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Walk through the main families of feature selection methods and when you'd reach for each.
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See plansFeature selection methods split into three families based on how tightly they couple to the downstream model. Filter methods score each feature independently of any model — variance threshold (drop near-constant features), correlation with the target, mutual information, or a univariate statistical test’s p-value — and are cheap enough to run on thousands of features, but they ignore feature interactions and redundancy between selected features.
Wrapper methods use the actual downstream model’s performance as the selection signal: forward selection greedily adds the feature that most improves validation performance until no addition helps, backward elimination starts with everything and greedily removes the least useful feature, and recursive feature elimination repeatedly fits the model and drops the lowest-importance feature. These capture interactions the filter methods miss, but cost grows with the number of models you have to fit, and both forward and backward selection are hill-climbing procedures that only guarantee a local optimum.
Embedded methods build selection into training itself — Lasso’s L1 penalty zeroes out coefficients as a side effect of fitting, and tree-based models’ split-based feature importance gives you a ranking for free — getting most of the wrapper method’s model-awareness at close to the filter method’s cost. In practice, start with a filter pass to cut obviously dead weight and correlated duplicates, then let an embedded method (Lasso or a gradient-boosted tree’s importances) do the real selection, reserving expensive wrapper search for when interactions are suspected and the feature count is small enough to afford it.