PCA ( I mentioned it's a dimensionality reduction, not a 'feature selection' method), Lasso (explained already), step-wise forward/backward (explained already), scheme depends on the machine learning algorithm. Interviewer had RFE in mind and insisted for 1 more name, I couldn't think of more. He finally revealed RFE, the name sounded new to me. So I discussed a CV scheme for recursive feature selection using accuracy - which was different from RFE. Interviewer was arguing that this CV scheme is computationally more expensive than RFE. I read about RFE after the interview. It uses weights for parametric model and feature importance for non-parametric model for eliminating 1 variable at a time. I don't see how this is "computationally cheaper" than step-wise backward for parametric models. For random forest, Variable Importance calculation for a given model with p variables is O(p), which makes the total complexity of full RFE around O(p^2). The CV scheme I used had the same order of complexity. But by now I lost my enthusiasm because I knew the outcome of the interview, so I stopped discussing further. I understood that the interviewer was just trying to find an algorithm that was in his arsenal but not in mine. I had been upfront with my knowledge and clearly mentioned "I don't know" if I did not have theoretical knowledge or practical experience. Outcome of the interview was no surprising.