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Suppose I have a binary classification problem and my data is imbalanced, I can build a classification model using any of the algorithms and use an oversampling or undersampling technique to handle the class imbalance.

What If I were to make two separate models independently, each model trained only for one class of data. Will this be a right approach?

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That doesn't make much sense, no. If you provide all the data to both models, they should perform exactly the same. If you only provide positive data to each model, you're making two incomplete models that (supposedly) won't learn as well as using all the available data. Making multiple models to a single response variable can make sense, but not when the response is binary.

If you happen to also have unlabeled then it's a different thing, because you can use techniques such as the two-view models. But in practice, it's often more useful to spend resources labeling data than developing a semi-supervised model.

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Giving a single label in a model is not the thing i have heard ever before for labeled data, if you give like that also internally it is binary model only for eg : take log regression model example we have a loss function for all model and for log regression we have : J(w)=∑i=1_to_m y(i)logP(y=your label)+(1−y(i))logP(y= not your label)? you are not showing the model other than your label value so it will not learn anything,

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