sklearn doesn't scale your data: The input data is centered but not scaled for each feature before applying the SVD. Your variances are high because your feature variances are high. In general, standardization is recommended because otherwise some of your features with low values won't be represented well.


LASSO, as it is, is not a good way to screen-out noisy covariates, for the reason mentioned above (correlations among covariates), but not only. Unless you have a truly strong signal in the dataset, you will never be able to screen out only the relevant covariates unless you adjust the procedure. Also, it is well known that cross-validation with LASSO leads ...

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