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https://lightgbm.readthedocs.io/en/latest/Python-API.html

I have compared both of them in the lightgbm documentation and could not figure out which one I would choose and why I would choose one over the other?

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Glancing at the source (available from your link), it appears that LGBMModel is the parent class for LGBMClassifier (and Ranker and Regressor). You should probably stick with the Classifier; it enforces proper loss functions, adds an array of data classes, translates the model's score into class probabilities and from there into predicted classes, etc.

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