The Metric Chronicles: Mighty Guardians of the Classification Realm

In the bustling metropolis of Classifia, where models thrived on predicting outcomes, five illustrious figures lived in a towering observatory. They were the evaluators of classification models, and their names —Accuracy, Precision, Recall, F1 Score and ROC-AUC— were known far and wide. Thanks to their evaluations and feedback, the classification models in this city could preserve their dignity and honor.

They were good at their job, but like all the powerful characters across all the narrative universes, their egos were also high. Even though they shared the common objective of measuring model performance, their disparate methods often sparked fiery discussions.

The Meeting

One cloudy afternoon, the four evaluators gathered in their observatory, the city skyline behind them. Rain was coming and it didn’t look like the sun would come out for a short while. A model that classified emails as spam or not-spam was their topic of debate under that gray sky.

Accuracy, the eldest and most popular among them, stood at the head of the table. “Let’s evaluate this model,” he said confidently. “I will start.”

Accuracy’s Argument

Accuracy, the wise leader, stood tall with a golden scale in hand. “I measure overall correctness,” Accuracy began. “If the model gets most predictions right, Classifia prospers.”

With a solemn gesture, Accuracy brought up a hologram of the confusion matrix belonging to the respective model. “This model correctly classified 95% of the emails; only 5% of its predictions are wrong,” he declared, his voice brimming with pride. “That’s a solid performance. It is doing a good job!”

Precision chuckled, leaning back in her chair. “Ah, my dear Accuracy, you’re so optimistic. But please tell me, how many of those ‘correct’ classifications are truly meaningful? You count all correct predictions the same, whether they are for spam or regular emails.”

Accuracy frowned. “I let everyone see the big picture. Most people trust me because I provide a clear and simple measure of success.”

Recall was observing the discussion with a great deal of excitement.

Accuracy continued, “I give our town, Classifia, a straightforward, clear view of how well the model is performing overall. Isn’t that what matters most?”

Recall, finally jumped in, “Straightforward doesn’t always mean insightful, Accuracy. You might look good even when the model fails, especially if one class dominates.”

Precision attacked again, “What if the model is simply just guessing not-spam most of the time? It would still look good, even though it is wrong about most of the spam. Because there are very few spam among all the emails.”

Accuracy muttered something under his breath, but no one understood what he said.

“That’s where I’m different,” continued Precision, “I focus on this: I make sure the model is not calling something spam unless it really is!”

Precision’s Point of View

Precision rose gracefully, pointing to the hologram. “Let’s focus on the details,” she said. “I measure the percentage of correctly identified spam emails out of all emails predicted as spam. For this model, precision is 75%. It means the model isn’t too bad, but it falsely flags 25% of emails as spam. They were actually simply regular emails. That’s a lot of false alarms.”

Recall, the ever-diligent worker, interjected. “You’re so selective, Precision. You are only interested in what the model predicts as spam. What about all the actual spam emails it misses as it predicted as not-spam?”

“Oh, here we go again,” said Accuracy.

“What is your suggestion, then?” asked Precision.

Recall’s Approach

Recall adjusted his glasses and stepped forward. “I care about capturing all the spam emails,” he said firmly. “For this model, recall value is 60%. That means it correctly identifies only 60% of the true spam emails, but it misses 40%. Your precision value might be better than this, but what good is a spam filter if it lets so many spam emails through?”

Precision rolled her eyes. “You are too generous, Recall. You would let a model call everything spam just to ensure no spam gets through. That’s not practical.”

F1’s Wisdom

At this point, Miss F1 Score, the youngest and most diplomatic of the group, cleared her throat. “Enough arguing,” she said with a calm but authoritative tone. “You are both right, and wrong. That’s why I exist.”

The others turned to her as she explained. “I balance Precision and Recall. My score is the harmonic mean of the two, ensuring neither is ignored. For this model, the F1 Score is 72%. It’s not perfect, but it gives a fair sense of the trade-off between catching spam and avoiding false alarms.”

Accuracy raised an eyebrow. “And what about me? You always leave me out.”

F1 Score smiled kindly. “You are useful when the data is balanced, Accuracy. But in cases like this —where spam is rare— your overall success rate can hide important details. Right now, we have an imbalanced email composition in terms of being or not being spam, and we need a more nuanced perspective.”

A Surprise Guardian Enters the Scene

Suddenly, the doors of the hall opened, and a figure robed in flowing, gradient-colored fabrics entered. It was Mr. ROC-AUC, the overseer of thresholds and separability.

“Wow, who’s here?” said Precision.

“Our cool friend with the rhyming name,” said Recall.

“Meh,” said Accuracy. He was not happy with that new member of the evaluation team.

Finally, Miss F1 Score showed the necessary courtesy and said, “Welcome, my friend!”

“Thank you, my dear, and greetings to you all, fellow guardians!” answered Mr. ROC-AUC.

“We were simply discussing how we evaluate the results of the model you see in this hologram,” explained Precision.

“What is your opinion?” asked Recall.

Mr. ROC-AUC gave the hologram a charismatic look. After thinking about what he was going to say for a moment, he began to speak.

“While each of you shines in your specific roles, I bring balance to the broader view. I evaluate how well the model distinguishes between all classes, not just specific instances. Whether the threshold shifts high or low, I measure performance across the spectrum. My role ensures the true picture of separability,” said Mr. ROC-AUC.

“So what?” asked Accuracy. He was a little moody that day. “You talk about balance and separability, but what do you really bring to the table?”

Mr. ROC-AUC was a little surprised by Accuracy’s outburst but answered briefly. “I ensure the model is evaluated on its ability to separate classes, regardless of threshold. While all of you rely on fixed thresholds, I evaluate the model across all possible thresholds. This way, I provide insights into how well the model can separate positive and negative classes, regardless of where the decision boundary is set.”

Accuracy was determined to continue his grudge. “But does that even help the Classifia day-to-day? People want a simple measure they can understand. All your curves and thresholds confuse more than they clarify.”

Mr. ROC-AUC started to get angry. “Confusion arises only when simplicity masks the truth. Your measure alone can mislead when class imbalances exist. A high accuracy in such cases could just be blind luck.”

“Luck?” shouted Accuracy, “my results are reliable. I capture the big picture, not cherry-picked nuances like you do.”

Precision and Recall chose not to speak out, as they wanted to stay away from the increasingly heated argument.

“Big picture?” asked Mr. ROC-AUC, “or an incomplete one? Without considering separability, your so-called ‘big picture’ is a blurry portrait. Classifia deserves clarity, not just convenience. Unlike you, which can be misleading in imbalanced datasets, I ensure fairness by examining how well the model performs in distinguishing the minority class from the majority class, independent of class distributions. Also, my results allow decision-makers to understand which model is inherently better at differentiating classes, even before setting a fixed threshold. I am not into only one model’s output, I can also compare different models in only one curve.”

“Ah, again, bla bla bla,” said Accuracy.

F1 Score interjected, “Enough, both of you! We all have our strengths. Classifia thrives because we work together, not against each other.”

The Verdict and Harmony

After a long discussion, the five mighty classification guardians and evaluators reached a consensus.

Accuracy admitted, “I may be the simplest, but I cannot handle imbalance well. But I would be happy to give my insights when the class distribution is balanced.”

Precision nodded. “And I am great for detecting false positives, but I can also ignore the big picture. I need to work closely with Recall.”

Recall agreed with her. “I sometimes focus on catching everything, but it lets me be too lenient with false positives. I always need to consult Precision to avoid this.”

Mr. ROC-AUC was calm now. “And I ensure that the model’s ability to distinguish between classes is evaluated holistically, giving you a fair and balanced view, no matter the threshold or class distribution. However, my curves sometimes make things seem better than they are, especially when the curve looks overall good but the actual predictions at specific thresholds fail to deliver. This might be a hidden danger time to time.”

Miss F1 Score concluded, “That’s why we’re stronger together. Each of us brings something unique to the table, and when used wisely, we give a complete picture of a model’s performance.”

As they reached an agreement, the sun unexpectedly emerged from behind the clouds and began to show itself above the tower of the observatory.

From that day on, the five evaluators worked as a team, ensuring that every classification model was judged fairly and comprehensively. Their combined wisdom guided the citizens of Classifia, reminding them that true understanding comes from multiple perspectives.