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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?

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  • $\begingroup$ You could call them noise variables, maybe. Just noise could be misunderstood as an error term. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jul 5, 2018 at 8:07

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More a comment on the other answer by @Adzil. Astrological sign is related to birth month, so astrological sign could be taken as a predictor (falsely so) of football (that is, soccer) talent in young players. See

A characteristic that has been proven to be crucial to identify at a young age is birth month, an effect known as the relative age effect difference (RAE). This effect among male players, who have been selected or identified as talented at a young age, is characterized by birth early in the year and especially during the first three months (Helsen, Van Winckelmann, & Williams 2005; Musch & Hay 1999; Peterson 2011, Verhulst 1992). This means that the players who are (sæther | identification of talent in soccer (idrottsforum.org | 2014-03-19 4)) perceived as talented have advantages over other athletes in their cohort, as a result of differences in maturation and development of the individual which takes place at different speeds (Gagne 2000; Martindale et al, 2007). Even though this effect has been known since 1985, the same effect still exists among Norwegian premier level players (Wiium, Ommundsen & Enksen 2010). As this effect is so well documented, there is risk that the coaches gamble on the wrong players, instead of players who might have major development potential and developed better skill.

This is from the paper Talent identification in Soccer What do Coaches Look for. Note especially that this effect is also seen in (Norwegian) elite footballers, so the wrong prediction, creating expectations, and caused by relative fast maturing as compared to later births in same age cohort, do have longtime effects ...

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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.

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  • $\begingroup$ 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
    Commented Jul 14, 2018 at 3:50
  • $\begingroup$ I’m afraid I don’t understand your answer. What is zero? What do you mean by noise in here? $\endgroup$
    – Tim
    Commented Jul 29, 2020 at 17:26
  • $\begingroup$ Even if it has no effect population-wide, it's going to have some effect in the training data, just from random chance. This causes overfitting. And it's "effect", not "affect". $\endgroup$
    – Acccumulation
    Commented Sep 14, 2020 at 20:53
  • $\begingroup$ Astrological sign is strongly correlated with birth date, and birth date my have effects! $\endgroup$
    – kjetil b halvorsen ♦
    Commented Jul 2 at 2:27

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