Let's say we want to predict job applicant' salary. We have a dataset with following features:

{Age, Experience, Education, Astrological_Sign, Weather_Today}

5 features in total.

In this set, features Astrological_Sign and Weather_Today are irrelevant to one's chances of getting a good (or bad) salary. If we train a model on all 5 of these features, it would perform worse than if we were to train it on Age, Experience and Education only, because it learns irrelevant information.

Q: Can these two features Astrological_Sign and Weather_Today, in terms of definitions, be called a Noise in our data? If no, how must they be called? Simply "irrelevant features" as I called them here?

  • $\begingroup$ You could call them noise variables, maybe. Just noise could be misunderstood as an error term. $\endgroup$ – kjetil b halvorsen Jul 5 '18 at 8:07

The question to ask is

"Do they have any affect at all?"

If your astrological sign can somehow impact your salary, then yes, if you do not include it in your model then it is white noise. However, if astrological sign has no impact on a person's salary then how can it even generate white noise different from zero?

An example off the top of my head...

Cucumber growth rate on average grades in a philosophy class.

Side note: In this specific instance, astrological sign is related to your birth month so that is something to consider.

  • $\begingroup$ I believe a feature can generate noise (misleading the model) if it's irrelevant. In your example: imagine that we observe that the higher cucumber growth rate is, the higher are average grades in a philosophy class. In this case a model may count cucumber growth rate as a very important feature that has a serious impact on average grades in a philosophy class, whereas it's obviously just a coincidence. $\endgroup$ – Mister Twister Jul 14 '18 at 3:50

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