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### Difference between training and test data distribution

I think you're confusing the underlying distribution from which both training and test distributions are drawn, with the distributions of the specific train and test draws. Unless the underlying distribution is eg time-sensitive, changed during the time between eg drawing the training and the testing samples, the underlying distribution is identical each time. The goal in learning a machine learning model is typically not to learn the training distribution, but to learn the latent underlying distribution, of which the training distribution is only a sample. Of course, you cannot actually see the underlying distribution, but eg, if you only really cared about learning the training samples, you could simply memorize the training samples in a lookup table, end of story. In reality, you are using the training sample as a proxy into the underlying distribution.

### The Machine Learning Dictionary

This problem can to some extent be avoided by stopping learning early. How does one tell when to stop? One method is to partition the training patterns into two sets (assuming that there are enough of them). The larger part of the training patterns, say 80% of them, chosen at random, form the training set, and the remaining 20% are referred to as the test set. Every now and again during training, one measures the performance of the current set of weights on the test set.

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### Why Hyper parameter tuning is important for your model ?

It is rare that a model will perform at the level you need for production just in the first instance. To find the right solution for your business problem, often you have to go through an iterative cycle. There are multiple pieces that come together to solve the intended machine learning puzzle. You may need to train and evaluate multiple models that include different data setup and algorithms, perform feature engineering a few times or even augment more data. This cycle also involves tweaking your model's hyperparameters.

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