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I know that high bias and low variance implies underfitting, while high variance and low bias implies overfitting. But what if both bias and variance are high?

Does this mean that the model is underfit and overfit at the same time? Or is it neither overfit nor underfit?

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It's not typical to have high degrees of both, but if it happens it's neither overfitting nor underfitting because these are defined with contrasting amounts of bias and variance. An overfitting model performs very well on the dataset it learns. So, it has low bias by definition. An underfitting model doesn't properly fit the data, which means it isn't very sensitive to the changes in the features, so having low variance.

Artificially, you can take an overfitted model, add an effective constant amount to its output and create a high bias and variance case, but I haven't encountered this case naturally before.

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