![]() Any equipment measuring data has limitations. Part of it may be simply measurement error. A better interpretation is that noise represents the unknown in our view of the world. Randomness isn't a statement about data, it's a statement about our state of knowledge. In orthodox statistics we often think of noise as just some randomness added to the data, but as a Bayesian I can't quite swallow this view. It's also worthwhile thinking about what "noise" is. No matter how clever our model is, we can never reduce our MSE to being less than the variance related to the noise. The variance of the noise in our data is an irreducible part of our MSE. It is important to stress here how important this insight is. Bias is used when we have an estimator, \(\hat(x)^2]$$Īnd here we see that one of the terms in our MSE reduced to \(\sigma^2\), or the variance in the noise in our process. We've talked about expectation and variance quite a bit on this blog, but we need to introduce the idea of bias. The primary mathematical tools we'll be using are expectation, variance and bias. We'll also find that baked into the definition of this metric is the idea that there is always some irreducible uncertainty that we can never quite get rid of. By breaking down Mean Squared Error into bias and variance, we'll get a better sense of how models work and ways in which they can fail to perform. Despite the relatively simple nature of this metric, it contains a surprising amount of insight into modeling. In this post we're going to take a deeper look at Mean Squared Error.
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