neliövirheeseen

Neliövirheeseen, or mean squared error (MSE) in English, is a common metric used to measure the performance of regression models. It quantifies the average of the squares of the errors, where an error is the difference between an observed value and the value predicted by the model. A lower MSE indicates a better fit of the model to the data.

The calculation of MSE involves subtracting the predicted value from the actual observed value for each data point, squaring this difference, and then averaging all these squared differences. This process penalizes larger errors more heavily due to the squaring operation. Mathematically, if $y_i$ is the actual value and $\hat{y}_i$ is the predicted value for the $i$-th data point, the MSE is calculated as:

$MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$

where $n$ is the number of data points.

MSE is widely used because it is differentiable, which makes it suitable for optimization algorithms used in training machine learning models. However, its sensitivity to outliers can be a drawback. Outliers, due to their large deviations from the predicted values, can significantly inflate the MSE, potentially misleading model evaluation. In such cases, metrics like Mean Absolute Error (MAE) might be preferred as they are less affected by extreme values. Despite this, MSE remains a fundamental and widely applied measure in statistical modeling and machine learning for assessing prediction accuracy.