Howtosignalprocessing
- What is the relation between bias-variance and MSE?
- How do you calculate MSE from bias?
- Can MSE be greater than 1?
- Is MSE equal to variance?
What is the relation between bias-variance and MSE?
It shows whether our predictor approximates the real model well. Models with high capacity have low bias and models with low capacity have high bias. Since both bias and variance contribute to MSE, good models try to reduce both of them. This is called bias-variance trade-off.
How do you calculate MSE from bias?
Definition 2.1 The mean squared error (mse) of an estimator ˆθ is Eθ[(ˆθ− θ)2]. = varθ(ˆθ) + bias2(ˆθ), where bias(ˆθ) = Eθ(ˆθ) − θ. [NB: sometimes it can be preferable to have a biased estimator with a low variance - this is sometimes known as the 'bias-variance tradeoff'.]
Can MSE be greater than 1?
However, the disadvantage of using MSE than R-squared is that it will be difficult to gauge the performance of the model using MSE as the value of MSE can vary from 0 to any larger number. However, in the case of R-squared, the value is bounded between 0 and 1.
Is MSE equal to variance?
To find an estimator with good MSE properties, we need to find estimators that control both variance and bias. For an unbiased estimator ˆθ, we have MSEˆθ = E(ˆθ − θ)2 = V ar(ˆθ) and so, if an estimator is unbiased, its MSE is equal to its variance.
