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In the field of machine learning, what do we mean by overfitting and underfitting? Why is it necessary to keep these phenomena in mind during model development?

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Interview question asked to Data Scientists interviewing at Rackspace, Improbable, Soundcloud and other companies. Original question asked: In the field of machine learning, what do we mean by overfitting and underfitting? Why is it necessary to keep these phenomena in mind during model development?.