From 33a94fb59f207fc85ca857127fd1dc494a7f14f1 Mon Sep 17 00:00:00 2001
From: udlbook <110402648+udlbook@users.noreply.github.com>
Date: Tue, 24 Oct 2023 13:10:47 +0100
Subject: [PATCH] Created using Colaboratory

---
 Notebooks/Chap05/5_1_Least_Squares_Loss.ipynb | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/Notebooks/Chap05/5_1_Least_Squares_Loss.ipynb b/Notebooks/Chap05/5_1_Least_Squares_Loss.ipynb
index f7e6a5e..66ed51c 100644
--- a/Notebooks/Chap05/5_1_Least_Squares_Loss.ipynb
+++ b/Notebooks/Chap05/5_1_Least_Squares_Loss.ipynb
@@ -4,7 +4,7 @@
   "metadata": {
     "colab": {
       "provenance": [],
-      "authorship_tag": "ABX9TyPX88BLalmJTle9GSAZMJcz",
+      "authorship_tag": "ABX9TyPDNteVt0SjrR97OiS386NZ",
       "include_colab_link": true
     },
     "kernelspec": {
@@ -306,7 +306,8 @@
       "source": [
         "# Return the negative log likelihood of the data under the model\n",
         "def compute_negative_log_likelihood(y_train, mu, sigma):\n",
-        "  # TODO -- compute the likelihood of the data -- don't use the likelihood function above -- compute the negative sum of the log probabilities\n",
+        "  # TODO -- compute the negative log likelihood of the data without using aproduct\n",
+        "  # In other words, compute minus one times the sum of the log probabilities\n",
         "  # Equation 5.4 in the notes\n",
         "  # You will need np.sum(), np.log()\n",
         "  # Replace the line below\n",
@@ -352,7 +353,7 @@
     {
       "cell_type": "code",
       "source": [
-        "# Return the squared distance between the predicted\n",
+        "# Return the squared distance between the observed data (y_train) and the prediction of the model (y_pred)\n",
         "def compute_sum_of_squares(y_train, y_pred):\n",
         "  # TODO -- compute the sum of squared distances between the training data and the model prediction\n",
         "  # Eqn 5.10 in the notes.  Make sure that you understand this, and ask questions if you don't\n",
@@ -372,9 +373,9 @@
       "source": [
         "# Let's test this again\n",
         "beta_0, omega_0, beta_1, omega_1 = get_parameters()\n",
-        "# Use our neural network to predict the mean of the Gaussian\n",
-        "y_pred = shallow_nn(x_train, beta_0, omega_0, beta_1, omega_1)\n",
-        "# Compute the log likelihood\n",
+        "# Use our neural network to predict the mean of the Gaussian, which is out best prediction of y\n",
+        "y_pred = mu_pred = shallow_nn(x_train, beta_0, omega_0, beta_1, omega_1)\n",
+        "# Compute the sum of squares\n",
         "sum_of_squares = compute_sum_of_squares(y_train, y_pred)\n",
         "# Let's double check we get the right answer before proceeding\n",
         "print(\"Correct answer = %9.9f, Your answer = %9.9f\"%(2.020992572,sum_of_squares))"
@@ -554,7 +555,7 @@
     {
       "cell_type": "markdown",
       "source": [
-        "Obviously, to fit the full neural model we would vary all of the 10 parameters of the network in the $\\boldsymbol\\beta_{0},\\boldsymbol\\omega_{0},\\boldsymbol\\beta_{1},\\boldsymbol\\omega_{1}$ (and maybe $\\sigma$) until we find the combination that have the maximum likelihood / minimum negative log likelihood / least squares.<br><br>\n",
+        "Obviously, to fit the full neural model we would vary all of the 10 parameters of the network in $\\boldsymbol\\beta_{0},\\boldsymbol\\omega_{0},\\boldsymbol\\beta_{1},\\boldsymbol\\omega_{1}$ (and maybe $\\sigma$) until we find the combination that have the maximum likelihood / minimum negative log likelihood / least squares.<br><br>\n",
         "\n",
         "Here we just varied one at a time as it is easier to see what is going on.  This is known as **coordinate descent**.\n"
       ],