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Assume that I trained a nonlinear model , one feature of the training data has very low variance, because of this, the same feature of the test could be quite different, at least in scale, from the one in the training data. Assume that this feature is really important to the prediction of the target. I found that in this case the model cannot learn the relation between the target and this feature, as the variance of this feature in the train set is very low. And for example , if the feature of the test set is 1/2 in scale compared to that in the train set, the model(like tree model) will predict the same value as for train set. My question is: how to train a model(linear or nonlinear) if the variance of one feature is very low and maybe very different in scale to the one in test set, but that feature is an important feature? thanks

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    $\begingroup$ It means that your training set is substantially different to your test set, and it is possible that your model may perform badly. Imagine having to build a model on 10 year-old children to predict the behaviour of adults - you might see some difference between those aged just 10 and those almost 11 and incorporate this into your model, but not enough to extrapolate a long way $\endgroup$
    – Henry
    Commented Aug 10, 2018 at 13:15
  • $\begingroup$ we have to add more datas so that every feature should have more variance, right? $\endgroup$
    – Hao Yu
    Commented Aug 12, 2018 at 2:19

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