Can features negatively correlated with the target be used?

Question

In feature selection (for a regression problem), can features that are negatively correlated with the target variable be chosen to predict the target?
I don't think negative correlation means the predictor does not provide any information about the target.

Some feature selection methods (like Filter method) are based on using only those predictors that have high correlation to the target variable, and dropping those with low correlation.

My question is - shouldn't negative correlated features also be considered? I think the problem of feature selection should be whether a feature is "simply correlate " with the target or not, rather than whether it is a Positive/Negative correlation. Am I right? Can someone please clear my confusion?

Answer 1

You are correct, don't mistake a low correlation (absolute value close to 0) with a negative correlation.

A large negative correlation is just as useful as a large positive correlation. The only difference is that for a positive correlation, as the feature increases, the target will increase. For a negative correlation, as the feature decreases, the target will increase.

Any model you choose should be able to handle the correlation sign (+/-).

If you are looking at feature reduction, select features with a correlation close to 0. This means that the feature does not have a useful relationship to the target, and won't help with any prediction.

Answer 2

Negative correlation is not the same as low correlation.
If variables $x$ and $y$ have a correlation value of $c$, then $-x$ and $y$ will have a correlation of $-c$.
When people talk about "low correlation" they usually mean correlation that is close to 0.

In the context of machine learning, negative correlation is just as good as positive correlation; do your filtering based on the absolute value of the correlation.