All About: Mean Squared Error (MSE), Mean Absolute Error (MAE) and RMSE
Performance Metrics or Loss Function in Machine Learning for Regression:
In data analysis, machine learning and statistics model performance assessment is an absolute must to evaluate how effective the predictive algorithms really are. Performance metrics act as a quantification scale for how well models make predictions compared to its real value. Of all of the many metrics available, Mean Squared Error (MSE), Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) are fundamental measures of prediction accuracy. In this chapter, we will explain in turn these three metrics their meaning, mathematical definition and how to interpret them.
Mean Squared Error (MSE):
Mean Squared Error(MSE) is a widely used metric and means the average of the squares of the errors between estimated and accurate values. It provides a measure of the model’s accuracy in terms of mean squared difference between it’s predictions and real world observations.
Advantages :
- Differentiable
- It has One Local & Global Minima
Disadvantages :
- Not Robust to Outlier
- It Change its Unit
Mean Absolute Error (MAE):
Mean Absolute Error (MAE) is yet another widely employed measure of regression model precision. Unlike MSE, MAE computes the average of absolute differences between predicted and actual values. It offers an average measure of the relative magnitude errors, ignoring their direction.
Advantages :
- It is Robust to Outlier
- It will be same Unit
Disadvantages :
- Convergence usually take more time
- In Optimization take complex process
Root Mean Squared Error (RMSE):
The Root Mean Squared Error (RMSE) comes from MSE and is a measure of the standard deviation of errors, or residuals, in other words mismatches between predicted and true values. RMSE turns out to be particularly handy because its error metric is expressed on the same scale as our target variable, making for a more intuitive interpretation of what really is going on here.
Advantages :
- The value of MSE is same as output unit, which makes the interpretation of loss easy.
Disadvantages :
- Not Robust to Outlier
Conclusion:
In summary, three common evaluation indexes for data analysis and machine learning include MSE, MAE, and RMSE. Where as mean square error measures the squared differences between predicted and actual values, mean absolute error focuses on magnitudes of difference and root mean square errors provide standardized measure for these gaps.
Each index has its own advantages and shortcomings, and the choice between them will depend of the data itself and personal taste of the analyst.Competent application of performance measures like these allows practitioners to choose models wisely and also boosts the quality of both predictions and the understanding gleaned from data analysis results.
Expected Question:
1. What is Residual Error?
Answer:👉Difference between the Actual Point & the Predicted point that’s called Residual Error.
2. What is the difference between MSE and RMSE and MAE?
Answer:👉 Mean Squared Error(MSE) and Root Mean Square Error penalizes the large prediction errors , vi-a-vis, Mean Absolute Error (MAE). However, RMSE is widely used than MSE to evaluate the performance of the regression model with other random models as it has the same units as the dependent variable (Y-axis).
3. Is RMSE higher than MSE?
Answer:👉RMSE is the square root of MSE. MSE is measured in units that are the square of the target variable, while RMSE is measured in the same units as the target variable. Due to its formulation, MSE, just like the squared loss function that it derives from, effectively penalizes larger errors more severely.
4. What is a good RMSE value?
Answer:👉 Although, the values of RMSE may range between zero and infinity, however, an RMSE value between 0.2 and 0.5 shows how accurate the model is in predicting the actual value.
5. What is a good MSE value?
Answer:👉 The value of the error ranges from zero to infinity. MSE increases exponentially with an increase in error. A good model will have an MSE value closer to zero.
6. Is high or low MSE better?
Answer:👉 MSE is used to check how close estimates or forecasts are to actual values. Lower the MSE,the closer is forecast to actual. This is used as a model evaluation measure for regression models and the lower value indicates a better fit.
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