Average Absolute Deviation Score

In predictive analytics and machine learning, evaluating the quality of predictions is crucial for understanding model performance. One of the most fundamental and interpretable metrics for measuring prediction accuracy is the Average Absolute Deviation (AAD) score, which quantifies the average magnitude of errors between predicted and actual values.

Unlike metrics that square the errors (which can over-emphasize large outliers), the AAD treats all errors linearly based on their absolute magnitude. This makes it particularly intuitive and interpretable—the AAD value is expressed in the same units as the original data, representing the average distance between predictions and reality.

Mathematical Definition:

Given a set of n actual values y₁, y₂, ..., yₙ and their corresponding predicted values ŷ₁, ŷ₂, ..., ŷₙ, the Average Absolute Deviation is computed as:

$$AAD = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i|$$

Where:

• |y_i - ŷ_i| represents the absolute difference between the actual and predicted value for the i-th sample
• n is the total number of samples

Key Properties:

1. Non-negative: AAD is always ≥ 0, with 0 indicating perfect predictions
2. Same units as data: If you're predicting temperature in Celsius, AAD is also in Celsius
3. Robust to outliers: Compared to squared-error metrics, AAD is less sensitive to extreme errors
4. Symmetric: Over-predictions and under-predictions of the same magnitude contribute equally

Your Task:

Implement a function that computes the Average Absolute Deviation score between two arrays: one containing the actual (ground truth) values and another containing the predicted values. Both arrays will have the same length and contain floating-point numbers.