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Mean Absolute Error (MAE)

Description: Mean Absolute Error (MAE) is a measure of the difference between two continuous variables. It is the average of the absolute differences between predicted values and observed values. MAE is a widely used metric for evaluating the performance of machine learning models.
Number of Questions: 15
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Tags: mean absolute error mae machine learning model evaluation
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What is the formula for calculating MAE?

  1. MAE = (1/n) * Σ|y_i - y_hat_i|

  2. MAE = (1/n) * Σ(y_i - y_hat_i)^2

  3. MAE = (1/n) * Σy_i * y_hat_i

  4. MAE = (1/n) * Σ(y_i + y_hat_i)

Show answer
Correct Option: A
Explanation:

MAE is calculated by taking the average of the absolute differences between the predicted values (y_hat_i) and the observed values (y_i).

What is the range of MAE values?

  1. [0, 1]

  2. [0, ∞)

  3. [-1, 1]

  4. [-∞, ∞)

Show answer
Correct Option: B
Explanation:

MAE values can range from 0 to infinity, with 0 indicating perfect agreement between predicted and observed values and larger values indicating greater disagreement.

Which of the following is NOT a disadvantage of MAE?

  1. It is sensitive to outliers.

  2. It is not a differentiable function.

  3. It is easy to interpret.

  4. It is not affected by the scale of the data.

Show answer
Correct Option: D
Explanation:

MAE is not affected by the scale of the data, unlike other metrics such as Mean Squared Error (MSE) and Root Mean Squared Error (RMSE).

Which of the following is a common application of MAE?

  1. Evaluating the performance of machine learning models

  2. Measuring the accuracy of weather forecasts

  3. Estimating the error in sensor measurements

  4. All of the above

Show answer
Correct Option: D
Explanation:

MAE is used in a variety of applications, including evaluating the performance of machine learning models, measuring the accuracy of weather forecasts, and estimating the error in sensor measurements.

How does MAE compare to other error metrics such as MSE and RMSE?

  1. MAE is always smaller than MSE and RMSE.

  2. MAE is always larger than MSE and RMSE.

  3. MAE is sometimes smaller and sometimes larger than MSE and RMSE.

  4. MAE is always equal to MSE and RMSE.

Show answer
Correct Option: C
Explanation:

The relationship between MAE, MSE, and RMSE depends on the distribution of the errors. In some cases, MAE may be smaller than MSE and RMSE, while in other cases it may be larger.

What is the relationship between MAE and the median absolute error (MdAE)?

  1. MAE is always equal to MdAE.

  2. MAE is always larger than MdAE.

  3. MAE is always smaller than MdAE.

  4. The relationship between MAE and MdAE depends on the distribution of the errors.

Show answer
Correct Option: D
Explanation:

The relationship between MAE and MdAE depends on the distribution of the errors. In some cases, MAE may be larger than MdAE, while in other cases it may be smaller.

Which of the following is NOT a limitation of MAE?

  1. It is sensitive to outliers.

  2. It is difficult to interpret.

  3. It is not a differentiable function.

  4. It is affected by the scale of the data.

Show answer
Correct Option: B
Explanation:

MAE is relatively easy to interpret, as it represents the average absolute difference between predicted and observed values.

How can MAE be used to improve the performance of machine learning models?

  1. By identifying the features that contribute most to the error.

  2. By tuning the hyperparameters of the model.

  3. By collecting more data.

  4. All of the above

Show answer
Correct Option: D
Explanation:

MAE can be used to improve the performance of machine learning models by identifying the features that contribute most to the error, tuning the hyperparameters of the model, and collecting more data.

Which of the following is NOT a potential advantage of using MAE over other error metrics?

  1. It is easy to interpret.

  2. It is robust to outliers.

  3. It is a differentiable function.

  4. It is not affected by the scale of the data.

Show answer
Correct Option: B
Explanation:

MAE is not robust to outliers, unlike other error metrics such as Median Absolute Error (MdAE) and Root Mean Squared Error (RMSE).

What is the relationship between MAE and the coefficient of determination (R^2)?

  1. MAE is always positively correlated with R^2.

  2. MAE is always negatively correlated with R^2.

  3. MAE is sometimes positively correlated and sometimes negatively correlated with R^2.

  4. MAE is never correlated with R^2.

Show answer
Correct Option: C
Explanation:

The relationship between MAE and R^2 depends on the distribution of the errors. In some cases, MAE may be positively correlated with R^2, while in other cases it may be negatively correlated.

Which of the following is NOT a common method for reducing MAE?

  1. Using a more complex model.

  2. Collecting more data.

  3. Tuning the hyperparameters of the model.

  4. Removing outliers from the data.

Show answer
Correct Option: A
Explanation:

Using a more complex model is not a common method for reducing MAE, as it can lead to overfitting and increased variance.

How can MAE be used to compare the performance of different machine learning models?

  1. By calculating the MAE for each model and selecting the model with the lowest MAE.

  2. By plotting the MAE of each model against the number of training examples.

  3. By using a statistical test to determine if there is a significant difference in the MAE of the models.

  4. All of the above

Show answer
Correct Option: D
Explanation:

MAE can be used to compare the performance of different machine learning models by calculating the MAE for each model, plotting the MAE of each model against the number of training examples, and using a statistical test to determine if there is a significant difference in the MAE of the models.

Which of the following is NOT a potential disadvantage of using MAE over other error metrics?

  1. It is not robust to outliers.

  2. It is difficult to interpret.

  3. It is not a differentiable function.

  4. It is affected by the scale of the data.

Show answer
Correct Option: B
Explanation:

MAE is relatively easy to interpret, as it represents the average absolute difference between predicted and observed values.

How can MAE be used to identify the features that contribute most to the error?

  1. By calculating the MAE for each feature.

  2. By plotting the MAE of each feature against the number of training examples.

  3. By using a statistical test to determine if there is a significant difference in the MAE of the features.

  4. All of the above

Show answer
Correct Option: D
Explanation:

MAE can be used to identify the features that contribute most to the error by calculating the MAE for each feature, plotting the MAE of each feature against the number of training examples, and using a statistical test to determine if there is a significant difference in the MAE of the features.

Which of the following is NOT a potential advantage of using MAE over other error metrics?

  1. It is easy to interpret.

  2. It is robust to outliers.

  3. It is a differentiable function.

  4. It is not affected by the scale of the data.

Show answer
Correct Option: B
Explanation:

MAE is not robust to outliers, unlike other error metrics such as Median Absolute Error (MdAE) and Root Mean Squared Error (RMSE).

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