Why is mean square error a bad measure of model performance? What would you suggest instead?

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Mean Squared Error (MSE) gives a relatively high weight to large errors — therefore, MSE tends to put too much emphasis on large deviations. A more robust alternative is MAE (mean absolute deviation).

Mean squared error (MSE) is not necessarily a “bad” measure of model performance, but it has some limitations and may not always be the most appropriate choice depending on the context of the problem. Here are some reasons why MSE might not be the best choice:

  1. Sensitive to outliers: MSE gives higher weights to larger errors, which means outliers can have a significant impact on the overall error. In cases where outliers are present, MSE might not provide an accurate representation of the model’s performance.
  2. Does not reflect real-world costs: In some situations, the cost associated with different types of errors varies. For example, in a medical diagnosis scenario, the cost of falsely diagnosing a disease as negative might be much higher than falsely diagnosing it as positive. MSE treats all errors equally, which might not align with the actual costs.
  3. Not intuitive: MSE is in the units of the squared target variable, which might not be easily interpretable or intuitive for stakeholders who are not familiar with the data.

Instead of MSE, depending on the problem domain and specific requirements, you might consider alternative evaluation metrics:

  1. Mean Absolute Error (MAE): MAE is less sensitive to outliers compared to MSE since it takes the absolute differences between predictions and actual values. It might be a better choice if outliers are present and need to be handled carefully.
  2. Root Mean Squared Error (RMSE): RMSE addresses the issue of units being squared in MSE by taking the square root of MSE. It is commonly used and provides a measure of the spread of errors around the mean.
  3. Median Absolute Error: Similar to MAE, but instead of averaging the absolute errors, it calculates the median absolute error. This metric is robust to outliers and can provide a more accurate representation of model performance when outliers are present.
  4. R-squared (Coefficient of Determination): R-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variables. It provides a measure of how well the model fits the data and can be useful for comparing different models.
  5. Customized loss functions: In some cases, you might need to define a custom loss function that aligns with the specific requirements and objectives of the problem. This allows you to incorporate domain knowledge and tailor the evaluation metric to the particular needs of the project.

Ultimately, the choice of evaluation metric depends on the specific characteristics of the data, the objectives of the problem, and the preferences of stakeholders. It’s essential to consider these factors carefully when selecting an appropriate metric for evaluating model performance.