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Mean Absolute Error (MAE)#

Mean Absolute Error (MAE) is a popular metric used in assessing regression model performance for its overall simplicity and interpretability. It measures the average magnitude of errors in predictions, without considering their direction.

MAE represents the mean of the absolute differences between predicted and actual values across a dataset, treating each discrepancy equally. A large value is indicative of poor performance, and communicates how much on average a prediction will deviate from the actual value in the units of the ground truth.

Implementation Details#

MAE is calculated by taking the average of the absolute differences between the predicted values and the actual values. This can be mathematically represented as:

\[ \frac{1}{N} \sum_{i=1}^{N}|x_i-y_i| \]

where \(x\) is the numerical value from the actual values, and \(y\) is the corresponding numerical value from the predicted values for a total of \(N\) number of predictions.


Temperature Estimation:

Ground Truth Temperature (°C) Predicted Temperature (°C)
25 27
35 30
\[ \begin{align} \text{MAE} &= \frac{|25 - 27| + |35 - 30|}{2} \\[1em] &= 3.5 \end{align} \]

Age Estimation:

Ground Truth Age (Years) Predicted Age (Years)
60 70
40 20
\[ \begin{align} \text{MAE} &= \frac{|60 - 70| + |40 - 20|}{2} \\[1em] &= 15 \end{align} \]

Limitations and Biases#

While Mean Absolute Error (MAE) is straightforward to interpret, it treats all errors equally, which might not reflect the true impact of outliers or extreme errors on the model's performance.

In scenarios where the dataset contains outliers or extreme values, MAE might not accurately represent the model's overall predictive capability in a wholistic manner. It's important to complement MAE with other evaluation metrics, such as Root Mean Squared Error (RMSE), which penalizes larger errors more heavily.

Thus, while MAE provides valuable insights into prediction accuracy, it's advisable to consider it alongside other metrics for a comprehensive evaluation of regression models.