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Mean Squared Error
The Mean Squared Error (MSE) of an estimator with respect to a parameter is the expected value of the squared error:
It can also be expressed as the sum of the squared bias of the estimator and its variance:
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Derivation for MSE to Bias Squared Plus Variance
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 that the total expected squared error of an estimator can be decomposed into two primary components, which statement best analyzes the error characteristics of these two models?
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.