The goal of this second notebook is to understand precision-recall in the context of classifiers.
Because we are using the full Amazon review dataset (not a subset of words or reviews), in this assignment we return to using GraphLab Create for its efficiency. As usual, let's start by firing up GraphLab Create.
Make sure you have the latest version of GraphLab Create (1.8.3 or later). If you don't find the decision tree module, then you would need to upgrade graphlab-create using
pip install graphlab-create --upgradeSee this page for detailed instructions on upgrading.
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import graphlab
from __future__ import division
import numpy as np
graphlab.canvas.set_target('ipynb')
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products = graphlab.SFrame('amazon_baby.gl/')
As in the first assignment of this course, we compute the word counts for individual words and extract positive and negative sentiments from ratings. To summarize, we perform the following:
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def remove_punctuation(text):
import string
return text.translate(None, string.punctuation)
# Remove punctuation.
review_clean = products['review'].apply(remove_punctuation)
# Count words
products['word_count'] = graphlab.text_analytics.count_words(review_clean)
# Drop neutral sentiment reviews.
products = products[products['rating'] != 3]
# Positive sentiment to +1 and negative sentiment to -1
products['sentiment'] = products['rating'].apply(lambda rating : +1 if rating > 3 else -1)
Now, let's remember what the dataset looks like by taking a quick peek:
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products
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train_data, test_data = products.random_split(.8, seed=1)
We will now train a logistic regression classifier with sentiment as the target and word_count as the features. We will set validation_set=None to make sure everyone gets exactly the same results.
Remember, even though we now know how to implement logistic regression, we will use GraphLab Create for its efficiency at processing this Amazon dataset in its entirety. The focus of this assignment is instead on the topic of precision and recall.
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model = graphlab.logistic_classifier.create(train_data, target='sentiment',
features=['word_count'],
validation_set=None)
We will explore the advanced model evaluation concepts that were discussed in the lectures.
One performance metric we will use for our more advanced exploration is accuracy, which we have seen many times in past assignments. Recall that the accuracy is given by
$$ \mbox{accuracy} = \frac{\mbox{# correctly classified data points}}{\mbox{# total data points}} $$To obtain the accuracy of our trained models using GraphLab Create, simply pass the option metric='accuracy' to the evaluate function. We compute the accuracy of our logistic regression model on the test_data as follows:
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accuracy= model.evaluate(test_data, metric='accuracy')['accuracy']
print "Test Accuracy: %s" % accuracy
Recall from an earlier assignment that we used the majority class classifier as a baseline (i.e reference) model for a point of comparison with a more sophisticated classifier. The majority classifier model predicts the majority class for all data points.
Typically, a good model should beat the majority class classifier. Since the majority class in this dataset is the positive class (i.e., there are more positive than negative reviews), the accuracy of the majority class classifier can be computed as follows:
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baseline = len(test_data[test_data['sentiment'] == 1])/len(test_data)
print "Baseline accuracy (majority class classifier): %s" % baseline
Quiz Question: Using accuracy as the evaluation metric, was our logistic regression model better than the baseline (majority class classifier)?
The accuracy, while convenient, does not tell the whole story. For a fuller picture, we turn to the confusion matrix. In the case of binary classification, the confusion matrix is a 2-by-2 matrix laying out correct and incorrect predictions made in each label as follows:
+---------------------------------------------+
| Predicted label |
+----------------------+----------------------+
| (+1) | (-1) |
+-------+-----+----------------------+----------------------+
| True |(+1) | # of true positives | # of false negatives |
| label +-----+----------------------+----------------------+
| |(-1) | # of false positives | # of true negatives |
+-------+-----+----------------------+----------------------+To print out the confusion matrix for a classifier, use metric='confusion_matrix':
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confusion_matrix = model.evaluate(test_data, metric='confusion_matrix')['confusion_matrix']
confusion_matrix
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Quiz Question: How many predicted values in the test set are false positives?
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false_positive = confusion_matrix['count'][(confusion_matrix['target_label'] == -1) & (confusion_matrix['predicted_label'] == +1)]
false_positive
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Put yourself in the shoes of a manufacturer that sells a baby product on Amazon.com and you want to monitor your product's reviews in order to respond to complaints. Even a few negative reviews may generate a lot of bad publicity about the product. So you don't want to miss any reviews with negative sentiments --- you'd rather put up with false alarms about potentially negative reviews instead of missing negative reviews entirely. In other words, false positives cost more than false negatives. (It may be the other way around for other scenarios, but let's stick with the manufacturer's scenario for now.)
Suppose you know the costs involved in each kind of mistake:
Quiz Question: Given the stipulation, what is the cost associated with the logistic regression classifier's performance on the test set?
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false_positive_test = confusion_matrix[(confusion_matrix['target_label'] == -1) & (confusion_matrix['predicted_label'] == +1)]['count'][0]
false_negative_test = confusion_matrix[(confusion_matrix['target_label'] == +1) & (confusion_matrix['predicted_label'] == -1)]['count'][0]
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cost_test = (100 * false_positive_test) + (1 * false_negative_test)
print cost_test
You may not have exact dollar amounts for each kind of mistake. Instead, you may simply prefer to reduce the percentage of false positives to be less than, say, 3.5% of all positive predictions. This is where precision comes in:
$$ [\text{precision}] = \frac{[\text{# positive data points with positive predicitions}]}{\text{[# all data points with positive predictions]}} = \frac{[\text{# true positives}]}{[\text{# true positives}] + [\text{# false positives}]} $$So to keep the percentage of false positives below 3.5% of positive predictions, we must raise the precision to 96.5% or higher.
First, let us compute the precision of the logistic regression classifier on the test_data.
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precision = model.evaluate(test_data, metric='precision')['precision']
print "Precision on test data: %s" % precision
Quiz Question: Out of all reviews in the test set that are predicted to be positive, what fraction of them are false positives? (Round to the second decimal place e.g. 0.25)
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false_positive/confusion_matrix['count'].sum()
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Quiz Question: Based on what we learned in lecture, if we wanted to reduce this fraction of false positives to be below 3.5%, we would: (see the quiz)
A complementary metric is recall, which measures the ratio between the number of true positives and that of (ground-truth) positive reviews:
$$ [\text{recall}] = \frac{[\text{# positive data points with positive predicitions}]}{\text{[# all positive data points]}} = \frac{[\text{# true positives}]}{[\text{# true positives}] + [\text{# false negatives}]} $$Let us compute the recall on the test_data.
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recall = model.evaluate(test_data, metric='recall')['recall']
print "Recall on test data: %s" % recall
Quiz Question: What fraction of the positive reviews in the test_set were correctly predicted as positive by the classifier?
Quiz Question: What is the recall value for a classifier that predicts +1 for all data points in the test_data?
recall = predicted positive / (predicted positive + false negative )
Since we predict positive for all, there is no false negative. Our formula becomes
In this part, we will explore the trade-off between precision and recall discussed in the lecture. We first examine what happens when we use a different threshold value for making class predictions. We then explore a range of threshold values and plot the associated precision-recall curve.
False positives are costly in our example, so we may want to be more conservative about making positive predictions. To achieve this, instead of thresholding class probabilities at 0.5, we can choose a higher threshold.
Write a function called apply_threshold that accepts two things
probabilities (an SArray of probability values)threshold (a float between 0 and 1).The function should return an array, where each element is set to +1 or -1 depending whether the corresponding probability exceeds threshold.
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def apply_threshold(probabilities, threshold):
### YOUR CODE GOES HERE
# +1 if >= threshold and -1 otherwise.
ans = graphlab.SArray([+1 if x >= threshold else -1 for x in probabilities])
return ans
Run prediction with output_type='probability' to get the list of probability values. Then use thresholds set at 0.5 (default) and 0.9 to make predictions from these probability values.
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probabilities = model.predict(test_data, output_type='probability')
predictions_with_default_threshold = apply_threshold(probabilities, 0.5)
predictions_with_high_threshold = apply_threshold(probabilities, 0.9)
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print "Number of positive predicted reviews (threshold = 0.5): %s" % (predictions_with_default_threshold == 1).sum()
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print "Number of positive predicted reviews (threshold = 0.9): %s" % (predictions_with_high_threshold == 1).sum()
Quiz Question: What happens to the number of positive predicted reviews as the threshold increased from 0.5 to 0.9?
By changing the probability threshold, it is possible to influence precision and recall. We can explore this as follows:
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# Threshold = 0.5
precision_with_default_threshold = graphlab.evaluation.precision(test_data['sentiment'],
predictions_with_default_threshold)
recall_with_default_threshold = graphlab.evaluation.recall(test_data['sentiment'],
predictions_with_default_threshold)
# Threshold = 0.9
precision_with_high_threshold = graphlab.evaluation.precision(test_data['sentiment'],
predictions_with_high_threshold)
recall_with_high_threshold = graphlab.evaluation.recall(test_data['sentiment'],
predictions_with_high_threshold)
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print "Precision (threshold = 0.5): %s" % precision_with_default_threshold
print "Recall (threshold = 0.5) : %s" % recall_with_default_threshold
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print "Precision (threshold = 0.9): %s" % precision_with_high_threshold
print "Recall (threshold = 0.9) : %s" % recall_with_high_threshold
Quiz Question (variant 1): Does the precision increase with a higher threshold?
Quiz Question (variant 2): Does the recall increase with a higher threshold?
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threshold_values = np.linspace(0.5, 1, num=100)
print threshold_values
For each of the values of threshold, we compute the precision and recall scores.
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precision_all = []
recall_all = []
probabilities = model.predict(test_data, output_type='probability')
for threshold in threshold_values:
predictions = apply_threshold(probabilities, threshold)
precision = graphlab.evaluation.precision(test_data['sentiment'], predictions)
recall = graphlab.evaluation.recall(test_data['sentiment'], predictions)
precision_all.append(precision)
recall_all.append(recall)
Now, let's plot the precision-recall curve to visualize the precision-recall tradeoff as we vary the threshold.
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import matplotlib.pyplot as plt
%matplotlib inline
def plot_pr_curve(precision, recall, title):
plt.rcParams['figure.figsize'] = 7, 5
plt.locator_params(axis = 'x', nbins = 5)
plt.plot(precision, recall, 'b-', linewidth=4.0, color = '#B0017F')
plt.title(title)
plt.xlabel('Precision')
plt.ylabel('Recall')
plt.rcParams.update({'font.size': 16})
plot_pr_curve(precision_all, recall_all, 'Precision recall curve (all)')
Quiz Question: Among all the threshold values tried, what is the smallest threshold value that achieves a precision of 96.5% or better? Round your answer to 3 decimal places.
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threshold_values[np.array(precision_all) >= 0.965].min()
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Quiz Question: Using threshold = 0.98, how many false negatives do we get on the test_data? (Hint: You may use the graphlab.evaluation.confusion_matrix function implemented in GraphLab Create.)
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threshold = 0.98
predictions = apply_threshold(probabilities, threshold)
confusion_matrix = graphlab.evaluation.confusion_matrix(test_data['sentiment'], predictions)
confusion_matrix
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confusion_matrix[(confusion_matrix['target_label'] == +1) & (confusion_matrix['predicted_label'] == -1)]['count'][0]
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This is the number of false negatives (i.e the number of reviews to look at when not needed) that we have to deal with using this classifier.
So far, we looked at the number of false positives for the entire test set. In this section, let's select reviews using a specific search term and optimize the precision on these reviews only. After all, a manufacturer would be interested in tuning the false positive rate just for their products (the reviews they want to read) rather than that of the entire set of products on Amazon.
From the test set, select all the reviews for all products with the word 'baby' in them.
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baby_reviews = test_data[test_data['name'].apply(lambda x: 'baby' in x.lower())]
Now, let's predict the probability of classifying these reviews as positive:
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probabilities = model.predict(baby_reviews, output_type='probability')
Let's plot the precision-recall curve for the baby_reviews dataset.
First, let's consider the following threshold_values ranging from 0.5 to 1:
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threshold_values = np.linspace(0.5, 1, num=100)
Second, as we did above, let's compute precision and recall for each value in threshold_values on the baby_reviews dataset. Complete the code block below.
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precision_all = []
recall_all = []
for threshold in threshold_values:
# Make predictions. Use the `apply_threshold` function
## YOUR CODE HERE
predictions = apply_threshold(probabilities, threshold)
# Calculate the precision.
# YOUR CODE HERE
precision = graphlab.evaluation.precision(baby_reviews['sentiment'], predictions)
# YOUR CODE HERE
recall = graphlab.evaluation.recall(baby_reviews['sentiment'], predictions)
# Append the precision and recall scores.
precision_all.append(precision)
recall_all.append(recall)
Quiz Question: Among all the threshold values tried, what is the smallest threshold value that achieves a precision of 96.5% or better for the reviews of data in baby_reviews? Round your answer to 3 decimal places.
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threshold_values[np.array(precision_all) >= 0.965].min()
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Quiz Question: Is this threshold value smaller or larger than the threshold used for the entire dataset to achieve the same specified precision of 96.5%?
Finally, let's plot the precision recall curve.
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plot_pr_curve(precision_all, recall_all, "Precision-Recall (Baby)")