From what I understand, there is a relationship between bias and underfitting; as well as variance and overfitting.
Is a 'biased model' another word for an 'underfitted model'? Likewise, is a "varianced' model" another word for an 'overfitted model'?
A good explanation of the relationship between these concepts is in
Briefly put, a neural network can achieve zero variance very easily by underfitting: just return a constant output value regardless of the input values. This is a case of extreme under-fitting, and there will be a big bias (tendency to be systematically off target) because the network made no effort to fit the training data.
A neural network can achieve zero bias easily by overfitting: just make it big and complicated enough to ensure that the outputs exactly match for all the data points from the training data. This is an extreme case of over-fitting, and assuming that there is actually noise in the training data set, you will end up with a large variance when you apply it to different data sets.
I suppose in a "perfect information about the universe" sense of the word, a biased model is underfitted. Philosophically, it's correct - the bias would go away if you could just include one (or more) terms. Practically speaking, issues like residual confounding may mean a model is biased even if the fit of the known variables is perfect.
As with others, I haven't heard of "varianced" as a term, but have heard overfitted models with very high errors around their estimates referred to as unstable, as mild changes in data, etc. produce wildly different estimates.
But in general, I think viewing over vs. underfitting through the lense of the bias vs. precision tradeoff is a valid one.
