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As far as I understand, learning curves let us determine the best value of parameters or train size in order to get best results and not over/under fit. Hyperparameter tuning does the same as it finds the best hyperparameters for us. So my question is if I am performing hyperparameter tuning, do I still need to plot learning curves for over/under fitting?

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Learning curve is used to see how training error increases and validation error decreases as we increase the training sizes. It is used to detect bias/Variance and whether its converging or not. Hyperparameter tuning selects the best possible parameters from the list by running the experiments multiple times. Both uses cross validation for better accuracy. In general we first find the best hyperparameter and then use scikitlearn learningCurve to plot the LearningCurve. You can also run learningCurve inside the HyperParameter experiments if you are a visualization fanatic.

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