluate cross validation method\n",
|
|
"std_mse_val_cv_knn = eval_k_fold_cross_validation(M=M_knn, k=k, fit_func=fit_knn_regressor,\n",
|
|
" predict_func=predict_knn_regressor)\n",
|
|
"\n",
|
|
"\n",
|
|
"# Plot the standard deviations\n",
|
|
"plot_bars(M_knn, std_mse_val_ho_knn, std_mse_val_cv_knn)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The first two rows in the cell above show the errorplots and the best model's prediction for hold out (first row) and cross validation (second row), respectively. The last row shows the standard deviation of the mean squarred error over the 20 different data sets incurred by each model."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### 3.4) Forests\n",
|
|
"We will now apply hold-out and $k$-fold-cross validation on regression with forests. As for k-nearest neighbor regression above, we provide a fit and an evaluate function for forests. Note that we have two different functions for fitting a forest model. In `fit_forest_fixed_n_trees` we investigate the behavior of the algorithm when fixing the number of trees to $1$ and varying the number of samples per leaf. In `fit_forest_fixed_n_samples_leaf` we fix the number of samples per leaf to $1$ and investigate the behavior of the algorithm when varying the number of trees. The evaluation function can be used for both models."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def fit_forest_fixed_n_trees(train_in: np.ndarray, train_out: np.ndarray, min_samples_leaf: int):\n",
|
|
" \"\"\"\n",
|
|
" This function will fit a forest model based on a fixed number of trees (can not be change when using this \n",
|
|
" function, is set globally)\n",
|
|
" :param train_in: the training input data, shape [N x input dim]\n",
|
|
" :param train_out: the training output data, shape [N x output dim]\n",
|
|
" :param min_samples_leaf: the number of samples per leaf to be used \n",
|
|
" \"\"\"\n",
|
|
" model = RandomForestRegressor(\n",
|
|
" n_estimators=1, min_samples_leaf=min_samples_leaf)\n",
|
|
" model.fit(train_in, train_out)\n",
|
|
" return model\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def fit_forest_fixed_n_samples_leaf(train_in: np.ndarray, train_out: np.ndarray, n_trees: int):\n",
|
|
" \"\"\"\n",
|
|
" This function will fit a forest model based on a fixed number of sample per leaf (can not be change when \n",
|
|
" using this function, is set globally)\n",
|
|
" :param train_in: the training input data, shape [N x input dim]\n",
|
|
" :param train_out: the training output data, shape [N x output dim]\n",
|
|
" :param n_trees: the number of trees in the forest \n",
|
|
" \"\"\"\n",
|
|
" model = RandomForestRegressor(n_estimators=n_trees, min_samples_leaf=1)\n",
|
|
" model.fit(train_in, train_out)\n",
|
|
" return model\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 22,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def predict_forest(model, data_in: np.ndarray) -> np.ndarray:\n",
|
|
" \"\"\"\n",
|
|
" This function will perform predictions using a forest regression model on the input data. \n",
|
|
" :param model: the forest model from scikit learn (fitted before)\n",
|
|
" :param data_in: :param data_in: the data we want to perform predictions (shape [N x input dimension])\n",
|
|
" :return prediction based on chosen minimum samples per leaf (shape[N x output dimension]\n",
|
|
" \"\"\"\n",
|
|
" y = model.predict(data_in)\n",
|
|
" if len(y.shape) == 1:\n",
|
|
" y = y.reshape((-1, 1))\n",
|
|
" return y\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### 3.4.1) Apply Hold-out and Cross-validation to Forests (Fixed Number of Trees)\n",
|
|
"\n",
|
|
"We apply forest regression with a fixed number of trees of $1$ and use hold-out and cross-validation to determine the complexity parameter of this model, i.e., the number of samples per leaf. As described above, we furthermore plot and compare the standard deviations of the mean squared errors for each model based on the 20 data sets to get a feeling of the robustness of hold-out and cross validation."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 23,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"M_n_samples_leaf = 10 # Maximum number of samples per leaf\n",
|
|
"split_coeff = 0.8 # Split coefficient for the hold-out method\n",
|
|
"k = 10 # Number of splits for the cross validation method\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 24,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Best model complexity determined with hold-out method: 9\n",
|
|
"Best model complexity determined with cross-validation method: 1\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 1440x360 with 2 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
|
|
"data": {
|
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"image/png": 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",
|
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"text/plain": [
|
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"<Figure size 1440x360 with 2 Axes>"
|
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]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Hold-out method\n",
|
|
"std_mse_val_ho_forest_fixed_n_trees = eval_hold_out(M=M_n_samples_leaf, split_coeff=split_coeff,\n",
|
|
" fit_func=fit_forest_fixed_n_trees,\n",
|
|
" predict_func=predict_forest)\n",
|
|
"# Cross validation method\n",
|
|
"std_mse_val_cv_forest_fixed_n_trees = eval_k_fold_cross_validation(M=M_n_samples_leaf, k=k, fit_func=fit_forest_fixed_n_trees,\n",
|
|
" predict_func=predict_forest)\n",
|
|
"\n",
|
|
"# Plot the standard deviations\n",
|
|
"plot_bars(M_n_samples_leaf, std_mse_val_ho_forest_fixed_n_trees,\n",
|
|
" std_mse_val_cv_forest_fixed_n_trees)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The first two rows in the cell above show the errorplots and the best model's prediction for hold out (first row) and cross validation (second row), respectively. The last row shows the standard deviation of the mean squarred error over the 20 different data sets incurred by each model."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### 3.4.2) Apply Hold-out and Cross-validation to Forests (Fixed Number of Samples per Leaf) \n",
|
|
"We apply forest regression with a fixed number of samples per leaf of $1$ and use hold-out and cross-validation to determine the complexity parameter of this model, i.e., the number of trees. As described above, we furthermore plot and compare the standard deviations of the mean squared errors for each model based on the 20 data sets to get a feeling of the robustness of hold-out and cross validation."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"M_n_trees = 20 # Maximum number of trees\n",
|
|
"split_coeff = 0.8 # Split coefficient for the hold-out method\n",
|
|
"k = 10 # Number of splits for the cross validation method\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 26,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Best model complexity determined with hold-out method: 15\n",
|
|
"Best model complexity determined with cross-validation method: 18\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
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"text/plain": [
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"<Figure size 1440x360 with 2 Axes>"
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]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
},
|
|
{
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"data": {
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"image/png": 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",
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"text/plain": [
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"<Figure size 1440x360 with 2 Axes>"
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]
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},
|
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"metadata": {
|
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"needs_background": "light"
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|
},
|
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"output_type": "display_data"
|
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},
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{
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"data": {
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"image/png": 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fCZwEHF+o5MkCYLOa96PzMjMz6yNFaiwHAVtGxGtldhwRT0p6XNKWEfEAsBcpOL1J0vbAdNIVX48AF0v6VkR8vWA2dwBvz81pC4DJwMfLlNPMzKpVJLA8DAwGSgWW7ARSsFgj76dj89TawEcj4iEASYeTO/trSboEmASMktQGnBQRP4mIpZKOB35Dutz4/IiY141yWhluOzezBooEln8AcyT9jprgEhGf7yphRMwBJjZY/8cO75cA59bZbkqDffwK+FVXZTEzs95RJLBcnR9mZmZd6jKwRMSM3JT1jrzogVyzMDOzVcUqNDNskavCJgEzgEcBAZtJOqLA5cZmZjYAFWkK+z7wwXxlF5LeAVwC7NjMgpmZWWsqMh/L4PagAhARfyFdJWZmZraSIjWWOyWdB1yU3x8G3Nm8IpmZDVD95FL+IoHlWOBzQPvlxTeT5joxMzNbSZGrwl4DTs8PMzOzhjoNLJIui4iPSrqPNDbYCiJi26aWzMysL6xCl+22qkY1lhPz8369URAzM+sfOr0qLCL+nl8eFxGP1T6A43qneGZm1mqKXG5cb+KtfeosMzMza9jHciypZvI2SffWrBoG/LF+KjMzG+ga9bH8DPg18B1WnKDrpYh4rqmlMjOzltVpYImIRcAiYAqApA2BIcBQSUMj4m+9U0Qz6zZf4WR9oMs+Fkn7S/oraYbHP5AGo/x1k8tlZmYtqkjn/beAnYG/RMRY0hTDtza1VGZm1rKKBJYlEbEQGCRpUETcQINZIc3MbGArMlbYC5KGAjeR5q9/Gni5ucUyM7NWVaTGciDwCvAF4FrgIWD/ZhaqN+S+o+mLFi3q66KYmfUrXQaWiHg5It6IiKURMSMizshNYy0tImZFxGdGjBjR10UxM+tXGt0geUtE7CrpJVYchFJARMTwppfOzMxaTqP7WHbNz8N6rzhmZtbqitzHcoakXXqjMGZm1vqKXBU2G/g3SVsCVwIzI8JTE5tZ83jEgJZWpPN+RkTsC7wbeAA4Nd+Jb2ZmtpIilxu3Gwe8E9gcuL85xTEzs1ZXpI/ltFxD+SZwHzAxIlr+PhYzM2uOIn0sDwG7RMSzzS6MmZm1viJNYecCe0v6BoCkt0raqbnFMjOzVlUksJwN7EKelwV4KS8zMzNbSZGmsPdExA6S7gaIiOclrdHkcpmZWYsqNGy+pNXIw7pI2gBY1tRSmZlZyyoSWM4g3Ri5oaRvA7cA/9HUUpmZWcvqsiksIi6WNJs0c6SAgyJiftNLZmZmLanR6Mbr17x9Grikdl1EPNfMgpmZWWtqVGOZTepXEfBW4Pn8el3gb8DYZhfOzMxaT6d9LBExNiLeBlwP7B8RoyJiJLAfcF1vFdDMzFpLkc77nSPiV+1vIuLXwHubVyQzM2tlRe5jeULS14GL8vvDgCeaVyQzM2tlRWosU4ANSJcc/yK/ntIwhZmZDVhFLjd+DjixF8piZmb9QJn5WMzMzLrkwGJmZpVyYDEzs0o1uvP+TPLAk/VExOebUiIzM2tpjWosd5Luvh8C7AD8NT8mAKv0sPmS1pE0Q9K5kg7r6/KYmQ0kje68nxERM4BtgUkRcWZEnEkajHJC0QwkrSbpbknXdLeQks6X9LSkuXXW7S3pAUkPSpqWFx8CXBERxwAHdDdfMzMrr0gfy3rA8Jr3Q/Oyok4E6o6GLGlDScM6LBtXZ9MLgL3rpF+NNJvlPsB4YIqk8cBo4PG82RslympmZj1UJLB8F7hb0gWSZgB3UXA+FkmjgQ8B53WyyR7AVZLWzNsfA5zZcaOIuAmoN5ryTsCDEfFwRLwOzAQOBNpIwQU6OUZJ+0uavmjRoiKHYmZmBTUMLJIGAQ8A72H5nfe75CayIn4AfJlOZpyMiMuB3wCX5r6Qo4FDC+4bYFOW10wgBZRNczk/LOkcYFYnec+KiM+MGDGiRHZmZtaVhnfeR8QySWdHxPbAL8vsWNJ+wNMRMVvSpAZ5nCZpJnAOsEVELC6TTyf7fBk4qqf7MTOz8oo0hf1O0oclqeS+3wccIOlRUhPVnpIu6riRpN2ArUk1opNK5rEA2Kzm/ei8zMzM+kiRwPLPwOXAa5JelPSSpBe7ShQRX42I0RExBpgM/D4iPlG7jaTtgemkfpGjgJGSvlWi/HcAb5c0VtIaOZ+rS6Q3M7OKdRlYImJYRAyKiDUiYnh+P7yrdAWtDXw0Ih6KiGXA4cBjHTeSdAnwJ2BLSW2SPpXLthQ4ntRPMx+4LCLmVVQ2MzPrhiLzsSBpPeDtpJslgTev1CokIm4Ebqyz/I8d3i8Bzq2zXafD9OdJyH7V2XozM+tdXQYWSZ8m3YsyGpgD7EyqPezZ1JKZmVlLKlJjORF4N3BrRPyTpHdS8D4Wa+zkGyeV274ppTAzq1aRzvtXI+JVAElrRsT9wJbNLZaZmbWqIjWWNknrAlcBv5X0PHU62M3MzKDY1MQH55cnS7oBGAFc29RSmZlZy2o0H8v6dRbfl5+HUn/sLjMzG+Aa1Vhmkyb6EvBW4Pn8el3gb8DYZhfOzMxaT6P5WMZGxNuA64H9I2JURIwE9gOu660CmplZaylyVdjO+SZEACLi18B7m1ckMzNrZUWuCntC0teB9gEkDwOeaF6RzMyslRWpsUwBNiCNPnwlsGFeZmZmtpIilxs/R7r73szMrEtFxgp7B/AlYEzt9hHhscLMzGwlRfpYLgd+RJq3/o3mFsfMzFpdkcCyNCLOaXpJzMysXygSWGZJOo7Ucf9a+8Lc92J9xCMjm9mqqkhgOSI//0vNsgDeVn1xzMys1RW5KsxDt5iZWWFFpybeGhjPilMT/7RZhTIzs9ZV5HLjk4BJpMDyK2Af4BbAgcXMzFZS5M77jwB7AU9GxFHAdqQ5WczMzFZSJLC8EhHLgKWShgNPA5s1t1hmZtaqivSx3JmnJj6XNEfLYuBPzSyUmZm1riJXhR2XX/5I0rXA8Ii4t7nFMjOzVtVlU5ik37W/johHI+Le2mVmZma1Gs15PwRYGxglaT3StMQAw4FNe6FsZmbWgho1hf0zMBXYhNS30h5YXgTOam6xrJnKDgcDHhLGzIrrNLBExA+BH0o6ISLO7MUymZlZC+u0j0XSuyW9pT2oSDpc0i8lnSFp/d4ropmZtZJGnfc/Bl4HkLQ78F3S3faLgOnNL1r3SVpH0gxJ50o6rK/LY2Y2kDQKLKvVDI3/MWB6RPw8Iv4NGNfVjiUNkXS7pHskzZN0SncLKel8SU9Lmltn3d6SHpD0oKRpefEhwBURcQxwQHfzNTOz8hoGFkntfTB7Ab+vWVfkxsrXgD0jYjtgArC3pJ1rN5C0oaRhHZbVC1oXAHt3XChpNeBs0vhl44EpksYDo4HH82ae9dLMrBc1CiyXAH+Q9EvgFeBmePPEv6irHUeyOL8dnB/RYbM9gKskrZn3fQyw0oUCEXETUG9isZ2AByPi4Yh4HZgJHAi0kYJLV8doZmYVa3RV2LfzjZAbA9dFRHtQGAScUGTnuUYxm9R0dnZE3NYhj8sljQUulXQ5cDTwgRLl35TlNRNIAeU9wBnAWZI+BMzqpGz7A/uPG9dlq56ZmZXQsEkrIm6ts+wvRXceEW8AE/JYY1dK2joi5nbY5jRJM4FzgC1qajndFhEvA0d1sc0sYNbEiROP6Wl+Zma2XK80E0XEC8AN1O8n2Q3YGrgSOKnkrhew4kjLo/MyMzPrI00LLJI2yDUVJK1FauK6v8M225MuXT6QVMMYKelbJbK5A3i7pLGS1gAmA1dXUHwzM+umZtZYNgZukHQvKQD8NiKu6bDN2sBHI+KhPOfL4cBjHXck6RLSUP1bSmqT9CmAiFgKHA/8BpgPXBYR85p2RGZm1qVCc953Rx5af/sutvljh/dLSPO+dNxuSoN9/Io0ZbKZma0CfCmumZlVyoHFzMwq5cBiZmaValofi9mqpuw8NCc3pRRm/Z8Di5XmE7SZNeKmMDMzq5QDi5mZVcqBxczMKuXAYmZmlXJgMTOzSjmwmJlZpRxYzMysUg4sZmZWKQcWMzOrlAOLmZlVyoHFzMwq5cBiZmaVcmAxM7NKeXRjswLKjugMHtXZBi7XWMzMrFKusViv8lwuZv2fA4tZL3BAtYHETWFmZlYpBxYzM6uUA4uZmVXKfSxmtsrx5d2tzTUWMzOrlAOLmZlVyoHFzMwq5cBiZmaVcmAxM7NK+aowM7MKeZQFBxazfs2X7VpfcFOYmZlVyjUWM2sKNwkNXK6xmJlZpRxYzMysUm4KM7NOuTmrd/WXz9uBxcyshq+k6zk3hZmZWaVcYzFbxfWX5hEbOBxYzMz6gVWpCc+Bxcz6Hdfy+pb7WMzMrFIOLGZmVik3hVlLcROH2aqvXwYWSesA/w28DtwYERf3cZHMzAaMpjWFSdpM0g2S/ixpnqQTe7Cv8yU9LWlunXV7S3pA0oOSpuXFhwBXRMQxwAHdzdfMzMprZh/LUuCLETEe2Bn4nKTxtRtI2lDSsA7LxtXZ1wXA3h0XSloNOBvYBxgPTMl5jAYez5u90cPjMDOzEpoWWCLi7xFxV379EjAf2LTDZnsAV0laE0DSMcCZdfZ1E/BcnWx2Ah6MiIcj4nVgJnAg0EYKLtDJMUraX9L0RYsWlT42MzPrXK9cFSZpDLA9cFvt8oi4HPgNcKmkw4CjgUNL7HpTltdMIAWUTYFfAB+WdA4wq17CiJgVEZ8ZMWJEiezMzKwrTe+8lzQU+DkwNSJe7Lg+Ik6TNBM4B9giIhb3NM+IeBk4qqf7MTOz8ppaY5E0mBRULo6IX3SyzW7A1sCVwEkls1gAbFbzfnReZmZmfaSZV4UJ+AkwPyJO72Sb7YHppH6Ro4CRkr5VIps7gLdLGitpDWAycHXPSm5mZj3RzBrL+4BPAntKmpMf+3bYZm3goxHxUEQsAw4HHuu4I0mXAH8CtpTUJulTABGxFDie1E8zH7gsIuY175DMzKwrioi+LkOfkvQMdYJZD40Cnu2j9K2at8s9cPJ2uVsr785sHhEb1F0TEX5U/ADu7Kv0rZq3yz1w8na5Wyvv7jw8CKWZmVXKgcXMzCrlwNIc0/swfavm7XIPnLxd7tbKu7QB33lvZmbVco3FzMwq5cBiZmaVcmCpUKN5Ywqk7dH8NZKGSLpd0j05/SndKMNqku6WdE030j4q6b58I+ydJdOuK+kKSfdLmi9pl4Lptqy5+XaOpBclTS2Z9xfy5zVX0iWShpRIe2JON69IvvW+H5LWl/RbSX/Nz+uVSHtoznuZpIkl8/1e/rzvlXSlpHVLpv/3nHaOpOskbVI0bc26L0oKSaNK5HuypAUNbrruMm9JJ+RjnyfptBJ5X1qT76OS5pTJW9IESbe2/49I2qlE2u0k/Sn/j82SNLyTtHXPI0W/Z5XpzWub+/sD2B3YAZjbjbQbAzvk18OAvwDjS6QXMDS/HkwaSXrnkmX4v8DPgGu6Uf5HgVHd/NxmAJ/Or9cA1u3GPlYDniTdtFU0zabAI8Ba+f1lwJEF024NzCWNHrE6cD0wruz3AzgNmJZfTwNOLZH2XcCWwI3AxJL5fhBYPb8+tbN8G6QfXvP688CPiqbNyzcjjZjxWGffm07yPRn4UsG/Ub30/5T/Vmvm9xuWKXfN+u8D3yiZ93XAPvn1vqTZbYumvQPYI78+Gvj3TtLWPY8U/Z5V9XCNpULR+bwxRdIWmb+mUfqI5SNDD86PwldmSBoNfAg4r3ChKyBpBOkf6ScAEfF6RLzQjV3tBTwUEWVHUVgdWEvS6qQg8UTBdO8CbouIf0QaWugPpJlLO9XJ9+NAUmAlPx9UNG1EzI+IB7oqaCdpr8vlBriV5fMXFU1fO1L5OnTyXWvwP/FfwJc7S9dF2kI6SX8s8N2IeC1v83TZvCUJ+ChwScm8A2ivaYygk+9aJ2nfAdyUX/8W+HAnaTs7jxT6nlXFgWUVpE7mrymQbrVcPX8a+G1ElEn/A9I/+rIyedYI4DpJsyV9pkS6scAzwP/kZrjzJK3Tjfwn0+AfvZ6IWAD8J/A34O/Aooi4rmDyucBukkZKWpv0C3SzLtLUs1FE/D2/fhLYqBv76KmjgV+XTSTp25IeBw4DvlEi3YHAgoi4p2ye2fG5Ge78bjTpvIP0d7tN0h8kvbsb+e8GPBURfy2ZbirwvfyZ/Sfw1RJp55GCA6Q5q7r8rnU4j/Tq98yBZRWjLuavaSQi3oiICaRfnztJ2rpgnvsBT0fE7LLlrbFrROxAmib6c5J2L5hudVK1/5yI2B54mVRVL0xpZOsDgMtLpluP9M86FtgEWEfSJ4qkjYj5pCak64BrgTn0cBrsSO0UvXr9v6SvkaYRv7hs2oj4WkRsltMeXzC/tYF/pUQg6uAcYAtgAunHwPdLpl8dWJ80Xfq/AJflGkgZUyj5IyY7FvhC/sy+QK6lF3Q0cJyk2aQmrtcbbdzoPNIb3zMHllWICsxfU0RuSroB2LtgkvcBB0h6lDS9856SLiqZ54L8/DRpbp26HZN1tAFtNbWrK0iBpox9gLsi4qmS6d4PPBIRz0TEEtLMo+8tmjgifhIRO0bE7sDzpPbssp6StDFAfq7bNNMMko4E9gMOyyeb7rqYTppm6tiCFMjvyd+30cBdkt5SJHFEPJV/QC0DzqX496xdG/CL3HR8O6mGXvfigXpyk+khwKUl8wU4gvQdg/QjqHDZI+L+iPhgROxICmoPNShjvfNIr37PHFhWEflXU8P5a7pIv0H7lT2S1gI+ANxfJG1EfDUiRkfEGFKT0u8jotAv95zfOpKGtb8mdQwXujIuIp4EHpe0ZV60F/Dnonln3f0F+TdgZ0lr589/L1KbdCGSNszPbyWdbH7WjTJcTTrhkJ9/2Y19lCZpb1LT5wER8Y9upH97zdsDKf5duy8iNoyIMfn71kbqbH6yYL4b17w9mILfsxpXkTrwkfQO0sUiZUb9fT9wf0S0lcwXUp/KHvn1nkDhprSa79og4OvAjzrZrrPzSO9+z5p5ZcBAe5BObn8HlpD+YT5VIu2upOrpvaRmlTnAviXSbwvcndPPpcEVK13sZxIlrwoD3gbckx/zgK+VTD8BuDOX/SpgvRJp1wEWAiO6ebynkE6Kc4ELyVcLFUx7MykI3gPs1Z3vBzAS+B3pJHM9sH6JtAfn168BTwG/KZH2QeDxmu9a3au6GqT/ef7M7gVmAZt253+CBlcTdpLvhcB9Od+rgY1LlnsN4KJc9ruAPcuUG7gA+Gw3/9a7ArPz9+U2YMcSaU8k1Yj/AnyXPGpKnbR1zyNFv2dVPTyki5mZVcpNYWZmVikHFjMzq5QDi5mZVcqBxczMKuXAYmZmlXJgsQEnj6h7Uc371SU9o5KjOucRbhveXFdkm2ZTGhH4S91Me56k8fn1v1ZbMuuvHFhsIHoZ2DrfSArpZtIFfVieVVZEfDoi2m9YdWCxQhxYbKD6FWk0Z+hw536eu+KqPNDhrZK2zctHKs09Mk/SeaSpCtrTfEJpPpw5kn4sabVGmUvaW9JdSvPn/K6LfE+WNEPSzZIek3SIpNOU5ua4Ng/h0V47al9+u6RxdfLdIqeZnff3zlxju0PSpLzNdyR9O7++UdJESd8ljQI9R9LFkr6pmjlolAakLDWHkPVfDiw2UM0EJitN7LUtK44kfQpwd0RsS/qV/tO8/CTglojYijQe2lsBJL0L+BjwvkiDgL5BGvG3LkkbkMa5+nBEbEcarbZRvpDG2NqTNNjmRcANEbEN8ArLAySkEZq3Ac4ijVjd0XTghEhjTn0J+O9Iw+cfCZwj6f2kMeZWmCguIqYBr0TEhIg4DDgfODwfzyDSUEClxpez/mv1vi6AWV+IiHvzsOJTSLWXWruSB1WMiN/nmspw0rwxh+Tl/0/S83n7vYAdgTvyQLlr0XiQv52BmyLikbyv9rk3OssX4NcRsUTSfaRJza7Ny+8DxtTs+5Ka5/+qzTSPePte4PKaAX3XzPnNk3QhcA2wS0Q0HD03Ih6VtFDS9qQh2O+OiIWN0tjA4cBiA9nVpHkxJpHGUuouATMiosz8GmW1T0y1TNKSWD4W0zJW/D+OTl5DaqF4Ideq6tkGeAHYsGCZziPVdN5CqsGYAW4Ks4HtfOCUiLivw/KbyU1Zud/h2UhzWtwEfDwv3wdon2Tqd8BHakagXV/S5g3yvRXYXdLY9u27yLeMj9U8/6l2Rd7XI5IOzXlI0nb59SGkeUp2B85sHym7gyXt/TnZlaRms3eTphk2A1xjsQEs0tDnZ9RZdTJwvqR7gX+wfLjxU4BLJM0D/pc07D4R8WdJXyfNoDmINCrt50jzudfL9xmlWTZ/kbd/mnRlWmf5lrFeTv8aqZmvo8NIfSlfJ01fPVPSAtKIuXtFxOOSzgJ+WCf/6cC9ku6KiMMi4nVJN5BqQT2a5Mz6F49ubNZPKE2cNTEiyswv0pP8BpGGnj80yk/Ta/2Ym8LMrLR80+SDwO8cVKwj11jMzKxSrrGYmVmlHFjMzKxSDixmZlYpBxYzM6uUA4uZmVXq/wMsXrlzIGnflQAAAABJRU5ErkJggg==",
|
|
"text/plain": [
|
|
"<Figure size 432x288 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Hold-out method\n",
|
|
"std_mse_val_ho_forest_fixed_n_samples = eval_hold_out(M=M_n_trees, split_coeff=split_coeff,\n",
|
|
" fit_func=fit_forest_fixed_n_samples_leaf,\n",
|
|
" predict_func=predict_forest)\n",
|
|
"# Cross-validation method\n",
|
|
"std_mse_val_cv_forest_fixed_n_samples = eval_k_fold_cross_validation(M=M_n_trees, k=k,\n",
|
|
" fit_func=fit_forest_fixed_n_samples_leaf,\n",
|
|
" predict_func=predict_forest)\n",
|
|
"\n",
|
|
"\n",
|
|
"# Plot the standard deviations\n",
|
|
"plot_bars(M_n_trees, std_mse_val_ho_forest_fixed_n_samples,\n",
|
|
" std_mse_val_cv_forest_fixed_n_samples)\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The first two rows in the cell above show the errorplots and the best model's prediction for hold out (first row) and cross validation (second row), respectively. The last row shows the standard deviation of the mean squarred error over the 20 different data sets incurred by each model."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### 3.5) Comparisons\n",
|
|
"\n",
|
|
"#### 3.5.1) (1 Point)\n",
|
|
"Comparing the error plots from section 3.4.2) to the error plots from 3.3.1) and 3.4.1) we observe that the validation error does not increase with the number of trees. Give an intution for this observation."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"Mean MSE plots of the two forests plot with fixed number of samples per leave (hold-out and cross-validation) show that an increasing model complexity leads to a decreasing MSE evaluation. In the fixed number of treas, we see that the model performance does not increase with an increasing model complexity. In the kNN case, we see that the model performance is highly dependet on the evaluation method (hold-out or cross-validation) with the best performance using cross-validation.\n",
|
|
"\n",
|
|
"The number of trees increases the model complexity and ensures that it is possible to better approximate non-linear functions. Therefore, a higher number of trees is more powerful in approximating the function and ensures a better generalization."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"#### 3.5.2) (1 Point)\n",
|
|
"Compare the standard deviation plots from the last three sections. What is the main difference between the hold-out and cross validation methods? Explain the reason for the observed behavior."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {
|
|
"pycharm": {
|
|
"name": "#%% md\n"
|
|
}
|
|
},
|
|
"source": [
|
|
"With increasing model complexity, the standard deviation of the cross-validation method decreases. Same behavior partially observable with the hold-out method but with less magnitude. The reason for this behavior is that with the cross-validation our model is trained on multiple train-test splits, which geaves us a better indication how well the model performs. With increasing model-complexity, the model can better approximate the underlying function. Therefore, the standard-deviation in the cross-validation setting decreases since our model performs on k-folds and gives a good overview over the performance. With the hold-out method, the standard deviation is highly dependent on the random split between training and test split. With the cross-validation, we take out the randomness of the hold-out method (high randomness --> high standard deviation)."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3 (ipykernel)",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 1
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}
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