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Derivation of the MSE Bias–Variance Decomposition
For an estimator of a fixed parameter , the mean squared error decomposes as follows: The third line is obtained by adding and subtracting ; its two terms are the squared bias and variance, respectively.
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General Implications of MSE for Machine Learning
Two different statistical models, Model A and Model B, are used to estimate a true parameter value which is known to be 100. After generating a large number of predictions with both models, the following observations are made:
- The average of all predictions from Model A is 105. The individual predictions from Model A are all very close to each other.
- The average of all predictions from Model B is 100. The individual predictions from Model B are spread out over a wide range of values.
Given
Calculating Error Components of a Statistical Estimator
A machine learning engineer is comparing two estimators, Estimator A and Estimator B, to predict a certain value. The primary goal is to minimize the expected squared error. After analysis, the following characteristics are determined:
- Estimator A: Has a bias of 0 and a variance of 4.
- Estimator B: Has a bias of 1 and a variance of 2.
Which estimator should be chosen, and why?
When comparing two statistical estimators for a specific task, the estimator with the lower bias will always result in a lower overall Mean Squared Error.
Derivation of the MSE Bias–Variance Decomposition