ML Docs: Update Regression notebook

Added a preliminary section that introduces roc curves

Author: xhlu

doc/python/ml-roc-pr.md

@@ -34,7 +34,58 @@ jupyter:
     thumbnail: thumbnail/ml-roc-pr.png
 ---
 
-## Basic Binary ROC Curve
+## Preliminary plots
+
+Before diving into the receiver operating characteristic (ROC) curve, we will look at two plots that will give some context to the thresholds mechanism behind the ROC and PR curves.
+
+In the histogram, we observe that the score spread such that most of the positive labels are binned near 1, and a lot of the negative labels are close to 0. When we set a threshold on the score, all of the bins to its left will be classified as 0's, and everything to the right will be 1's. There are obviously a few outliers, such as **negative** samples that our model gave a high score, and *positive* samples with a low score. If we set a threshold right in the middle, those outliers will respectively become **false positives** and *false negatives*. 
+
+As we adjust thresholds, the number of positive positives will increase or decrease, and at the same time the number of true positives will also change; this is shown in the second plot. As you can see, the model seems to perform fairly well, because the true positive rate decreases slowly, whereas the false positive rate decreases sharply as we increase the threshold. Those two lines each represent a dimension of the ROC curve.
+
+```python
+import plotly.express as px
+import plotly.graph_objects as go
+from sklearn.linear_model import LogisticRegression
+from sklearn.metrics import roc_curve, auc
+from sklearn.datasets import make_classification
+
+X, y = make_classification(n_samples=500, random_state=0)
+
+model = LogisticRegression()
+model.fit(X, y)
+y_score = model.predict_proba(X)[:, 1]
+fpr, tpr, thresholds = roc_curve(y, y_score)
+
+# The histogram of scores compared to true labels
+fig_hist = px.histogram(
+    x=y_score, color=y, nbins=50, 
+    labels=dict(color='True Labels', x='Score')
+)
+
+# Evaluating model performance at various thresholds
+fig_thresh = go.Figure([
+    go.Scatter(x=thresholds, y=fpr, name='False Positive Rate'),
+    go.Scatter(x=thresholds, y=tpr, name='True Positive Rate')
+])
+fig_thresh.update_layout(
+    title='TPR and FPR at every threshold',
+    xaxis_title='Threshold',
+    yaxis_title='Rate',
+    yaxis=dict(scaleanchor="x", scaleratio=1),
+    xaxis=dict(constrain='domain')
+)
+fig_thresh.update_xaxes(range=[0, 1])
+
+# Display plots
+fig_hist.show()
+fig_thresh.show()
+```
+
+## Basic binary ROC curve
+
+Notice how this ROC curve looks similar to the True Positive Rate curve from the previous plot. This is because they are the same curve, except the x-axis consists of increasing values of FPR instead of threshold, which is why the line is flipped and distorted.
+
+We also display the area under the ROC curve (ROC AUC), which is fairly high, thus consistent with our intepretation of the previous plots.
 
 ```python
 import plotly.express as px
@@ -59,6 +110,10 @@ fig.add_shape(
     type='line', line=dict(dash='dash'), 
     x0=0, x1=1, y0=0, y1=1
 )
+fig.update_layout(
+    yaxis=dict(scaleanchor="x", scaleratio=1),
+    xaxis=dict(constrain='domain')
+)
 fig.show()
 ```
 
@@ -112,7 +167,9 @@ for i in range(y_scores.shape[1]):
 
 fig.update_layout(
     xaxis_title='False Positive Rate',
-    yaxis_title='True Positive Rate'
+    yaxis_title='True Positive Rate',
+    yaxis=dict(scaleanchor="x", scaleratio=1),
+    xaxis=dict(constrain='domain')
 )
 fig.show()
 ```
@@ -144,6 +201,11 @@ fig.add_shape(
     type='line', line=dict(dash='dash'), 
     x0=0, x1=1, y0=1, y1=0
 )
+fig.update_layout(
+    yaxis=dict(scaleanchor="x", scaleratio=1),
+    xaxis=dict(constrain='domain')
+)
+
 fig.show()
 ```
 
@@ -195,7 +257,16 @@ for i in range(y_scores.shape[1]):
 
 fig.update_layout(
     xaxis_title='Recall',
-    yaxis_title='Precision'
+    yaxis_title='Precision',
+    yaxis=dict(scaleanchor="x", scaleratio=1),
+    xaxis=dict(constrain='domain')
 )
 fig.show()
 ```
+
+## References
+
+Learn more about `px`, `px.area`, `px.hist`:
+* https://plot.ly/python/histograms/
+* https://plot.ly/python/filled-area-plots/
+* https://plot.ly/python/line-charts/