Merge pull request #219 from jhrcek/jhrcek/fix-duplicate-words

Fix duplicate word occurrences in notebooks

Blogs/BorealisGradientFlow.ipynb

@@ -31,7 +31,7 @@
       "source": [
         "# Gradient flow\n",
         "\n",
-        "This notebook replicates some of the results in the the Borealis AI [blog](https://www.borealisai.com/research-blogs/gradient-flow/) on gradient flow.  \n"
+        "This notebook replicates some of the results in the Borealis AI [blog](https://www.borealisai.com/research-blogs/gradient-flow/) on gradient flow.  \n"
       ],
       "metadata": {
         "id": "ucrRRJ4dq8_d"

Blogs/BorealisNTK.ipynb

@@ -166,7 +166,7 @@
     {
       "cell_type": "markdown",
       "source": [
-        "Routines to calculate the empirical and analytical NTK (i.e. the NTK with infinite hidden units) for the the shallow network"
+        "Routines to calculate the empirical and analytical NTK (i.e. the NTK with infinite hidden units) for the shallow network"
       ],
       "metadata": {
         "id": "mxW8E5kYIzlj"

CM20315/CM20315_Coursework_IV.ipynb

@@ -128,7 +128,7 @@
         "\n",
         "In part (b) of the practical we calculate the volume of a hypersphere of radius 0.5 (i.e., of diameter 1) as a function of the radius.  You will find that the volume decreases to almost nothing in high dimensions.  All of the volume is in the corners of the unit hypercube (which always has volume 1). Double weird.\n",
         "\n",
-        "Note that you you can check your answer by doing the calculation for 2D using the standard formula for the area of a circle and making sure it matches."
+        "Note that you can check your answer by doing the calculation for 2D using the standard formula for the area of a circle and making sure it matches."
       ],
       "metadata": {
         "id": "b2FYKV1SL4Z7"

CM20315/CM20315_Loss_II.ipynb

@@ -199,7 +199,7 @@
     {
       "cell_type": "markdown",
       "source": [
-        "The left is model output and the right is the model output after the sigmoid has been applied, so it now lies in the range [0,1] and represents the probability, that y=1.  The black dots show the training data.  We'll compute the the likelihood and the negative log likelihood."
+        "The left is model output and the right is the model output after the sigmoid has been applied, so it now lies in the range [0,1] and represents the probability, that y=1.  The black dots show the training data.  We'll compute the likelihood and the negative log likelihood."
       ],
       "metadata": {
         "id": "MvVX6tl9AEXF"

CM20315/CM20315_Loss_III.ipynb

@@ -218,7 +218,7 @@
     {
       "cell_type": "markdown",
       "source": [
-        "The left is model output and the right is the model output after the softmax has been applied, so it now lies in the range [0,1] and represents the probability, that y=0 (red), 1 (green) and 2 (blue)   The dots at the bottom show the training data with the same color scheme.  So we want the red curve to be high where there are red dots, the green curve to be high where there are green dotsmand the blue curve to be high where there are blue dots  We'll compute the the likelihood and the negative log likelihood."
+        "The left is model output and the right is the model output after the softmax has been applied, so it now lies in the range [0,1] and represents the probability, that y=0 (red), 1 (green) and 2 (blue)   The dots at the bottom show the training data with the same color scheme.  So we want the red curve to be high where there are red dots, the green curve to be high where there are green dotsmand the blue curve to be high where there are blue dots  We'll compute the likelihood and the negative log likelihood."
       ],
       "metadata": {
         "id": "MvVX6tl9AEXF"

CM20315_2023/CM20315_Coursework_IV.ipynb

@@ -128,7 +128,7 @@
         "\n",
         "In part (b) of the practical we calculate the volume of a hypersphere of radius 0.5 (i.e., of diameter 1) as a function of the radius.  You will find that the volume decreases to almost nothing in high dimensions.  All of the volume is in the corners of the unit hypercube (which always has volume 1). Double weird.\n",
         "\n",
-        "Note that you you can check your answer by doing the calculation for 2D using the standard formula for the area of a circle and making sure it matches."
+        "Note that you can check your answer by doing the calculation for 2D using the standard formula for the area of a circle and making sure it matches."
       ],
       "metadata": {
         "id": "b2FYKV1SL4Z7"

CM20315_2023/CM20315_Coursework_V_2023.ipynb

@@ -214,7 +214,7 @@
     {
       "cell_type": "code",
       "source": [
-        "# Compute the derivative of the the loss with respect to the function output f_val\n",
+        "# Compute the derivative of the loss with respect to the function output f_val\n",
         "def dl_df(f_val,y):\n",
         "  # Compute sigmoid of network output\n",
         "  sig_f_val = sig(f_val)\n",

Notebooks/Chap05/5_3_Multiclass_Cross_entropy_Loss.ipynb

@@ -211,7 +211,7 @@
         "id": "MvVX6tl9AEXF"
       },
       "source": [
-        "The left is model output and the right is the model output after the softmax has been applied, so it now lies in the range [0,1] and represents the probability, that y=0 (red), 1 (green) and 2 (blue).  The dots at the bottom show the training data with the same color scheme.  So we want the red curve to be high where there are red dots, the green curve to be high where there are green dots, and the blue curve to be high where there are blue dots  We'll compute the the likelihood and the negative log likelihood."
+        "The left is model output and the right is the model output after the softmax has been applied, so it now lies in the range [0,1] and represents the probability, that y=0 (red), 1 (green) and 2 (blue).  The dots at the bottom show the training data with the same color scheme.  So we want the red curve to be high where there are red dots, the green curve to be high where there are green dots, and the blue curve to be high where there are blue dots  We'll compute the likelihood and the negative log likelihood."
       ]
     },
     {

Notebooks/Chap08/8_4_High_Dimensional_Spaces.ipynb

@@ -134,7 +134,7 @@
       "source": [
         "# Volume of a hypersphere\n",
         "\n",
-        "In the second part of this notebook we calculate the volume of a hypersphere of radius 0.5 (i.e., of diameter 1) as a function of the radius.  Note that you you can check your answer by doing the calculation for 2D using the standard formula for the area of a circle and making sure it matches."
+        "In the second part of this notebook we calculate the volume of a hypersphere of radius 0.5 (i.e., of diameter 1) as a function of the radius.  Note that you can check your answer by doing the calculation for 2D using the standard formula for the area of a circle and making sure it matches."
       ],
       "metadata": {
         "id": "b2FYKV1SL4Z7"

Notebooks/Chap19/19_2_Dynamic_Programming.ipynb

@@ -393,7 +393,7 @@
     {
       "cell_type": "code",
       "source": [
-        "# Update the state values for the current policy, by making the values at at adjacent\n",
+        "# Update the state values for the current policy, by making the values at adjacent\n",
         "# states compatible with the Bellman equation (equation 19.11)\n",
         "def policy_evaluation(policy, state_values, rewards,  transition_probabilities_given_action, gamma):\n",
         "\n",

Notebooks/Chap21/21_1_Bias_Mitigation.ipynb

@@ -137,7 +137,7 @@
         "id": "CfZ-srQtmff2"
       },
       "source": [
-        "Why might the distributions for blue and yellow populations be different? It could be that the behaviour of the populations is identical, but the credit rating algorithm is biased; it may favor one population over another or simply be more noisy for one group. Alternatively, it could be that that the populations genuinely behave differently. In practice, the differences in blue and yellow distributions are probably attributable to a combination of these factors.\n",
+        "Why might the distributions for blue and yellow populations be different? It could be that the behaviour of the populations is identical, but the credit rating algorithm is biased; it may favor one population over another or simply be more noisy for one group. Alternatively, it could be that the populations genuinely behave differently. In practice, the differences in blue and yellow distributions are probably attributable to a combination of these factors.\n",
         "\n",
         "Let’s assume that we can’t retrain the credit score prediction algorithm; our job is to adjudicate whether each individual is refused the loan ($\\hat{y}=0$)\n",
         " or granted it ($\\hat{y}=1$). Since we only have the credit score\n",
@@ -382,7 +382,7 @@
       "source": [
         "# Equal opportunity:\n",
         "\n",
-        "The thresholds are chosen so that so that the true positive rate is is the same for both population. Of the people who pay back the loan, the same proportion are offered credit in each group. In terms of the two ROC curves, it means choosing thresholds so that the vertical position on each curve is the same without regard for the horizontal position."
+        "The thresholds are chosen so that so that the true positive rate is the same for both population. Of the people who pay back the loan, the same proportion are offered credit in each group. In terms of the two ROC curves, it means choosing thresholds so that the vertical position on each curve is the same without regard for the horizontal position."
       ]
     },
     {