I am working through Google’s Machine Learning Crash Course. The notes in this post cover the “Classification” module.

New metrics for evaluating classification performance:

  • Accuracy
  • Precision
  • Recall
  • ROC
  • AUC


“Accuracy” simply measures percentage of correct predictions.

It fails on class-imbalance, aka “skewed class”, problems, though. Neptune AI states is bluntly: “You shouldn’t use accuracy on imbalanced problems.” Heuristic: is the percent accuracy > the imbalance? For example, if a population is 99% disease-free, an accuracy of 99% requires no intelligence. This is called the “accuracy paradox”. Precision and recall are better suited to class-imbalance problems.

Tip: calculate odds independently if possible to compare with accuracy.

Confusion matrix

A “confusion matrix”, aka “classification matrix”, quantifies predicted vs actual outcomes, which is useful for evaluating model performance.

A false positive is a “type one” error. A false negative is a “type two” error. When the cost of error is high, type two must be minimized. In other words, when the cost of error is high, maximize recall.

Precision and recall

Andrew Ng’s “Lecture 11.4 — Machine Learning System Design | Trading Off Precision And Recall” provides a helpful phrasing:

  • Precision = true positive / predicted positive
  • Recall = true positive / actual positive

Regarding the accuracy paradox, if a model simply predicts negative all the time (eg because 99% of email isn’t spam), it will fail recall and precision because it never has a true positive.

Wikipedia makes a point: “It is trivial to achieve recall of 100% by returning all documents in response to any query”

Precision and recall are important, and in tension. Classification depends on a “threshold”. Increasing the threshold increases precision, but decreases recall. Wikipedia uses surgery for a brain tumor to illustrate: a conservative approach increases the risk of false negative; an aggressive approach increases risk of false positive. Plotting the “precision-recall curve” can also help demonstrate the relationship, as demonstrated by Andrew Ng.

Wikipedia has a nice visualization differentiating precision and recall:


The “ROC curve” helps identify the best threshold.

“AUC” compares ROCs, helping identify the best model.

StatQuest’s “ROC and AUC, Clearly Explained!” states precision is a better metric than the false positive rate for class imbalance problems because it doesn’t take true negatives into account.

Keras gives us AUC for a model, but what’s the corresponding threshold? The crash course clarifies: “AUC is classification-threshold-invariant. It measures the quality of the model’s predictions irrespective of what classification threshold is chosen.” Ok, then why use anything but AUC? Neptune AI summarizes: “… use it when you care equally about positive and negative classes.”

Prediction bias

Seems like this is another way of quantifying model performance. If we know a probability of occurrence and the model produces a significantly different probability, that indicates something’s amiss.

The formal definition is: average predicted occurrence – average actual occurrence. There’s a helpful note that a model simply returning the average occurrence would have zero prediction bias, but would still be a bad model.

The crash course gives a few causes for bias. StatQuest’s “Machine Learning Fundamentals: Bias and Variance” adds another: the inability of a ML algorithm to capture the true relationship between features and labels, eg linear regression trying to capture a curved relationship.

Fix prediction bias in the model, rather than adjusting the model output.

Interesting clarification that predicted values are a probability range, but actual values are discrete, so we need to segment values and average them to make a comparison.

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