Identifying Simultaneous High Bias and High Variance

Dev Error in High Bias and Variance Scenarios

Necessary Algorithmic Adjustments for _____ Problem

Interpreting Learning Curve Components

Steps for Diagnosing High Bias and Variance

Question:
Explain what a learning curve looks like when an algorithm has both high bias and high variance, and what general conclusion must be drawn about next steps for the algorithm.

Sample answer:
The learning curve will show a training error that is large, meaning it is much higher than the desired level of performance, which indicates high bias. Additionally, the dev error will be much larger than the training error, which indicates high variance. The conclusion drawn from this pattern is that you will have to find a way to reduce both bias and variance in your algorithm.

Key points:
- Training error is much higher than desired performance.
- Dev error is much higher than training error.
- Algorithm changes must aim to reduce both bias and variance.

Rubric:
A strong answer must clearly state the relationship between training error and desired performance (high bias), the relationship between dev error and training error (high variance), and the required action (reducing both).

Addressing Simultaneous Bias and Variance Issues

Case context:
You are reviewing the learning curve for a new prediction system. The desired error rate is 2%, but the training error has plateaued at 15%. Furthermore, the dev error is currently sitting at 28%.

Question:
Based on this learning curve data, what should you diagnose about the system's bias and variance, and what is your broad recommendation for the algorithm?

Sample answer:
The system has significant bias because the training error (15%) is much higher than the desired level of performance (2%). It also has significant variance because the dev error (28%) is much larger than the training error. The broad recommendation is to find ways to reduce both bias and variance in the algorithm.

Key points:
- Significant bias is present due to 15% training error vs 2% desired performance.
- Significant variance is present due to 28% dev error vs 15% training error.
- Recommendation is to reduce both bias and variance.

Rubric:
The response must correctly identify high bias due to the high training error, identify high variance due to the gap between training and dev error, and recommend reducing both.

Diagnostic Report on a New System

Question:
What specific relationship between dev error and training error indicates significant variance when an algorithm already shows significant bias?

Sample answer:
The dev error is much larger than the training error.

Key points:
- Dev error is larger than training error.

Rubric:
The answer should explicitly state that dev error is much higher or larger than the training error.

Recognizing the Dual Problem Pattern

Action Required for High Bias and Variance

Training Error Indicator for Bias

A learning curve can indicate both significant bias and significant variance when training error is much higher than the desired performance level and dev error is much higher than training error. In this case, the algorithm needs changes that reduce both bias and variance.

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Plotting both training error and dev error on the same learning curve makes it easier to extrapolate dev-error behavior. Looking at the full curve gives a more comprehensive picture of algorithm performance across different training-set sizes than measuring training and dev error only at the largest available training set size.

Interpreting Learning Curves with Training and Dev Error

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A standard learning-curve pattern for high avoidable bias occurs when, at the largest training-set size, training error remains far above the desired performance level. If the gap between training error and dev error is small, this indicates small variance despite the large avoidable bias.

Learning Curve Pattern for High Avoidable Bias

When training-set performance is already close to the optimal error rate, there is little room for bias improvement. If the algorithm is not generalizing well to the dev set, there is ample room for variance improvement.

Learning Curve Pattern for High Variance

Learning Curve Pattern for Both High Bias and High Variance

Purpose of plotting training and dev error together

Measuring error only at the rightmost point

Extrapolating the _____ curve

Key Concepts of Interpreting Learning Curves

Steps to comprehensively evaluate algorithm performance

Question:
Contrast the insights gained from examining a full learning curve (plotting both training and dev error) versus measuring error only at the rightmost point. Why is the full curve preferred?

Sample answer:
Measuring error at only the rightmost point provides a static snapshot of performance corresponding strictly to using all currently available training data. This gives no insight into trends or data scaling. By plotting the full learning curve with both training and dev error across different dataset sizes, we gain a comprehensive picture of how the algorithm's performance changes as data increases. Viewing both curves on the same plot allows us to more confidently extrapolate the dev error curve to predict whether gathering more data will be beneficial.

Key points:
- The rightmost point only shows performance for all currently available data.
- The full curve gives a comprehensive picture across different training set sizes.
- Plotting both curves together helps in confidently extrapolating the dev error curve.

Rubric:
A strong response should state that the rightmost point only shows performance on maximum available data, while the full curve reveals performance across different sizes. It must mention that plotting both curves aids in extrapolating the dev error curve.

Advantages of the full learning curve over a single point

Case context:
A machine learning team has measured their algorithm's training and dev set error using their entire dataset of 10,000 examples (representing the rightmost point of their data). They are unsure if they should spend a month collecting 5,000 more examples.

Question:
What visual tool should the team construct, and what specific curves should it include to help them make a confident decision about data collection?

Sample answer:
The team should plot a full learning curve showing both the training error curve and the dev error curve across different subset sizes of their data (e.g., 2,000, 4,000, 6,000, 8,000, and 10,000). By examining the full curves together on the same plot rather than just the final point, they can more confidently extrapolate the dev error curve's trajectory to see if more data is likely to lower the error.

Key points:
- Construct a full learning curve across different training set sizes.
- Include both the training error curve and the dev error curve on the same plot.
- Extrapolate the dev error curve visually to inform the decision.

Rubric:
The answer must propose plotting a full learning curve across different dataset sizes, rather than relying on the single rightmost point. It must also specify plotting both training and dev error to allow for dev error extrapolation.

Deciding whether to collect more training data

Question:
What is the primary advantage of examining both the training error curve and the dev error curve on the same plot, as opposed to looking at them separately?

Sample answer:
Examining both curves on the same plot allows us to more confidently extrapolate the dev error curve.

Key points:
- Helps extrapolate the dev error curve.
- Provides more confidence in the extrapolation.

Rubric:
The response should explicitly state that plotting them together aids in the confidence of extrapolating the dev error.

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