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I have 500 observations and 200 predictors, and I want to do the prediction while selecting some important features. I know that regularisation method (ridge, lasso) are shrinkage method for high-dimensional setting, and the lasso also has an advantage of model selection. It is the fact that the setting with 500 observations and 200 predictors is not a high-dimensional setting, but I want to do some feature selection since I have 200 features. Can I use lasso when it is not a high dimensional setting?

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    $\begingroup$ 200 predictors is a very high dimensional setting. $\endgroup$ – Peter Flom Jun 8 '17 at 12:02
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There's nothing that suggests you need a number of predictors ($p$) as large as 200 or sample size ($n$) as large 500, let alone larger. (You might find it surprising to read some of the early papers on both methods.)

You can very successfully use regularization methods like ridge regression and lasso on problems with only a few predictors -- the benefits of regularization are still present (indeed the illustration here shows ridge regression can be useful with two predictors, and one can make an argument for considering it even with a single predictor.)

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Whether a given setting is high-dimensional or not depends on both the number of samples you have and the number of dimensions. Increasing the number of dimensions requires exponentially more data to "fill up" the feature space - look up the curse of dimensionality.

200 predictors for 500 observations is a huge number of predictors.

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I suppose you are talking about the setting when p n or p > n (as high dimensional), lasso has an additional advantage of solving the singularity problem that occurs in the above setting,which was prior motivation for developing regularisation (Thats why it is much used in higher dimensions). More on this here. As for your case here , apart from the above advantage of lasso , as mentioned by other answers it retains its other advantages like reduction of model variance,subset selection etc.

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