Which cost function calculates the average difference between estimated and actual values without factoring in their signs?

The Mean Absolute Error (MAE) is the appropriate cost function when you want to calculate the average difference between estimated and actual values without considering the direction of the errors (i.e., whether they are positive or negative). MAE accomplishes this by taking the absolute value of each individual error, which means that it treats all discrepancies equally regardless of their signs. As a result, MAE effectively captures the magnitude of errors, providing a straightforward interpretation of average error in terms of the original data units.

In contrast, other options such as Root Mean Squared Error (RMSE) and Mean Squared Error (MSE) square the differences, which could introduce a bias towards larger errors due to squaring. While this may highlight significant outliers, it doesn't fulfill the requirement of disregarding the sign of the errors. Mean Absolute Percentage Error (MAPE) is another useful metric but measures errors in percentage terms and can be influenced by extreme values, especially when actual values are small or zero. Hence, MAE remains the best choice for the specific need of averaging differences without considering their signs.