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If I have generated features using state of the art feature engineering methods of a dataset, can I use it for any kind of algorithm to build the model apart from few modifications in the features so as to plug in different algorithm?

Is there any dependency of algorithm while building features from dataset?

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No.

An example: feature engineering for Gradient Boosting algorithms.

XGBoost can't handle categorical variables - you need to use one-hot encoding, target encoding, or something like that if you want to use it.

On the other hand more recent GBM libraries like CatBoost or LightGBM can handle categorical data and have reasonable defaults for doing that.

I wouldn't say encoding categorical variables would be 'few modifications' because depending on what you do (one-hot encode vs target encoding) your model's behavior can change significantly.

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