Which of the following reasons makes mean squared error (MSE) often preferable over mean absolute error (MAE) in machine learning?

Mean squared error (MSE) is often preferred over mean absolute error (MAE) in machine learning primarily because it is differentiable. This characteristic makes MSE particularly useful for optimization algorithms that rely on gradient descent, which is a common approach in training machine learning models. When the loss function, like MSE, is differentiable, it allows for the computation of gradients, enabling algorithms to update model parameters effectively in the direction that minimizes the error.

The differentiability of MSE means that it provides a smooth surface for optimization, enabling more precise updates to model parameters during training. In contrast, MAE has points of non-differentiability that can complicate optimization, especially when the absolute value function leads to kinks in the error surface.

While MSE does always yield a positive value and is generally easy to compute, these aspects are not as impactful for model training as differentiability. The size of the training set does not directly relate to the choice between MSE and MAE; the preference is more about how these metrics respond to errors and how that affects the training process itself.