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I have come across statsmodels.stats which focuses on methods for statistical tests. Some basic tests are like comparing different ML models, identify statistical significance for columns and compare different datasets to infer about the population. Are there any other statistical tests required to build sophesticated ML models? A few examples with code will be really helpful

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"sophisticated" is not really a wel-defined description, but machine learning models typically do not rely on statistical tests at all. Many, as in, winning Kaggle contests, being used in industry or being published about. Statistical feature selection prior to training your model is not really needed, instead, models such as random forests and neural networks select their own features. To validate and compare models, cross-validation or just a train- and testset (possibly a validation set) are used. Statistical tests are used in the field of A/B testing however.

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