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Is it important to have the same amount of positives and negatives in our training dataset for a binary classification problem? Or for example, it doesn't matter if we have 70% positives and 30% negatives.

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In general it is better to have a good mix of positive and negative labels for a model to learn from. That said, many classification problems suffer from significant label imbalance (e.g. fraud detection).

I don't see an obvious problem with a 70/30 mix of labels, but as you start modeling be sure to check the confusion matrix and look for where you model isn't performing well. If it appears that the imbalance is causing issues, you could try techniques like under-sampling or SMOTE to create a better balance (artificially). The linked article below has more details if you are interested:

https://www.jeremyjordan.me/imbalanced-data/

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