CPSC 330 Lecture 9: Classification Metrics

Varada Kolhatkar

Focus on the breath!

Announcements

  • Important information about midterm 1
    • https://piazza.com/class/mekbcze4gyber/post/162
    • Good news for you: You’ll have access to our course notes in the midterm!
  • HW4 was due on Monday, Oct 6th 11:59 pm.
  • HW5 has been released. It’s a project-type assignment and you get till Oct 27th to work on it.

ML workflow

Accuracy

  • So far, we’ve been measuring model performance using Accuracy.
  • Accuracy is the proportion of all predictions that were correct — whether positive or negative.

\[ \text{Accuracy} = \frac{\text{correct classifications}}{\text{total classifications}} \]

  • But is accuracy always the right metric to evaluate a model? 🤔

A fraud classification example

(139554, 29)
Class Time Amount V1 V2 V3 V4 V5 V6 V7 ... V19 V20 V21 V22 V23 V24 V25 V26 V27 V28
64454 0 51150.0 1.00 -3.538816 3.481893 -1.827130 -0.573050 2.644106 -0.340988 2.102135 ... -1.509991 1.345904 0.530978 -0.860677 -0.201810 -1.719747 0.729143 -0.547993 -0.023636 -0.454966
37906 0 39163.0 18.49 -0.363913 0.853399 1.648195 1.118934 0.100882 0.423852 0.472790 ... 0.810267 -0.192932 0.687055 -0.094586 0.121531 0.146830 -0.944092 -0.558564 -0.186814 -0.257103
79378 0 57994.0 23.74 1.193021 -0.136714 0.622612 0.780864 -0.823511 -0.706444 -0.206073 ... 0.258815 -0.178761 -0.310405 -0.842028 0.085477 0.366005 0.254443 0.290002 -0.036764 0.015039
245686 0 152859.0 156.52 1.604032 -0.808208 -1.594982 0.200475 0.502985 0.832370 -0.034071 ... -1.009429 -0.040448 0.519029 1.429217 -0.139322 -1.293663 0.037785 0.061206 0.005387 -0.057296
60943 0 49575.0 57.50 -2.669614 -2.734385 0.662450 -0.059077 3.346850 -2.549682 -1.430571 ... 0.157993 -0.430295 -0.228329 -0.370643 -0.211544 -0.300837 -1.174590 0.573818 0.388023 0.161782

5 rows × 31 columns

DummyClassifier

Let’s try a DummyClassifier, which makes predictions without learning any patterns.

dummy = DummyClassifier()
cross_val_score(dummy, X_train, y_train).mean()
np.float64(0.9983017327649726)
  • The accuracy looks surprisingly high!
  • Should we be happy with this model and deploy it?

Problem: Class imbalance

y_train.value_counts()
Class
0    139317
1       237
Name: count, dtype: int64

  • In many real-world problems, some classes are much rarer than others.

  • A model that always predicts “no fraud” could still achieve >99% accuracy!

  • This is why accuracy can be misleading in imbalanced datasets.

  • We need metrics that differentiate types of errors.

DummyClassifier: Confusion matrix

Which types of errors would be most critical for the bank to address? Missing a fraud case or flagging a legitimate transaction as fraud?

LogisticRegression: Confusion matrix

Are we doing better with logistic regression?

Understanding the confusion matrix

  • TN \(\rightarrow\) True negatives
  • FP \(\rightarrow\) False positives
  • FN \(\rightarrow\) False negatives
  • TP \(\rightarrow\) True positives

Practice: confusion matrix terminology

Confusion matrix questions

Imagine a spam filter model where emails labeled 1 = spam, 0 = not spam.

If a spam email is incorrectly classified as not spam, what kind of error is this?

    1. A false positive
    1. A true positive
    1. A false negative
    1. A true negative

Confusion matrix questions

In an intrusion detection system, 1 = intrusion, 0 = safe.

If the system misses an actual intrusion and classifies it as safe, this is a:

    1. A false positive
    1. A true positive
    1. A false negative
    1. A true negative

Confusion matrix questions

In a medical test for a disease, 1 = diseased, 0 = healthy.

If a healthy patient is incorrectly diagnosed as diseased, that’s a:

    1. A false positive
    1. A true positive
    1. A false negative
    1. A true negative

Metrics other than accuracy

Now that we understand the different types of errors, we can explore metrics that better capture model performance when accuracy falls short, especially for imbalanced datasets.

We’ll start with three key ones:

  • Precision
  • Recall
  • F1-score

Precision and recall

Let’s revisit our fraud detection scenario. The circle below represents all transactions predicted as fraud by an imaginary toy model designed to detect fraudulent activity.

Intuition behind the two metrics

  • Precision: Of all the transactions predicted as fraud, how many were actually fraud?
    • High precision \(\rightarrow\) few false alarms (low false positives).
  • Recall: Of all the actual fraud cases, how many did the model catch?
    • High recall \(\rightarrow\) few missed frauds (low false negatives).

Trade-off between precision and recall

  • Increasing recall often decreases precision, and vice versa.
  • Example:
    • Predict “fraud” for every transaction \(\rightarrow\) perfect recall, terrible precision.
    • Predict “fraud” only when 100% sure \(\rightarrow\) high precision, low recall.

The right balance depends on the application and cost of errors.

F1-score

  • Sometimes, we want a single metric that balances precision and recall.
  • The F1-score is the harmonic mean of the two:

\[ F1 = 2 \times \frac{\text{Precision} \times \text{Recall}}{\text{Precision} + \text{Recall}} \]

  • High F1 means both precision and recall are strong.
  • Useful when we care about both false positives and false negatives.

Summary

Metric What it measures High value means
Accuracy Overall correctness Model gets most predictions right
Precision Quality of positive predictions Few false alarms
Recall Quantity of true positives caught Few missed positives
F1-score Balance of precision & recall Both precision and recall are high

iClicker Exercise 9.1

Select all of the following statements which are TRUE.

    1. In medical diagnosis, false positives are more damaging than false negatives (assume “positive” means the person has a disease, “negative” means they don’t).
    1. In spam classification, false positives are more damaging than false negatives (assume “positive” means the email is spam, “negative” means they it’s not).
    1. If method A gets a higher accuracy than method B, that means its precision is also higher.
    1. If method A gets a higher accuracy than method B, that means its recall is also higher.

Counter examples

Method A - higher accuracy but lower precision

Negative Positive
90 5
5 0

Method B - lower accuracy but higher precision

Negative Positive
80 15
0 5

Takeaway

  • Accuracy summarizes overall correctness but hides class-specific behaviour.
  • You can have high accuracy but poor precision or recall,
    especially in imbalanced datasets.
  • Always check multiple metrics before deciding which model is better.

Threshold-based classification

Predicting with logistic regression

  • Most classification models don’t directly predict labels. They predict scores or probabilities.
  • To get a label (e.g., “fraud” or “non fraud”), we choose a threshold (often 0.5). If the threshold changes, predictions change, and so do the errors.
  • What happens to precision and recall if we change the probability threshold?
  • Play with classification thresholds

PR curve

  • Calculate precision and recall (TPR) at every possible threshold and graph them.
  • Top left \(\rightarrow\) Very high threshold (strict model = high precision)
  • Bottom right \(\rightarrow\) Very low threshold (linient model = high recall)

PR curve different thresholds

  • Which of the red dots are reasonable trade offs?

Average Precision (AP) Score

  • AP score summarizes the PR curve by calculating the area under the curve
  • It measures the ranking ability of a model; how well it assigns higher probabilities to positive examples than to negative ones, regardless of the specific threshold.

iClicker Exercise

Choose the appropriate evaluation metric for the following scenarios:

Scenario 1: Balance between precision and recall for a threshold.

Scenario 2: Assess performance across all thresholds.

    1. F1 for 1, AP for 2
    1. AP for 1, F1 Score for 2
    1. AP for both
    1. F1 for both

iClicker Exercise 9.2

Select all of the following statements which are TRUE.

    1. If we increase the classification threshold, both true and false positives are likely to decrease.
    1. If we increase the classification threshold, both true and false negatives are likely to decrease.
    1. Lowering the classification threshold generally increases the model’s recall.
    1. Raising the classification threshold can improve the precision of the model if it effectively reduces the number of false positives without significantly affecting true positives.

ROC Curve

  • Compute the True Positive Rate (TPR) and False Positive Rate (FPR) at every possible threshold, and plot TPR vs FPR.
  • How well does the model separate positive and negative classes in terms of predicted probability?
  • A good choice when the dataset is reasonably balanced or not extremely imbalanced (e.g., fraud detection, disease diagnosis).

ROC Curve example

  • Bottom-left \(\rightarrow\) very high threshold (almost everything predicted negative: low recall, low FPR).
  • Top-right \(\rightarrow\) very low threshold (almost everything predicted positive: high recall, high FPR).

AUC

  • The area under the ROC curve (AUC) represents the probability that the model, if given a randomly chosen positive and negative example, will rank the positive higher than the negative.

ROC AUC questions

Consider the points A, B, and C in the following diagram, each representing a threshold. Which threshold would you pick in each scenario?

    1. If false positives (false alarms) are highly costly
    1. If false positives are cheap and false negatives (missed true positives) highly costly
    1. If the costs are roughly equivalent

Source

What did we learn?

  • Why accuracy is not always a good metric?
  • Confusion matrix
  • Precision, recall, & f1-score
  • Precision-recall curves & average precision
  • Receiver Operator Characteristic (ROC) curves & AUC