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I have a little knowledge on Lasso, from what i know its pretty good at feature selection and also finds the best sweet spot between bias and variance trade-off. If we are to come up with a regression model from a dataset automatically, we may have features that are not linearly dependent but log of the feature is linearly dependent, in some cases may be sqaure root of the feature is linearly dependent. How do we identify such relationships automatically without assessing the data as the features change dynamically?

If we can find such relationships, Can we pass the sqrt(feature) as a linear value to lasso to find its relevance?

I am new to regression analysis, so please if you could give a detail explanation I highly appreciate it, also please suggest if there is better plan than using lasso?

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