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I'm learning about penalized/sparse regression and I noticed that the examples used for penalized/sparse regression, e.g. Lasso, are usually cases where the number of observations is significantly smaller than the number of covariates/independent variables/predictors, $n << p$.

I was wondering if it would still be useful to apply such methods to datasets where we also have a large number of $p$ but the number of observations $n$ is significantly larger, $n >> p$.

For reference, we have a dataset that has $n = 19,051$ observations and each observation has $p = 336$ predictors.

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