Case context: You are leading a machine learning team building a vision system for a self-driving car. Your current system has a 10% overall error rate in detecting road obstacles. You conduct an error analysis on a set of misclassified examples and find that 5% of the mistakes are due to misidentifying traffic cones, while 40% of the mistakes are due to failing to detect pedestrians at night. Your team is debating which issue to address first, as fixing traffic cones seems like a much easier engineering task.

Question: Based on the concept of the error category fraction ceiling, which project should you prioritize and why? Calculate the best possible overall error rate you could achieve in each scenario if you perfectly fixed the respective category.

Sample answer: You should prioritize the pedestrian detection project. The error category fraction serves as a ceiling on potential improvement. For traffic cones, they account for only 5% of the errors. Therefore, even if you perfectly fix cone detection, you can only remove 5% of your errors, reducing the overall error rate from 10% to 9.5%. By contrast, pedestrians at night account for 40% of the errors. Perfectly fixing this category could reduce your total errors by 40%, bringing the overall error rate down from 10% to 6.0%. Therefore, despite the perceived difficulty, the potential impact of fixing pedestrian detection is vastly higher.

Key points:

• Identifies the pedestrian detection project as the correct priority.
• Applies the concept of the error category fraction as a ceiling on possible error reduction.
• Calculates the best possible error rate for fixing traffic cones (9.5%).
• Calculates the best possible error rate for fixing pedestrian detection (6.0%).

Rubric: The learner must identify the pedestrian project as the priority, correctly apply the concept of the error category fraction as a ceiling, and accurately calculate the theoretical best overall error rates for both scenarios.