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    $\begingroup$ there is no theoretical reason not to use same (class of) algorithms both for feature selection and as model $\endgroup$ Commented Jan 5, 2021 at 18:27
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    $\begingroup$ In theory, a drawback of using different models could be that features being important to your model being used as a filter to select features might not have the same importance for your model applied during inference $\endgroup$ Commented Jan 5, 2021 at 20:34